^

19

ToFTrtE

tmiVEB$ITY OF

University of California • Berkeley

1

CONVERSATIONS

THE ELEMENTS OF THAT SCIENCE

ARE

FAMILIARLY EXPLAINED,

AND ADAPTED TO THE

COMPREHENSION OF YOUNG PUPILS.

3(nu0trateii iDttti piate^.

BY THE AUTHOR OF CONVERSATIONS ON CHEMISTRV,

AND CONVERSATIONS ON POLITICAL

ECONOMY.

NEW-YORK :

PUBLISHED BY A. T. GOODRICH, W. B. GILLEY, AND CHARLES WILEY k CO.

Clayton fy Kingdand, Printers.

1820.

^-^•-

A

5^^: V

recommendation/

The very pleasing style in which the Conver- sations on Chemistry were written^ and the re- markable clearness with which they illustrated the leading facts 6/ that science^ have undqnbt- edly contributed to render the study of it more popular. The same observation applies to the Conversations on Political Economy — a 'subr- ject so obscure as to have been considered as fit only for philosophers and statesmen has been brought to the level of common understandings^ and devested of all its repulsive features. Upon looking hastily into the present volume^ it ap- pears to me to be distinguished by the same clearness of elucidation as the former produc- tions of the amiable author; and it will^ I have no doubt^ prove to be a valuable addition to the popular works on natural philosophy,

J. GRISCOM.

New-York, llth month 24th, 1819.

■is^y

*?«:>

PREFACE,

It is with increased diffidence that the author offers this little work to the public. The encouraging reception which the Conversations on Chemistry and Political Economy have met with, has induced her to venture on publishing a short course on Natural Philosophy ; but not without the greatest apprehensions for its success. Her ignorance of mathematics, and the imperfect knowledge of natural philoso- phy which that disadvantage necessarily implies, renders her fully sensible of her incompetency to treat the subject in any other way than in the form of a familiar explanation of the first elements, for the use of very young pupils. It is the hope of having done this in a manner that may engage their attention, which encourages

her to offer them these additional lessons, 1*

VI PREFACE.

They are intended, in a course of ele- mentary science, to precede the Conver- sations on Chemistry; and were actually written previous to either of her former publications.

CONTENTS.

CONVERSATION I.

ON GENERAL PROPERTIES OF BODIES.

Introduction — General Properties of Bodies — Impenetrability > Extension — Figure — Divisibility — Inertia — Attraction — At- traction of Cohesion — Density — Rarity — Heat — Attraction of Gravitation, 13

CONVERSATION II.

ON THE ATTRACTION OF GRAVITY.

Attraction of Gravitation, continued — Of Weight — Of the Fall of Bodies — Of the Resistance of the Air — Of the Ascent of Light Bodies, • 29

CONVERSATION III.

ON THE LAWS OF MOTION.

Of Motion — Of the Inertia of Bodies — Of Force to Produce Motion — Direction of Motion — Velocity, absolute and rela- tive— Uniform Motion — Retarded Motion — Accelerated iVIo- tion — Velocity of Falling Bodies — Momentum — Action and Reaction Equal — Elasticity of Bodies — Porosity of Bodies — Reflected Motion — Angles of Incidence and Reflection, 43

CONVERSATION IV.

ON COMPOUND MOTION.

Compound Motion, the result of two opposite forces — Of Circu- lar Motion, the result of two forces, one of which confines the body to a fixed point — Centre of Motion, the point at rest while the other parts of the body move round it — Centre of Magnitude, the middle of a body — Centripetal Force, that

Vlll CONTENTS.

which confines a body to a fixed central point — Centrifugal Force, that which impels a body to fly from the centre — Fall of Bodies in a Parabola — Centre of Gravity, the Centre of Weight, or point about which the parts balance each other, 59

CONVERSATION V.

ON THE MECHANICAL POWERS.

Of the Power of Machines — Of the Lever in General' — Of the Lever of the first kind, having the Fulcrum between the Power and the Weight — Of the Lever of the second kind, having the Weight between the Power and the Fulcrum — Of the Lever of the third kind, having the Power between the Fulcrum and the Weight— Of the Pulley— Of the Wheel and Axle— Of the Inclined Plane — Of the Wedge— of the Screw,

79

CONVERSATION VI.

ASTRONOMy. CAUSES OF THE EARTH's ANNUAL MOTION.

Of the Planets, and their Motion — Of the Diurnal Motion of the Earth and Planets, 90

CONVERSATION VII.

ON THE PLANETS.

Of the Satellites or Moons — Gravity Diminishes as the Square of the Distance— Of the Solar System — Of Comets— Constel- lations, signs of the Zodiac — Of Copernicus, Newton, kc. 102

CONVERSATION VIII.

ON THE EARTH.

Of the Terrestrial Globe— Of the Figure of the Earth— Of the Pendulum— Of the Variation of the Seasons, and of the Length of Days and Nights — Of the Causes of the Heat of Summer— Of Solar, Sidereal, aad Equal or Mean Time, 114

CONTENTS. iX

CONVERSATION IX

ON THE MOON.

Of the Moon's Motion — Phases of the Moon — Eclipses of the Moon — Eclipses of Jupiter's Moons — Of the Latitude and Longitude — Of the Transits of the Inferior Planets — Of the Tides, 134

CONVERSATION X.

HYDROSTATICS. ON THE MECHANICAL PROPERTIES OF FLUIDS.

Definition of a Fluid — Distinction between Fluids and Liquids — Of Non-Elastic Fluids, scarcely susceptible of Compression — Of the Cohesion of Fluids — Of their Gravitation — Of their Equilibrium—Of their Pressure — Of Specific Gravity — Of the Specific Gravity of Bodies heavier than Water — Of those of the same weight as Water — Of those lighter than Water — Of the Specific Gravity of Fluids, 146

CONVERSATION XI.

OF SPRINGS, FOUNTAINS, k,C.

Of the Ascent of Vapour and the Formation of Clouds — Of the Formation and Fall of Rain, &,c. — Of the Formation of Springs — Of Rivers and Lakes — Of Fountains, 159

CONVERSATION XII.

PNEUMATICS. ON THE MECHANICAL PROPERTIES OF AIR.

Of the Spring or Elasticity of the Air— Of the Weight of the Air — Experiments with the Air Pump — Of the Barometer — Mode of Weighing Air — Specific Gravity of Air — Of Pumps — De- scription of the Sucking Pump— Description of the Forcing Pump, 168

X CONTEWrS..

eONVERSATION XIII.

ON WIND AND SOUND.

Of Wind in General— Of the Trade Wind— Of the Periodica Trade Winds— Of the Aerial Tides— Of Sound in General— Of Sonorous Bodies— Of Musical Sounds— Of Concord or Harmony, and Melody, ' 180

CONVERSATION XIV.

ON OPTICS.

Of Luminous, Transparent, and Opaque Bodies— Of the Radia- tion of Light — Of Shadows — Of the Reflection of Light — Opaque Bodies seen only by Reflected Light — Vision Ex- plained— Camera Obscura — Image of Objects on the Retina,

194

CONVERSATION XV.

ON THE ANGLE OF VISION, AND THE REFLECTION OF MIRRORS.

Angle of Vision — Reflection of Plain Mirrors — Reflection of Convex Mirrors — Reflection of Concave Mirrors, 208

CONVERSATION XVF.

ON REFRACTION AND COLOURS.

Transmission of Light by Transparent Bodies — Refraction — Refraction of the Atmosphere — Refraction of a Lens — Re- fraction of the Prism— Of the Colours of Rays of Light— Of the Colours of Bodies, 223

CONVERSATION XVII.

OPTICS. O^ THE STRUCTURE OF THE EYE, AND OPTICAL INSTRUMENTS.

Description of the Eye — Of the Image on the Retina — Refrac- tion of the Humours of the Eye — Of the Use of Spectacles — Of the Single Microscope — Of the Double Microscope — Of the Solar Microscope — Magic Lauthorn — Refracting Tele- scope— Reflecting Telescope, 241

DIRECTIONS

FOR PLACING THE ENGRAVINGS.

late I. to face page 34
II.	- 66
III.	62
IV.	- 70
V.	79
VI.	- - 91
VII.	- 104
VIII.	- 108
IX.	- 116
X.	- • - 128
XI.	- 132
XII.	- 136
XIII.	- 148
XIV.	- 164
XV.	- 195
XVI.	- 203
XVII.	- 208
XVIII.	. 217
XIX.	. 224
XX.	- 228
XXI.	- 241
XXII.	- .246
XXIII.	- 249

ERRATUM. Page 62, for Plate III. read Plate IV.

CONVERSATION I.

ON GENERAL PROPERTIES OF BODIES.

Introduction. — General Properties of Bodies. — Impe- netrability.— Extension. Figure. Divisibility. —

Inertia. — .Attraction. — Attraction of Cohesion. — Den- sity.— Rarity. — Heat. — Attraction of Gravitation.

EjMILY. I must request your assistance, my dear Mrs. B., in a charge which I have lately undertaken : it is that of instructing my youngest sister, a task, whicli I find proves more difficult than I had at first imagined. I can teach her the common routine of children's lessons tolerably well ; but she is such an inquisitive little creature, that she is not satisfied without an explanation of every difficulty that occurs to her, and frequently asks me questions which I am at a loss to answer. This morning, for instance, when I had explained to her that the world was round like a ball, instead of being flat as she had sup- posed, and that it was surrounded by the air, she ask- ed me what supported it. I told her that it required no support ; she then inquired why it did not fall as every thing else did ? This I confess perplexed me ; for I had myself been satisfied with learning that the world floated in the air, without considering how un- natural it was that so heavy a body, bearing the weight of all other things, should be able to support itself.

Mrs. B. 1 make no doubt, my dear, but that 1 shall be able to explain this difficulty to you ; but I believe that it would be almost impossible to render it intelli- 2

14 GENERAL PROrERTiES OF BODIES.

gible to the comprehension of so young a child as your sister Sophia. You, who are now in your thir- teenth year, may, I think with great propriety, learn not only the cause of this particular fact, but acquire a general knowledge of the laws by which the natural world is governed.

Emily. Of all things, it is what I should most like to learn ; but I was afraid it was too difficult a study even at my age.

Mrs. B. Not when familiarly explained : if you have patience to attend, I will most willingly give you all the information in my power. You may perhaps find the subject rather dry at first ; but if I succeed in explaining the laws of nature, so as to make you understand them, I am sure that you will derive not only instruction, but great amusement from that study.

Emily. I make no doubt of it, Mrs. B. ; and pray begin by explaining why the earth requires no sup- port ; for that is the point which just now most strong- ly excites my curiosity.

Mrs. B. My dear Emily, if I am to attempt to give you a general idea of the laws of nature, which is no less than to introduce you to a knowledge of the sci- ence of natural philosophy, it will be necessary for us to proceed with some degree of regularity. I do not wish to confine you to the systematic order of a scien- tific treatise ; but if we were merely to examine eve- ry vague question that may chance to occur, our pro- gress would be but very slow. Let us, therefore^ begin by taking a short survey of the general proper- ties of bodies, some of which must necessarily be ex- plained before I can attempt to make you understand Tvhy the earth requires no support.

When I speak of bodies, I mean substances, of what- ever nature, whether solid or fluid ; and matter is the general term used to denote the substance, whatever its nature be, of which the different bodies are com- posed. Thus, wood is tliQ matter of which this table

GENERAL PROPERTIES OF BODIES. lb

IS made ; water is the matter with which this glass is tilled, &c-

Emily. I am very glad you have explained the meaning of the word matter, as it has corrected an er- roneous conception I had formed of it : I thought that it was applicable to solid bodies only.

Mrs. B. There are certain properties which ap- pear to be common to all bodies, and are hence called the essential properties of bodies ; these are, Impene- (rability, Extension, Figure, Divisibility, Inertia, and Attraction. These arc called the general properties of bodies, as we do not suppose any body to exist with- out them.

By impenetrability, is meant the property which bodies have of occupying a certain space, so that, where one body is, another cannot be, without dis- placing the former ; for tvvo bodies cannot exist in the same place at the same time. A liquid may be more easily removed than a solid body ; yet it is not the less substantial, since it is as impossible for a liquid and a solid to occupy the same space at the same time, as for two solid bodies to do so. For instance, if you put a spoon into a glass full of water, the water will flow over to make room for the spoon.

Emily. 1 understand this perfectly. Liquids are in reality as substantial or as impenetrable as solid bodies, and they appear less so, only because they are more easily displaced.

Mrs. B. The air is a fluid differing in its nature from liquids, but no less impenetrable. If I endea- vour to till this phial by plunging it into this basin of water, the air, you see, rushes out of the phial in bubbles, in order to make way for the water, for the air and the water cannot exist together in the same space, any more than two hard bodies ; and if I re- verse this goblet, and plunge it perpendicularly into the water, so that the air will not be able to escape, the water will no longer be able to till the goblet.

Emily, But it rises a considerable way into the glass.

16 GENERAL PROPERTIES OF BODIES.

Mrs. B. Because the water compresses or squeezes the air into a small space in the upper part of the glass . but, as long as it remains there, no other body can occupy the same place.

Emily. A difficulty has just occurred to me, with regard to the impenetrability of solid bodies ; if a nail is c!riven into a piece of wood, it penetrates it, and both the wood and the nail occupy the same space that the wood alone did before ?

Mrs. B. The nail penetrates between the parti- cles of the V ood, by forcing them to make way for it; for you know that not a single atom of wood can remain in the space which the nail occupies ; and if the wooo is not increased in size by the addition of the nail, it is because wood is a porous substance, like sponge, the particles of which may be compressed or squeezed closer together ; and it is thus that they make way for the nail.

We may now proceed to the next general property (ji bodies, extension. A body which occupies a cer- tain space must necessarily have extension ; that is to say, length, breadth, and depth; these are called the dimensions of extension : can you form an idea of any body without them ?

Emily. No ; certainly I cannot ; though these di- mensions must, of course, vary extremely in different bodies. The length, breadth, and depth of a box, or of a tJ. nble, are very different from those of a walk- ing-stic'., or of a hair.

But is not height also a dimension of extension ?

Mrs. B. Height and depth are the same dimension, considered in different points of view ; if you measure a body, or a space, from the top to the bottom, you call it depth ; if from the bottom upwards, you call it height ; thus the depth and height of a box are, in fact, the same thing.

Emily. Very true ; a moment's consideration %vould have enabled me to discover that ; and breadth and width are also the same dimension.

Mrs. B. Yes ; the limits of extension constitute

GENERAL PROPERTIES OP BODIES. 17

figure or shape. You conceive that a body having length, breadth, and depth, cannot be without form, either symmetrical or irregular ?

Emily. Undoubtedly ; and this property admits of almost an infinite variety.

Mrs. B. Nature has assigned regular forms to her productions in general. The natural form of mineral substances is that of crystals, of which there is a great variety. Many of them are very beautiful, and no less remarkable by their transparency, or colour, than by the perfect regularity of their forms, as may be seen in the various museums and collections of natu- ral history. The vegetable and animal creation ap- pears less symmetrical, but is still more diversified in figure than the mineral kingdom. Manufactured sub- stances assume the various arbitrary forms which the art of man designs for them; and an infinite number of irregular forms are produced by fractures, and by the dismemberment of the parts of bodies.

Emily. Such as a piece of broken china, or glass ?

Mrs. B. Or the fragments of mineral bodies which are broken in being dug out of the earth, or decayed by the effect of torrents and other causes. The pic- turesque effect of rock-scenery is in a great measure owing to accidental irregularities of this kind.

We may now proceed to divisibility ; that is to say, a susceptibility of being divided into an indefinite num- ber of parts. Take any small quantity of matter, a grain of sand for instance, and cut it into two parts; these two parts might be again divided, had we in- struments sufficiently fine for the purpose ; and if, by- means of pounding, grinding, and other similar me- thods, we carry this division to the greatest possible extent, and reduce the body to its finest imaginable particles, yet not one of the particles will be destroy- ed, and the body will continue to exist, though in this altered state.

The melting of a solid body in a liquid affords a ve- ry striking example of the extreme divisibility of mat- ter ; when you sweeten a cup of tea, for instance, 2*

18 GENERAL PROPERTIES OT BODTES.

with what minuteness the sugar must be divided to be diffused throughout the whole of the hquid.

Emily. And if you pour a few drops of red wine into a glass of water, they immediately tinge the whole of the water, and must therefore be diffused throughout it.

Mrs. B. Exactly so ; and the perfume of this la- vender-water will be almost as instantaneously diffu- sed throughout the room, if I take out the stopper.

Emily., But in this case it is only the perfume of the lavender, and not the water itself, that is diffused in the room ?

Mrs. B. The odour or smell of a body is part of the body itself, and is produced b}' very minute parti- cles or exhalations which escape from odoriferous bo- dies. It would be impossible that you should smell the lavender-water, if particles of it did not come in actual contact with your nose.

Emily. But when I smell a flower, I see no va- pour rise from it ; and yet I can perceive the smell at a considerable distance.

Mrs. B. You could, I assure you, no more smell a flower, the odoriferous particles of which did not touch your nose, than you could taste a fruit, the flavoured particles of which did not come in contact with your tongue.

Emily. That is wonderful indeed; the particles then, which exhale from the flower and from the la- vender-water, are, I suppose, too small to be visible ?

Mrs. B. Certainly : you may form some idea of their extreme minuteness, from the immense number which must have escaped in order to perfume the whole room ; and yet there is no sensible diminution of the liquid in the phial.

Emily. But the quantity must really be diminish- ed?

Mrs. B. Undoubtedly ; and were you to leave the bottle open a sufficient length of time, the whole of the water would evaporate and disappear. But though so minutely subdivided as to be imperceptible

GENERAL PROPERTIES OF BODIES. 19-

to any of our senses, each particle would continue to exist ; for it is not within the power of man to de- stroy a single particle of matter ; nor is there any rea- son to suppose that in nature an atom is ever annihi- lated.

Emily. Yet, when a body is burnt to ashes, part of it, at least, appears to be effectually destroyed ? Look how small is the residue of ashes beneath the grate, from all the coals which have been consumed within it.

Airs. B. That part of the coals, which you sup- pose to be destroyed, evaporates in the form of smoke and vapour, whilst the remainder is reduced to ashes. A body, in burning, undergoes no doubt very remarkable changes ; it is generally subdivided ; its form and colour altered ; its extension increased : but the various parts, into which it has been separa- ted by combustion, continue in existence, and retain all the essential properties of bodies.

Emily. But that part of a burnt body which eva- porates in smoke has no figure : smoke, it is true, as- cends in columns into the air, but it is soon so much diffused as to lose all form; it becomes indeed invisi- ble.

Mrs. B. Invisible, I allow ; but we must not ima- gine that what we no longer see no longer exists. Were every particle of matter that becomes invisible annihilated, the world itself would in the course of time be destroyed. The particles of smoke, when difi'used in the air, continue still to be particles of matter, as well as when more closely united in the form of coals: they are really as substantial in the one state as in the other, and equally so when by their extreme subdivision they become invisible. No particle of matter is ever destroyed : this is a princi- ple you must constantly remember. Every thing in nature decays and corrupts in the lapse of time. We die, and our bodies moulder to dust ; but not a single atom of them is lost ; they serve to nourish the earth, whence, while living, they drew their support.

20 GfiT!?ERAL PROPERTIES OF BODIES.

The next essential property of matter is called in- ertia; this word expresses the resistance which inac- tive matter makes to a change of state. Bodies ap- pear to be equally incapable of changing their actual state, whether it be of motion or of rest. You know that it requires force to put a body which is at rest ia motion ; an exertion of strength is also requisite to stop a body which is already in motion. The resist- ance of the body to a change of state, in either case, is called its inertia.

Emily. In playing at base-ball I am obliged to use all my strength to give a rapid motion to the ball ; and when I have to catch it, I am sure I feel the'resistance it makes to being stopped. But if I did not catch it, it would soon fall to the ground and stop of itself.

Mrs. B. Inert matter is as incapable of stopping of itself, as it is of putting itself into motion: when the ball ceases to move, therefore, it must be stopped by some other cause or power; but as it is one with which you are yet unacquainted, we cannot at present investigate its effects.

The last property which appears to be common to all bodies is attraction. All bodies consist of infinite- ly small particles of matter, each of which possesses the power of attracting or drawing towards it, and uniting with any other particle sufficiently near to be within the influence of its attraction ; but in minute particles this power extends to so very small a dis- tance around them, that its effect is not sensible, un- less they are (or at least appear to be) in contact; it then makes them stick or adhere together, and is hence called the attraction of cohesion. Without this power, solid bodies would fall in pieces, or rather crumble to atoms.

Emily. I ara so much accustomed to see bodies firm and solid that it never occurred to me that any power was requisite to unite the particles of which they are composed. But the attraction of cohesion does not, 1 suppose, exist in liquids ; for the particles

GENERAL PROPERTIES OF BODIES. 21

of liquids do not remain together so as to form a body, unless confined in a vessel ?

Mrs. B. I beg your pardon ; it is the attraction of cohesion which holds this drop of water suspended at the end of ray finger, and keeps the minute watery particles of which it is composed united. But as this power is stronger in proportion as the particles of bodies are more closely united, the cohesive at- traction of solid bodies is much greater than that of fluids.

The thinner and lighter a fluid is, the less is the co- hesive attraction of its particles,because they are fur- ther apart; and in elastic fluids, such as air, there is no cohesive attraction among the particles.

Emily. That is very fortunate ; for it would be im- possible to breathe the air in a solid mass ; or even in a liquid state.

But is the air a body of the same nature as other bodies ?

Mrs. B. Undoubtedly, in all essential properties.

Emily. Yet you say that it does not possess one of the general properties of bodies — cohesive attrac- tion?

Mrs. B. The particles of air are not destitute of the power of attraction, but they are too far distant from each other to be influenced by it; and the ut- most efforts of human art have proved ineff*ectual in the attempt to compress them, so as to bring them within the sphere of each other's attraction, and make them cohere.

Emily. If so, how is it possible to prove that they are endowed with this power?

Mrs. B. The air is formed of particles precisely of the same nature as those which enter into the com- position of liquid and solid bodies, in which state we have a proof of their attraction.

Emily. It is then, I suppose, owing to the diff*er- ent degrees of attraction of diff'erent substances, that they are hard or soft; and that liquids are thick or thin ?

22 GENERAL PROPERTIES OF BODIES,

Mrs. B. Yes ; but you would express your meati- ing better by the term density, which denotes the de- gree of closeness and compactness of the particles of a body : thus you may say, both of solids and of li- quids, that the stronger the cohesive attraction, the greater is the density of the body. In philosophical language, density is said to be that property of bodies by which they contain a certain quantity of matter, under a certain bulk or magnitude. Rarity is the cor»trary of density ; it denotes the thinness and sub- tlety of bodies : thus you would say that mercury or quicksilver was a very dense fluid ; ether, a very rare one, &c.

Caroline. But how are we to judge of the quantity of matter contained in a certain bulk?

Mrs. B. By the weight: under the same bulk, bodies are said to be dense in proportion as they are heavy.

Emily. Then we may say that metals are dense bodies, wood comparatively a rare one, &c. But, Mrs. B., when the particles of a body are so near as to attract each other, the effect of this power must increase as they are brought by it closer together ; so that one would suppose that the body would gra- dually augment in density, till it was impossible for its particles to be more closely united. Now, we know that this is not the case ; for soft bodies, such as cork, sponge, or butter, never become, in conse- quence of the increasing attraction of their particles, as hard as iron ?

Mrs. B. In such bodies as cork and sponge, the particles which come in contact are so few as to pro- duce but a slight degree of cohesion : they are po- rous bodies, which, owing to the peculiar arrange- ment of their particles, abound with interstices which separate the particles ; and these vacancies are filled with air, the spring or elasticity of which prevents the closer union of the parts. But there is another fluid much more subtle than air, which pervades all bodies, this is heat. Heat insinuates itself more or

GENERAL PROPERTIES OF BODIES. 23

less between the particles of all bodies, and forces them asunder ; you may therefore consider heat, and the attraction of cohesion, as constantly acting in op- position to each other.

Emily. The one endeavouring to rend a body to pieces, the other to keep its parts firmly united.

Mrs. B. And it is this struggle between the con- tending forces of heat and attraction, which prevents the extreme degree of density which would result from the sole influence of the attraction of cohesion.

Emily. The more a body is heated then, the more its particles will be separated.

Mrs. B, Certainly : we find that bodies swell or dilate by heat : this effect is very sensible in butter, for instance, which expands by the application of heat, till at length the attraction of cohesion is so far dimi- nished that the particles separate, and the butter be- comes liquid. A similar effect is produced by heat on metals, and all bodies susceptible of being melted. Liquids, you know, are made to boil by the appli- cation of heat ; the attraction of cohesion then yields entirely to the expansive po>ver ; the particles are totally separated and converted into steam or va- pour. But the agency of heat is in no body more sensible than in air, which dilates and contracts by its increase or diminution in a very remarkable de- gree.

Emily. The effects of heat appear to be one of the most interesting parts of natural philosophy.

Mrs. B. That is true ; but heat is so intimately connected with chemistry, that you must allow me to defer the investigation of its properties till you be- come acquainted with that science. To return to its antagonist, the attraction of cohesion ; it is this pow- er which restores to vapour its liquid form, which unites it into drops when it falls to the earth in a show- er of rain, which gathers the dew into brilliant gems on the blades of grass.

Emily. And I have often observed that after a shower, the water collects into large drops on the

'24 GENERAL PROPERTIES OF BODIES.

leaves of plants ; but I cannot say that I perfectly unr derstand how the attraction of cohesion produces this effect.

Mrs. B. Rain does not fall from the clouds in the form of drops, but in that of mist or vapour, which is composed of very small watery particles ; these, in their descent, mutually attract each other, and those that are sufficiently near in consequence unite and form a drop, and thus the mist is transformed into a shower. The dew also was originally in a state of vapour, but is, by the mutual attraction of the parti- cles, formed into small globules on the blades of grass : in a similar manner the rain upon the leaf collects in- to large drops, which, when they become too heavy for the leaf to support, fall to the ground.

Emily. All this is wonderfully curious ! I am al- most bewildered with surprise and admiration at the number of new ideas I have already acquired.

Mrs. B. Every step that you advance in the pur- suit of natural science, will fill your mind with admi- ration and gratitude towards its Divine Author. In the study of natural philosophy, we must consider ourselves as reading the book of nature, in which the bountiful goodness and wisdom of God is revealed to all mankind ; no study can then tend more to purify the heart, and raise it to a religious contemplation of the Divine perfections.

There is another curious effect of the attraction of cohesion which I must point out to you. - It enables liquids to rise above their level in capillary tubes : these are tubes the bores of which are so extremely small that liquids ascend within them, from the cohe- sive attraction between the particles of the liquid and the interior surface of the tube. Do you perceive the water rising above its level in this small glass tube, which I have immersed in a goblet full of water ?

Emily. Oh yes ; I see it slowly creeping up the tube, but now it is stationary : will it rise no higher ?

Mrs. B. No ; because the cohesive attraction be- tween the water and the internal surface of the tube

GENERAL PROPERTIES OF BODIES. 26

is now balanced by the weight of the water within it : if the bore of the tube were narrower the water would rise higher; and if you immerse several tubes of bores of different sizes, you will see it rise to differ- ent heights in each of them. In making this expe- riment you should colour the water with a little red wine, in order to render the effect more obvious.

All porous substances, such as sponge, bread, linen, &c., may be considered as collections of capillary tubes : if you dip one end of a lump of sugar into wa- ter, the water will rise in it, and wet it considerably above the surface of that into which you dip it.

Emily. In making tea I have often observed that effect, without being able to account for it,

Mrs. B. Now that you are acquaintted with the attraction of cohesion, I must endeavour to explain to you that oi Gravitation, which is a modification of the same power ; the first is perceptible only in very mi- nute particles, and at very small distances ; the other acts on the largest bodies, and extends to immense distances.

Emily. You astonish me : surely you do not mean to say, that large bodies attract each other.

Mrs. B. Indeed I do : let us take, for example, one of the largest bodies in nature, and observe whe- ther it does not attract other bodies. What is it that occasions the fall of this book, when I no longer sup- port it?

Emily. Can it be the attraction of the earth ? I thought that all bodies had a natural tendency to fall.

Mrs. B. They have a natural tendency to fall, it is true ; but that tendency is produced entirely by the attraction of the earth : the earth being so much larger than any body on its surface, forces every body, which is not supported, to fall upon it

Emily. If the tendency which bodies U,ave to fall results from the earth's attractive power, the earth itself can have no such tendency, since it cannot at- tract itself, and therefore it requires no support to prevent it from falling. Yet the idea that bodies do 3

Jb GENERAL PROPERTIES OJP BODIES.

not fall of their own accord, but that they are drawn towards the earth by its attraction, is so new and strange to me, that I know not how to reconcile my- self to it.

Mrs. B. When you are accustomed to consider the fall of bodies as depending on this cause, it will ap- pear to you as natural, and surely much more satisfac- tory, than if the cause of their tendency to fall were totally unknown. Thus you understand, that all matter is attractive, from the smallest particle to the largest mass ; and that bodies attract each other with a force proportional to the quantity of matter they contain.

Emily. I do not perceive any difference between the attraction of cohesion and that of gravitation ; is it not because every particle of matter is endowed with an attractive power, that large bodies, consist- ing of a great number of particles, are so strongly at- tractive ?

Mrs. B. True. There is, however, this differ- ence between the attraction of particles and that of masses, that the former is stronger than the latter, in proportion to the quantity of matter. Of this you have an instance in the attraction of capillary tubes, in which liquids ascend by the attraction of cohesion, in opposition to that of gravity. It is on this account that it is necessary that the bore of the tube should be extremely small; for if the column of water within the tube is not very minute, the attraction would not be able either to raise or support its weight, in oppo- sition to that of gravity.

You may observe, also, that all solid bodies are enabled by the force of the cohesive attraction of their particles to resist that of gravity, which would otherwise disunite them, and bring them to a level with the ground, as it does in the case of liquids, the cohesive attraction of which is not sufficient to enable it to resist the power of gravity.

Emily. And some solid bodies appear to be of this

GENERAL PROPERTIES OF BODIES. 27

nature, as sand and powder for instance ; there is no attraction ofcohesion between their particles ?

Mrs. B. Every grain of powder or sand is com- posed of a great number of other more minute parti- cles, tirmly united by the attraction ofcohesion ; but amongst the separate grains there is no sensible at- traction, because they are not in sufficiently close contact.

Emily. Yet they actually touch each other ?

Mrs. B. The surf<ice of bodies is in general so rough and uneven, that when in actual contact, they touch each other only by a ^qw points. Thus, if I lay upon the table this book, the binding of which ap- pears perfectly smooth, yet so few of the particles of its under surface come in contact with the table, that no sensible degree of cohesive attraction takes place ; for you see, that it does not stick, or cohere to the table, and I find no difficulty in lifting it off.

It is only when surfaces perfectly flat and well po- lished are placed in contact, that the particles ap- proach in sufficient number, and closely enough to produce a sensible degree of cohesive attraction* Here are two hemispheres of polished metal, I press their flat surfaces together, having previously inter- posed a {qw drops of oil, to fill up every little porous vacancy. Now try to separate them.

Emily. It requires an eflbrt beyond my strength, though there are handles for the purpose of pulling them asunder. Is the firm adhesion of the two hemispheres merely owing to the attraction of cohe-

sion

Mrs. B. There is no force more powerful, since it is by this that the particles of the hardest bodies are held together. It would require a weight of se- veral pounds to separate these hemispheres.

Emily. In making a kaleidoscope, I recollect that the two plates of glass, which were to serve as mir- rors, stuck so fast together, that I imagined some of the gum I had been using had by chance been inter- posed between them ; but now I make no doubt but

28 GENERAL PROPERTIES OF BODIES.

that it was their own natural cohesive attractioii which produced this effect.

Mrs. B. Very probably it was so ; for plate-glass has an extremely smooth flat surface, admitting of the contact of a great number of particles, between two plates, laid one over the other.

Emily. But, Mrs. B., the cohesive attraction of some bodies is much greater than that of others ; thus glue, gum, and paste, cohere with singular tena- city.

Mrs. B. That is owing to the peculiar chemical properties of those bodies, independently of their co- hesive attraction.

There are some other kinds or modifications of at- traction peculiar to certain bodies ; namely, that of magnetism, and of electricity ; but we shall confine our attention merely to the attraction of cohesion and of gravity ; the examination of the latter we shall re- sume at our next meeting.

CONVERSATION 11.

ON THE ATTRACTION OF GRAVITY.

Attraction of Gravitation, continued. — Of Weight. — Of the Fall of Bodies. — Of the Resistance of the Air. — Of the Ascent of Light Bodies.

EjMILY. I have related to my sister Caroline all that you have taught me of natural philosophy, and she has been so much delighted by it, that she hopes you will have the goodness to admit her to your les- sons.

Mrs. B. Very willingly ; but I did not think you had any taste for studies of this nature, Caroline?

Caroline. I confess, Mrs. B., that hitherto I had formed no very agreeable idea, either of philosophy, or philosophers ; but what Emily has told me, has excited my curiosity so much, that I shall be highly pleased if you will allow me to become one of your pupils.

Mrs. B. I fear that I shall not find you so tract- ablie a scholar as Emily ; I know that you are much biassed in favour of your own opinions.

Caroline. Then you will have the greater meri{ in reforming them, Mrs. B. ; and after all the wonders that Emily has related to me, I think I stand but little chance against you and your attractions.

Mrs. B. You will, 1 doubt not, advance a number of objections ; but these I shall willingly admit, as they will be a means of elucidating the subject. Emily, do you recollect the names of the general pro- perties of bodies?

3*

30 ON THE ATTRACTION OF GRAVITY.

Emily. Impenetrability, extension, figure, divisi- bility, inertia, and attraction.

Mrs, B. Very well. You must remember that these are properties common to all bodies, and of which they cannot be deprived ; all other properties of bodies are called accidental, because they depend on the relation or connexion of one body to another.

Caroline. Yet surely, Mrs. B., there are other properties which are essential to bodies, besides those you have enumerated. Colour and weight, for in- stance, are common to all bodies, and do not arise from their connexion with each other, but exist in the bodies themselves ; these, therefore, cannot be accidental qualities ?

Mrs. B. I beg your pardon ; these properties do not exist in bodies independently of their connexion with other bodies.

Caroline. What I have bodies no weight? Does not this table weigh heavier than this book; and, if one thing weighs heavier than another, must there not be such a thing as weight?

Mrs. B. No doubt : but this property does not ap- pear to be essential to bodies ; it depends upon their connexion with each other. Weight is an effect of the power of attraction, without which the table and the book would have no weight whatever.

Emily. I think 1 understand you ; is it not the at- traction of gravity, which makes bodies heavy ?

Mrs. B. You are right. I told you that the at- traction of gravity was proportioned to the quantity of matter which bodies contained ; now the earth con- sisting of a much greater quantity of matter than any body upon its surface, the force of its attraction must necessarily be greatest, and must draw every thing towards it; in consequence of which, bodies that are unsupported fall to the ground, whilst those that are supported press upon the object which prevents their fall, with a weight equal to the force with which they gravitate towards the earth.

Caroline. The same cause then which occasion?

ON THE ATTRACTION OP GRAVITr. 31

the fall of bodies, produces also their weight. It was very dull in me not to understand this before, as it is the natural and necessary consequence of attraction ; but the idea that bodies were not really heavy of themselves, appeared to me quite incomprehensible. But, Mrs. B., if attraction is a property essential to matter, weight must be so likewise ; for how can one exist without the other ?

Mrs. B. Suppose there were but one body exist- ing in universal space, what would its weight be ?

Caroline. That would depend upon its size ; or, more accurately speaking, upon the quantity of mat- ter it contained.

Emily. No, no ; the body would have no weight, whatever were its size ; because nothing would at- tract it. Am 1 not right, Mrs. B. ?

Mrs. B. You are ; you must allow, therefore, that it would be possible for attraction to exist with- out weigi.t ; for each of the particles of which the body was composed, would possess the power of at- traction ; but they could exert it only amongst them- selves ; the whole mass, having nothing to attract, or to be attracted by, would have no weight.

Caroline. 1 am now well satisfied that weight is not essential to the existence of bodies ; but what have you to object to colours, Mrs. B. ; you will not, I think, deny that they really exist in the bodies themselves.

Mrs. B. When we come to treat of the subject of colours, I trust that I shall be able to convince you, that colours are likewise accidental qualities, quite distinct from the bodies to which they appear to belong.

Caroline. Ob do pray explain it to us now, I am so very curious to know how that is possible.

Mrs. B. Unless we proceed with some degree of order and method, you will in the end find yourself but little the wiser for all you learn. Let us there- fore go on regularly, and make ourselves well ac- quainted with the general properties of bodies, before we proceed further.

32 ON THE ATTRACTION OF GRAVITY.

Emily. To return, then, to attraction, (which ap- pears to me by far the most interesting of them, since it belongs equally to all kinds of matter,) it must be mutual between two bodies; and if so, when a stone falls to the earth, the earth should rise part of the way to meet the stone ?

Mrs. B. Certainly ; but you must recollect that the force of attraction is proportioned to the quantity of matter which bodies contain, and if you consider the difference there is in that respect, between a stone and the earth, you will not be surprised that you do not perceive the earth rise to meet the stone ; for though it is true that a mutual attraction takes place between the earth and the stone, that of the latter is so very small in comparison to that of the former, as to render its effect insensible.

Emily. But since attraction is proportioned to the quantity of matter which bodies contain, why do not the hills attract the houses and churches towards them ?

Caroline. Heavens, Emily, what an idea 1 How can the houses and churches be moved, when they are so firmly fixed in the ground ?

Mrs. B. Emily's question is not absurd, and your answer, Caroline, is perfectly just ; but can you tell lis why the houses and churhes are so firmly fixed in the ground ?

Caroline. I am afraid I have answered right by mere chance ; for 1 begin to suspect that bricklayers and carpenters could give but little stability to theit buildings, without the aid of attraction.

Mrs. B. It is certainly the cohesive attraction between the bricks and the mortar, which enables them to build walls, and these are so strongly attract- ed by the earth, as to resist every other impulse ; otherwise they would necessarily move towards the hills and the mountains ; but the lesser force must yield to the greater. There are, however, some circumstances in which the attraction of a large body has sensibly counteracted that of the earth. If,

ON THE ATTRACTION OF GRAVITY. 33

whilst standing on the declivity of a mountain, you hold a plumb-line in your hand, the weight will not fall perpendicular to the earth, but incline a little to- wards the mountain ; and this^ owing to the lateral, or sideways attraction of the mountain, interfering with the perpendicular attraction of the earth.

Emily. But the size of a mountain is very trifling, compared to the whole earth ?

Mrs. B. Attraction, you must recollect, diminishes with distance ; and in the example of the plumb-line, the weight suspended is considerably nearer to the mountain than to the centre of the earth.

Caroline. Pray, Mrs. B., do the two scales of a balance hang parallel to each other ?

Mrs. B. You mean, I suppose, in other words, to inquire whether two lines which are perpendicular to the earth, are parellel to each other ? I believe I guess the reason of your question? but I wish you would endeavour to answer it without my assistance.

Caroline. I was thinking that such lines must both tend by gravity to the same point, the centre of the earth ; now lines tending to the same point cannot be parallel, as parallel lines are always at an equal dis- tance from each other, and would never meet.

Mrs. B. Very well explained : you see now the use of your knowledge of parallel lines ; had you been ignorant of their properties, you could not have drawn such a conclusion. This may enable you to form an idea of the great advantage to be derived even from a slight knowledge of geometry, in the stu- dy of natural philosophy ; and if, after I have made you acquainted with the first elements, you should be tempted to pursue the study, I would advise you to prepare yourselves by acquiring some knowledge of geometry. This science would teach you that lines which fall perpendicular to the surface of a sphere cannot be parallel, because they would all meet, if prolonged to the centre of the sphere ; while lines that fall perpendicular to a plane or flat surface, are

34 ON THE ATTRACTION OF GRAVITY.

always parallel, because, if prolonged, they would never meet.

Emily. And yet a pair of scales, hanging perpen- dicular to the earth, aopear parallel?

Mrs. B. Because the sphere is so large, and the scales consequently converge so little, that their in- clination is not perceptible to our senses ; if we could construct a pair of scales whose beam would extend several degrees, their convergence would be very obvious ; but as this cannot be accomplished, let us draw a small tigure of the earth, and then we may make a pair of scales of the proportion wc please, (fig. 1. Plate I.)

Caroline. This figure renders it very clear : then two bodies cannot fall to the earth in parallel lines ?

Mrs. B. Never.

Caroline. The reason that a heavy body falls quicker than a light one, is, I suppose, because the earth attracts it more strongly ?

Mrs. B. The earth, it is true, attracts a heavy body more than a light one ; but that would not make the one fall quicker than the other.

Caroline. Yet, since it is attraction that occasions the fall of bodies, surely the more a body is attracted, the more rapidly it will fall. Besides, experience proves it to be so. Do we not every day see heavy bodies fall quickly, and light bodies slowly.

Emily. It strikes me, as it does Caroline, that as attraction is proportioned to the quantity of matter, the earth must necessarily attract a body which con- ' tains a great quantity more strongly, and therefore bring it to the ground sooner than one consisting of a smaller quantity.

Mrs. B. You must consider, that if heavy bodies are attracted more strongly than light ones, they re- quire more attraction to make them fall. Remem- ber that bodies have no natural tendency to fall, any more than to rise, or to move laterally, and that they will not fall unless impelled by some force ; now this force must be proportioned to the quantity of

TLATE I.

Jij. 2.

%• 1-

ON THE ATTRACTION OF GRAVITY. 35

matter it has to move : a body consisting of 1000 particles of matter, for instance, requires ten times as much attraction to bring it to the ground in the same space of time as a body consisting of only 100 particles.

Caroline. I do not understand that ; for it seems to me, that the heavier a body is, the more easily and readily it falls.

Emily. I think I now comprehend it : let me try if I can explain it to Caroline. Suppose that 1 draw towards me two weighty bodies, the one of lOOlbs. the other of lOOOlbs., must I not exert ten times as much strength to draw the larger one to me, in the same space of time as is required for the smaller one ? Aij if the earth draws a body of lOOOlbs. weight to it in the same space of time that it draws a body of lOOlbs., does it not follow that it attracts the body of lOOOlbs. weight with ten times the force that it does that of lOOlbs.?

Caroline. 1 comprehend your reasoning perfectly ; but if it were so, the body of lOOOlbs. weight, and that of lOOlbs. would fall with the same rapidity; and the consequence would be, that all bodies, whe- ther light or heavy, being at an equal distance from the ground, would fall to it in the same space of time : now it is very evident that this conclusion is absurd ; experience eve- stant contradicts it: observe how much sooner this book reaches the floor than this sheet of paper, when 1 let them drop together.

Emily. That is an objection I cannot answer. I must refer it to you, Mrs. B.

Mrs. B. I trust that we shall not find it insurmount- able. It is true that, according to the laws of attrac- tion, all bodies at an equal distance from the earth, should fall to it in the same space of time ; and this would actually take place if no obstacle intervened to impede their fall. But bodies fall through the air, and it is the resistance of the air which makes bodies of different density fall with different degrees of ve- locity. They must all force their way through the

36 ox THE ATTRACTION OT GRAVITY.

air, but dense heavy bodies overcome this obstacle more easily than rarer and lighter ones.

The resistance which the air opposes to the fall of bodies is proportioned to their surface, not to their weight ; the air being inert, cannot exert a greater force to support the weight of a cannon ball, than it does to support the weight of a ball (of the same size) made of leather ; but the cannon ball will overcome this resistance more easily, and fall to the ground, consequently, quicker than the leather ball.

Caroline. This is very clear, and solves the diffi- culty perfectly. The air offers the same resistance to a bit of lead and a bit of feather of the same size ; yet the one seems to meet with no obstruction in its fall, whilst the other is evidently resisted and sup- ported for some time by the air.

Emily. The larger the surface of a body, then, the more air it covers, and the greater is the resist- ance it meets with from it.

Mrs. B. Certainly ; observe the manner in which this sheet of paper falls ; it floats a while in the air, and then gently descends to the ground. I will roll the same piece of paper up into a ball : it offers now but a small surface to the air, and encounters therefore but little resistance : see how much more rapidly it falls.

The heaviest bodies may be made to float a while in the air, by making the extent of their surface counterbalance their weight. Here is some gold, which is the most dense body we are acquainted ^vith, but it has been beaten into a very thin leaf, and offers so great an extent of surface in proportion to its weight, that its fall, you see, is still more retarded by the resistance of the air than that of the sheet of paper.

Caroline. That is very curious ; and it is, I sup- pose, upon the same principle that iron boats may be made to float on water ?

But, Mrs. B., if the air is a real body, is it not al- so subjected to the laws of gravity ?

Mrs. B, Undoubtedly.

OxV THE ATTRACTIOX OF GRAVITY. 3V

Caroline. Then why does it not, like all other bo- dies, fall to the ground ?

Mrs. B. On account of its spring or elasticity. The air is an elastic Jluid ; a species of bodies, the peculiar property of which is to resume, after com- pression, their original dimensions ; and you must consider the air of which the atmosphere is compo- sed as existing in a state of compression, for its parti- cles being drawn towards the earth by gravity, are brought closer together than they would otherwise be, but the spring or elasticity of the air by which it endeavours to resist compression, gives it a constant tendency to expand itself, so as to resume the dimen- sions it would naturally have, if not under the influ- ence of gravit3^ The air may therefore be said con- stantly to struggle with the power of gravity without being able to overcome it. Gravity thus confines the air to the regions of our globe, whilst its elasticity prevents it from falling like other bodies to the ground.

Emily. The air then is, I suppose, thicker, or 1 should rather say more dense, near the surface of the earth than in the higher regions of the atmosphere ; for that part of the air which is nearer the surface of the earth, must be most strongly attracted.

Mrs. B. The diminution of the force of gravity, at so small a distance as that to which the atmosphere extends (compared with the size of the earth) is so inconsiderable as to be scarcely sensible ; but the pressure of the upper parts of the atmosphere on those beneath, renders the air near the surface of the earth much more dense than the upper regions. The pressure of the atmosphere has been compared to that of a pile of fleeces of wool, in which the low- er fleeces are pressed together by the weight of those above ; these lie light and loose, in proportion as they approach the uppermost fleece, which re- ceives no external pressure, and is confined merely by the force of its own gravity.

Caroline. It has just occurred to me that there are 4

38 ON THE ATTRACTION OF GRAVITY.

some bodies which do not gravitate towards the earth. Smoke and steam, for instance, rise instead of falling.

Mrs. B. It is still gravity which produces their ascent ; at least, were that power destroyed, these bodies would not rise.

Caroline. I shall be out of conceit with gravity, if it is so inconsistent in its operations.

Mrs. B. There is no difficulty in reconciling this apparent inconsistency of effect. The air near the earth is heavier than smoke, steam, or other vapours ; it consequently not only supports 'these light bodies, but forces them to rise, till they reach a part of the atmosphere, the weight of which is not greater than their own, and then they remain stationary. Look at this basin of water ; why does the piece of paper which I throw into it float on the surface ?

Emily. Because, being lighter than the water, it is supported by it.

Mrs. B. And now that I pour more water into the basin, why does the paper rise ?

Emily. The water being heavier than the paper, gets beneath it, and obliges it to rise.

Mrs. B. In a similar manner are smoke and va- pour forced upwards by the air ; but these bodies do not, like the paper, ascend to the surface oi the fluid, because, as we observed before, the air being thinner and lighter as it is more distant from the earth, vapours rise only till they attain a region of air of their own density. Smoke, indeed, ascends but a very little way; it consists of minute particles of fuel carried up by a current of heated air from the fire below : heat, you recollect, expands all bodies ; it consequently rarefies air, and renders it lighter than the colder air of the atmosphere ; the heated air from the fire carries up with it vapour and small particles of the combustible materials which are burning in the fire. When this current of hot air is cooled by mixing with that of the atmosphere, the minute particles of coal or other com- bustible fall, and it is this which produces the small

ON THE ATTRACTION OF GRAVITY. 3d

black flakes which render the air and every thing in contact with it, in London, so dirty.

Caroline. You must, however, allow me to make one more objection to the universal gravity of bodies ; which is the ascent of air balloons, the materials of which are undoubtedly heavier than air ; how, there- tbre, can they be supported by it ?

Mrs. B. 1 admit that the materials of which bal- loons are made are heavier than the air; but the air with which they are tilled is an elastic fluid, of a dif- ferent nature from the atmospheric air, and consider- ably lighter : so that, on the whole, the balloon is lighter than the air which it displaces, and conse- quently will rise, on the same principle as smoke and vapour. Now, Emily, let me hear if you can ex- plain how the gravity of bodies is modified by the ef- fect of the air ?

Emily. The air forces bodies which are lighter than itself to ascend ; those that are of an equal weight will remain stationary in it ; and those that are heavier will descend through it : but the air will have some eifect on these last ; for if they are not much heavier, they will with difficulty overcome the resistance they meet with in passing through it, they will be borne up by it, and their fall will be more or less retarded.

Mrs. B. Very well. Observe how slowly this light feather falls to the ground, while a heavier bo- dy, like this marble, overcomes the resistance which the air makes to its descent much more easily, and its fall is proportionally more rapid. 1 now throw a pebble into this tub of water ; it does not reach the bottom near so soon as if there were no water in the tub, because it meets with resistance from the water. Suppose that we could empty the tub, not only of water, but of air also, the pebble would then fall quicker still, as it would in that case meet with no resistance at all to counteract its gravity.

Thus you see that it is not the differe^it degrees of gravity, but the resistance of the air, wnich prevents

40 ON THE ATTRACTION OF GRAVITY.

bodies of different weight from falling with equal ve- locities ; if the air did not bear up the feather, it would reach the ground as soon as the marble.

Caroline. I make no doubt that it is so ; and yet I do not feel quite satisfied. I wish there was any place void of air, in which the experiment could be made.

Mrs. B. If that proof will satisfy your doubts, I can give it you. Here is a machine called an air punip^ (fig. 2. pi. 1.) by means of which the air may be expelled from any close vessel which is placed over this opening, through which the air is pumped out. Glasses of various shapes, usually called receiv- ers, are employed for this purpose. We shall now exhaust the air from this tall receiver which is placed over the opening, and we shall find that bodies of whatever weight or size within it, will fall from the top to the bottom in the same space of time.

Caroline. Oh, I shall be delighted with this expe- riment! what a curious machine! how can you put the two bodies of different weight within the glass, without admitting the air.

Mrs. B. A guinea and a feather are already pla- ceji there for the purpose of the experiment: here is, you see, a contrivance to fasten them in the upper part of the glass ; as soon as the air is pumped out, I shall turn this little screw, by which means the brass plates which support them will be inclined, and the two bodies will fall. — Now 1 believe I have pretty well exhausted the air.

Caroline. Fray let me turn the screw. — I declare, they both reached the bottom at the same instant ? Did you see, Emily, the feather appeared as heavy as the guinea ?

Emily. Exactly ; and fell just as quickly. How wonderful this is ! what a number of entertaining ex- periments might be made with this machine I

Mrs. B. No doubt there are a great variety ; but we shall reserve them to elucidate the subjects to which they relate : if I had not explained to you why

ON THE ATTRACTION OP GRAVITY. 4t

the guinea and the feather fell with equal velocity, you would not have been so well pleased with the experiment.

Emihj. I should have been as much surprised, but not so much interested ; besides, experiments help to imprint on the memory the facts they are in- tended to illustrate ; it will be better therefore for us to restrain our curiosity, and wait for other experi- ments in their proper places.

Caroline. Pray by what meansis the air exhaust- ed in this receiver ?

Mrs. B. You must learn something of mechanics in order to understand tlte construction of a pump. At our next meeting, therefore, I shall endeavour to make you acquainted with the law^ of motion, as an introduction to that subject.

4*

CONVERSATION III.

ON THE LAWS OF MOTION.

Of Motion. — Of the Inertia of Bodies.— Of Force to Produce Motion. — Direction of Motion. — Velocity, Absolute and Relative. — Uniform Motion. — Retard- ed Motion. — Accelerated Motion. — Velocity of Fall- ing Bodies. — .Momentum. — Action and Re-action Equal.— Elasticity of Bodies. — Porosity of Bodies. — Reflected Motion. — Angles of Incidence and Re- flection. "**-

MRS. B. The science of mechanics is founded on the laws of motion ; it will therefore be necessary to make you acquainted with these laws before we exa- mine the mechanical powers. Tell me, Caroline, what do you understand by the word motion ?

Caroline. I think I understand it perfectly, though I am at a loss to describe it. Motion is the act of mo- ving about, going from one place to another, it is the contrary of remaining at rest.

Mrs. B. Very well. Motion then consists in a change of place; a body is in motion whenever it is changing its situation with regard to a fixed point.

Now, since we have observed that one of the general properties of bodies is Inertia, that is, an entire pas- siveness either with r^ard to motion or rest, it fol- lows that a body cannot move without being put into motion : the power which puts a body into motion is called force ; thus the stroke of the hammer is the

ON THE LAWS OF MOTION. 43

force which drives the nail ; the pulling of the horse that which draws the carriage, &c. Force then is the cause which produces niotion.

Emily. And may we not sa\ that gravity is the force which occasions the fall of bodies ?

Mrs. B. Undoubtedly. I had given you the most familiar illustrations in order to render the explana- tion clear ; but since you seek for more scientific examples, you may say that cohesion is the force which binds the particles of bodies together, and heat that which drives them asunder.

The motion of a body acted upon by a single force is always in a straight line, in the direction in which it received the impulse.

Caroline. That is ver}' natural ; for as the body is inert, and can move only because it is impelled, it will move only in the direction in which it is impel- led. The degree of quickness with which it moves must, I suppose, also depend upon the degree of force with which it is impelled.

Mrs. B. Yes ; the rate at which a body moves, or the shortness of the time which it takes to move from one place to another, is called its velocity ; and it is one of the laws of motion that the velocity of the mo- ving body is proportional to the force by which it is put in motion. We must distinguish between abso- lute and relative velocity.

The velocity of a body is called absolute, if we con- sider the motion of the body in space, without any reference to that of other bodies. When for in- stance a horse goes fifty miles in ten hours, his velo- city is five miles an hour.

The velocity of a body is termed relative, when compared with that of another body which is itself in motion. For instance, if one man walks at the rate of a mile an hour, and another at the rate of two miles an hour, the relative velocity of the latter is double that of the former ; but the absolute velocity of the one is one mile, and that of the other two miles aa hour.

44 ON THE LAWS OF MOTION.

Emily. Let me see if 1 understand it — The rela- tive velocity of a body is the degree of rapidity of its motion compared with that of another body ; thus, if one ship sail three times as far as another ship in the same space of time, the velocity of the former is equal to three times that of the latter.

Mrs. B. The general rule may be expressed thus : the velocity of a body is measured by the space over which it moves, divided by the time which it employs in that motion : thus, if you travel one hundred miles in twenty hours, what is your velocity in each hour ?

Emily. I must divide the space, which is one hundred miles, by the time, which is twenty hours, and the answer will be five miles an hour. Then, Mrs. B., may we not reverse this rule and say, that the time is equal to the space divided by the veloci- ty ; since the space one hundred miles, divided by the velocity five miles, gives twenty hours for the time?

Mrs. B. Certainly; and we may say also that space is equal to the velocity multiplied by the time. Can you tell me, Caroline, how many miles you will have travelled, if your velocity is three miles an hour and you travel six hours ?

Caroline. Eighteen miles ; for the product of 3 multiplied by 6, is 18.

Mrs. B. I suppose that you understand what is meant by the terms uniform^ accelerated and retarded motion.

Emily. I conceive uniform motion to be that of a body whose motion is regular, and at an equal rate throughout ; for instance, a horse that goes an equal number of miles every hour. But the hand of a watch is a much better example, as its motion is so regular as to indicate the time.

Mrs. B. You have a right idea of uniform motion ; but it would be more correctly expressed by saying, that the motion of a body is uniform w hen it passes over equal spaces in equal times. Uniform motion is produced by a force having acted on a body once,

ON THE LAWS OF MOTION. 46

and having ceased to act ; as ibr instance, the stroke of a bat on a cricket ball.

Caroline. But the motion of a cricket ball is not uniform ; its velocity gradaally diminishes till it falls to the ground.

Mrs. B. Recollect that the cricket ball is inert, and has no more power to stop than to put itself in motion; if it falls, therefore, it must be stopped by some force superior to that by which it was project- ed, and which destroys its motion.

Caroline. And it is no doubt the force of gravity which counteracts and destroys that of projection; but if there were no such power as gravity, would the cricket ball never stop?

Mrs. B. If neither gravity nor any other force, such as the resistance of the air, opposed its motion, the cricket ball, or even a stone thrown by the hand, would proceed onwards in a right line, and with a uniform velocity, for ever.

Caroline. You astonish me ! I thought that it was impossible to produce perpetual motion ?

Mrs. B. Perpetual motion cannot be produced by art, because gravity ultimately destroys all motion that human powers can produce.

Emily. But independently of the force of gra- vity, I cannot conceive that the little motion I am capable of giving to a stone would put it in motion for ever.

Mrs. B. The quantity of motion you communica- ted to the stone would not influence its duration ; if you threw it with little force it would move slowly, for its velocity, you must remember, will be propor- tional to the force with which it is projected ; but if there is nothing to obstruct its passage, it will conti- nue to move with the same velocity, and in the same direction as when you first projected if.

Caroline. This appears to me quite incomprehen- sible ; we do not meet with a single instance of it in na- ture.

Mrs. B. I beg your pardon. When you come to

46 ON THE LAWS OF MOTION.

study the motion of the celestial bodies, you will llnd that nature abounds with examples of perpetual mo- tion ; and that it conduces as much to the harmony of the system of the universe, as the prevalence of it would to the destruction of all comfort on our globe. The wisdom of Providence has therefore ordained insurmountable obstacles to perpetual motion here below, and though these obstacles often compel us to contend with great difficulties, yet there results from it that order, regularity and repose, so essential to the preservation of all the various beings of which this world is composed.

Now can you tell me what is retarded motion ?

Carolme. Retarded motion is that of a body which moves every moment slower and slower ; thus when I am tired with walking fast, I slacken my pace ; or when a stone is thrown upweirds, its velocity is gra- dually diminished by the power of gravity.

Mrs. B. Retarded motion is produced by some force acting upon the body in a direction opposite to that which lirst put it in motion : you who are an ani- mated being, endowed with power and will, may slacken your pace, or stop to rest when you are tired ; but inert matter is mcapable of any feeling of fatigue, can never slacken its pace, and never stop, unless retarded or arrested in its course by some op- posing force ; and as it is the laws of inert bodies which mechanics treats of, I prefer your illustration of the stone retarded in its ascent. Now, Emily, it is your turn ; what is accelerated motion?

Emily. Accelerated motion, I suppose, takes place when the velocity of a body is increased ; if you had not objected to our giving such active bodies as ourselves as examples, I should say that my mo- tion is accelerated if I change my pace from walking to running. 1 cannot think of any instance of accele- rated motion in inanimate bodies ; all motion of inert matter seems to be retarded by gravity.

Mrs. B. Not in all cases ; for the power of gravi- tation sometimes produces accelerated motion ; for

ON THE LAWS OF MOTION. 47

instance, a stone falling from a height moves with a regularly accelerated motion.

Emily. True ; because the nearer it approaches the earth, the more it is attracted by it.

Airs. B. You have mistaken the cause of its acce- leration of motion ; for though it is true that the force of gravity increases as a body approaches the earth, the difference is so trifling at any small distance from its surface as not to be perceptible.

Accelerated motion is produced when the force which put a body in motion continues to act upon it during its motion, so that its motion is continually in- creased. When a stone falls from a height, the im- pulse which it receives from gravity during the first instant of its fall, would be sufficient to bring it to the ground with a uniform velocity : for, as we have ob- served, a body having been once acted upon by a force, will continue to move with a uniform velocity; but the stone is not acted upon by gravity merely at the first instant of its fall, this power continues to im- pel it during the whole of its descent, and it is this continued impulse which accelerates its motion.

Emily. 1 do not quite understand that.

Mrs. B. Let us suppose that the instant after you have let fall a stone from a high tower, the force of gravity were annihilated, the body would nevertheless continue to move downwards, for it would have re- ceived a first impulse from gravity, and a body once put in motion will not stop unless it meets with some obstacle to impede its course ; in this case its veloci- ty would be uniform, for though there would be no obstacle to obstruct its descent, there would be no force to accelerate it.

Emily. That is very clear.

Mrs. B. Then you have only to add the power of gravity constantly acting on the stone during its de- scent, and it will not be difficult to understand that its motion will become accelerated, since the gravity which acts on the stone durins the first instant of its

48 ON THE LAWS OF MOTIOX.

descent, will continue in force every instant till it reaches the ground. Let us suppose that the impulse given by gravity to the stone during the first instant of its descent be equal to one, the next instant we shall find that an additional impulse gives the stone an additional velocity equal to one, so that the accumu- lated velocity is now equal to two ; the following in- stant another impulse increases the velocity to three, and so on till the stone reaches the ground.

Caroline. Now I understand it ; the effects of pre- ceding impulses must be added to the subsequent ve- locities.

Mrs. B. Yes ; it has been ascertained, both by experiment and calculations, which it would be too difficult for us to enter into, that heavy bodies de- scending from a height, by the force of gravity, fall sixteen feet the first second of time, three times that distance in the next, five times in the third second, seven times in the fourth, and so on, regularly increasing their velocities according to the number of seconds during which the body has been falling.

Einilij. If you throw a stone perpendicularly up- wards, is it not the same length of time ascending that it is descending ?

Mrs. B. Exactly ; in ascending, the velocity is di- minished by the force of gravity ; in descending, it is accelerated by it.

Caroline. I should then have imagined that it would have f\dlen quicker than it rose ?

Mrs. B. You must recollect that the force with which it is projected must be taken into the account ; and that this force is overcome and destroyed by gra- vity before the body falls.

Caroline. But the force of projection given to a stone in throwing it upwards, cannot always be equal to the force of gravity in bringing it down again, for the force of gravity is always the same, whilst the de- gree of impulse given to the stone is optional ; I may throw it up gently, or with violence.

QN THE LAWS OF MOTION. 49

Mrs, B. If you throw it gently, it will not rise high ; perhaps only sixteen feet, in which case it will fall in one second of time. Now it is proved by ex- periment, that an impulse requisite to project a body sixteen ^QGi upwards, will make it ascend that height in one second ; here then the times of the ascent and descent are equal. But supposing it be required to throw a stone twice that height, the force must be proportionally greater.

You see then, that the impulse of projection in throwing a body upwards, is always equal to the ac- tion of the force of gravity during its descent ; and that it is the greater or less distance to which the body rises, that makes these two forces balance each other.

I must now explain to you what is meant by the momentum of bodies. It is the force, or power, with which a body in motion strikes against another body. The momentum of a body is composed of its quantity of matter, multiplied by its quantity of motion; in other words, its weight and its velocity.

Caroline. The quicker a body moves, the greater, no doubt, must be the force with which it would strike against another body.

Emily, Therefore a small body may have a great- er momentum than a large one, provided its velocity be sufficiently greater ; for instance, the momentum of an arrow shot from a bow must be greater than a stone thrown by the hand.

Caroline. We know also by experience, that the heavier a body is, the greater is its force ; it is not therefore difficult to understand, that the whole pow- er or momentum of a body must be composed of these two properties : but I do not understand why they should be multiplied the one by the other ; I should have supposed that the quantity of matter should have been added to the quantity of motion ?

Mrs. B. It is found by experiment, that if the weight of a body is represented by the number 3, and its velocity also by 3, its momentum will be re- 6

50 ON THE LAWS OP MOTION,

presented by 9 ; not 6, as would be the case were these figures added, instead of being multiplied toge- ther. 1 recommend it to you to be careful to re- member the definition of the momentum of bodies, as it is one of the most important points in mechanics ; you will find, that it is from opposing motion to mat- ter, that machines derive their powers.*

The reaction of bodies is the next law of motion which I must explain to you. When a body in mo- tion strikes against another body, it meets with resist- ance from it ; the resistance of the body at rest will be equal to the blow struck by the body in motion ; or, to express myself in philosophical language, action and re-action wiW be equal, and in opposite directions.

Caroline, Do you mean to say, that the action of the body which strikes is returned with equal force by the body which receives the blow.

Mrs. B. Exactly.

Caroline. But if a man strikes another on the face with his fist, he surely does not receive as much pain by the re-action as he inflicts by the blow ?

Mrs. B. No ; but this is simply owing to the knuckles having much less feeling than the face.

Here are two ivory balls suspended by threads, (Plate I. fig. 3.) draw one of them, A, a little on one side, — now let it go ; — it strikes, you see, against the other ball B, and drives it off, to a distance equal to that through which the first ball fell ; but the motion of A is stopped, because when it struck B, it received in return a blow equal to that it gave, and its motion was consequently destroyed.

* In comparing together the momenta of different bodies, we must be attentive to measure their weights and velocities, by the same denomination of weights and of spaces, otherwise the re- sults would not agree. Thus, if we estimate the weight of one body in ounces, we must estimate the weight of the rest also in ounces, and not in pounds ; and in computing the velocities, in like manner, we should adhere to the same standard of measure, both of space and of time; as for instance, the number of feet in one second, or of mile? in one hour.

ON THE LAWS OF MOTION. 51

Emily. I should have supposed, that the motion of the ball A was destroyed, because it had communica- ted all its motion to B.

Mrs. B. It is perfectly true, that when one body strikes against another, the quantity of motion com- municated to the second body, is lost by the first ; but this loss proceeds from the action of the body which is struck.

Here are six ivory halls hanging in a row, (fig. 4.) draw the first out of the perpendicular, and let it fall against the second. None of the balls appear to move, you see, except the last, which flies off as far as the first ball fell ; can you explain this ?

Caroline. I believe so. When the first ball struck the second, it received a blow in return, which destroyed its motion ; the second ball, though it did not appear to move, must have struck against the third ; the re-action of which set it at rest ; the actioa of the third ball must have been destroyed by the re- action of the fourth, and so on, till motion was com- municated to the last ball, which, not being re-acted upon, flies off.

Mrs. B. Very well explained. Observe, that it is only when bodies are elastic, as these ivory balls are, that the stroke returned is equal to the stroke given. I will show you the difference with these two balls of clay, (fig. 5.) which are not elastic ; when you raise one of these, D, out of the perpendi- cular, and let it fall against the other, E, the re-action of the latter, on account of its not being elastic, is not sufficient to destroy the motion of the former ; only part of the motion of D will be comolunicated to E, and the two balls will move on together to d and e, which is not to so great a distance as that through which D fell.

Observe how useful re-action is in nature. Birds, in flying, strike the air with their wings, and it is the re-action of the air which enables them to rise, or advance forw-ards ; re-action being always in a contrary direction to action.

d2 ON THE LAWS OF MOTION.

Caroline, I thought that birds might be lighter than the air when their wings were expanded, and \)y that means enabled to fly.

Mrs. B. When their wings are spread, they are better supported by the air, as they cover a greater extent of surface ; but they are still much too heavy to remain in that situation, without continually flap- ping their wings, as you may have noticed, when birds hover over their nests ; the force with which their wings strike against the air must equal the weight of their bodies, in order that the re-action of the air may be able to support that weight ; the bird will then remain stationary. If the stroke of the wings is greater than is required merely to support the bird, the re-action of the air will make it rise ; if it be less, it will gently descend ; and you may have observed the larlf, sometimes remaining with its wings extended, but motionless ; in this state it drops rapidly into its nest.

Caroline, What a beautiful eflect this is of the law of re-action ! But if flying is merely a mechanical operation, Mrs. B., why should we not construct wings, adapted to the size of our bodies, fasten them to our shoulders, move them with our arms, and soar into the air.

Mrs. B. Such an experiment has been repeatedly attempted, but never with success ; and it is now considered as totally impracticable. The muscular power of birds is greater in proportion to their weight than that of man ; were we therefore furnished with wings sufficiently large to enable us to fly, we should not have strength to put them in motion.

In swimming, a similar action is produced on the water, as that on the air in flying : and also in rowing ; you strike the water with the oars, in a direction op- posite to that in which the boat is required to move, and it is the re-action of the water on the oars which drives the boat along.

Emily. You said, that it was in elastic bodies only

ON THE LAWS OF MOTION. S3

that re-action was equal to action ; pray what bodies are elastic besides the air ?

Mrs, B. In speaking of the air, I think we defined elasticity to be a property, by means of which bodies that are compressed return to their former state, if I bend this cane, as soon as I leave it at liberty it re- covers its former position ; if I press my finger upon your arm, as soon as I remove it, the flesh, by virtue of its elasticity, rises and destroys the impression I made. Of all bodies, the air is the most eminent for this property, and* it has thence obtained the name of elastic fluid. Hard bodies are in tli€ next degree elastic ; if two ivory, or metallic balls are struck to- gether, the parts at which they touch will be flatten- ed ; but their elasticity will make them instantane- ously resume their former shape.

Caroline. But when two ivory balls strike against each other, as they constantly do on a biUiard table, no mark or impression is made by the stroke.

Mrs, B. I beg your pardon ; but you cannot per^ ceive any mark, because their elasticity instantly de- stroys all trace of it.

Soft bodies, which easily retain impressions, such as clay, wax, tallow, butter, &c. have very little elas- ticity ; but of all descriptions of bodies liquids are the least elastic.

Emily. If sealing-wax were elastic, instead of re- taining the impression of a seal, it would resume a smooth surface as soon as the weight of the seal was removed. But pray what is it that produces the elasticity of bodies ?

Mrs. B. There is great diversity of opinion upon that point, and I cannot pretend to decide which ap- proaches nearest to the truth. Elasticity implies sus- ceptibility of compression, and the susceptibility of compression depends upon the porosity of bodies, for were there no pores or spaces between the par- ticles of matter of which a body is composed, it could not be compressed.

Caroline, That is to say, that if the particles of 6*

54 ox THE LAWS OP MOTION.

bodies were as close together as possible, they could not be squeezed closer.

Emily. Bodies then, whose particles are most dis- tant from each other, must be most susceptible of compression, and consequently most elastic ; and this you say is the case with air, which is perhaps the least dense of all bodies ?

Mrs. B. You will not in general find this rule hold good, for liquids have scarcely any elasticity, whilst hard bodies are eminent for this property, though the latter are certainly of much greater den- sity than the former ; elasticity impHes, therefore, not only a susceptibility of compression, but depends upon the power of resuming its former state after compression.

Caroline. But surely there can be no pores in ivory and metals, Mrs. B. * how then can they be Susceptible of compression ?

Mrs. B. The pores of such bodies are invisible to the naked eye, but you must not thence conclude that they have none ; it is, on the contrary, well as- certained that gold, one of the most dense of all bo- die!^, is extromely porous, and that these pores are sufTiciently large to admit water when strongly com- pressed to pass through them. This was shown by a f -Jebrated experiment made many years ago at Florence.

Emily. If water can pass through gold, there must certainly be pores or interstices which afford it a passage ; and if gold is so porous, what must other Ijodies be, which are so much less dense than gold !

Mrs. B. The chief difference in this respect is, I believe, that the pores in some bodies are larger thao in others ; in cork, sponge, and bread, they form con- liderable cavities ; in wood and stone, when not po- lished, they are generally perceptible to the naked eye ; whilst in ivory, metals, and all varnished and polished bodies, they cannot be discerned. To give you an idea of the extreme porosity of bodies, Sir Isaac Newtoa conjectured that if the earth were so

ON THE LAWS OF MOTIOfiT. 5#

compressed as to be absolutely without pores, its dimensions might possibly not be more than a cubic inch.

Caroline, What an idea ! Were we not indebted to Sir Isaac Newton for the theory of attraction, I should be tempted to laugh at him for such a supposi- tion. What insigniticant Httle creatures we should be J

Mrs. B. If our consequence arose from the size of our bodies we should indeed be but pigmies, but remember that the mind of Newton was not circum- scribed by the dimensions of its envelope.

Emily. It is, however, fortunate that heat keeps the pores of matter open and distended, and prevents the attraction of cohesion from squeezing us into a nutshell.

Mrs. B. Let us now return to the subject of re- action, on which we have some further observations to make. It is re-action being contrary to action which produces reflected motion, if you throw a ball against the wall, it rebounds ; this return of the ball is owing to the re-action of the wall against which it struck, and is called reflected motion.

Emily. And I now understand why balls filled with air rebound better than those stuffed with bran or wool; air being most susceptible of compression and most elastic, the re-action is more complete.

Caroline. I have observed that when I throw a ball straight against the wall, it returns straight to my hand ; but if I throw it obliquely upwards, it rebounds still higher, and I catch it when it falls.

Mrs. B. You should not say straight, but perpen- dicularly against the wall ; for straight is a general term for lines in all directions which are neither curved nor bent, and is therefore equally applicable to oblique or perpendicular lines.

Caroline. I thought that perpendicularly meant either directly upwards or downwards ?

Mrs. B. In those directions lines are perpendicu- lar to the earth. A perpendicular line has always a reference to something towards which it is perpen-

56 ON THE LAWS OF MOTION.

dicular ; that is to say, that it inclines neither to the one side or the other, but makes an equal angle on every side. Do you understand what an angle is ?

Caroline. Yes, I believe so : it is two lines meet- ing in a point.

Mrs. B. Well then, let the line A B (plate II, fig. 1.) represent the floor of the room, and the line C D that in which you throw a ball against it ; the line C D, you will observe, forms two angles with the line A B, and those two angles are equal.

Emily. How can the angles be equal, while the lines which compose them are of unequal length ?

Mrs. B. An angle is not measured by the length of the lines, but by their opening.

Emily. Yet the longer the lines are, the greater is the opening between them.

Mrs. B. Take a pair of compasses and draw a cir- cle over these angles, making the angular point the centre.

Emily. To what extent must I open the com- passes ?

Mrs. B. You may draw the circle what size you please, provided that its cuts the lines of the angles we are to measure. All circles, of whatever dimen- sions, are supposed to be divided into 360 equal parts, called degrees ; the opening of an angle, being there- fore a portion of a circle, must contain a certain num- ber of degrees ; the larger the angle, the greater the number of degrees, and two angles are said to be »cqual when they contain an equal number of degrees.

Emily. Now 1 understand it. As the dimensions of an angle depend upon the number of degrees con- tained between its lines, it is the opening, and not the length of its lines, which determines the size of the angle.

Mrs. B. Very well : now that you have a clear idea of the dimensions of angles, can you tell me how many degrees are contained in the two angles formed by one line falling perpendicularly on another, as in the figure 1 have just drawn ?

PLATE n.

n

»

ON THE LAWS OF MOTION. 61

Emily. You must allow me to put one foot ol* the compasses at the point of the angles, and draw a circle round them, and then I think 1 shall be able to answer your question : the two angles are together just equal to half a circle, they contain therefore 90 degrees each ; 90 degrees being a quarter of 360.

Mrs. B. An angle of 90 degrees is called a right angle, and when one line is perpendicular to another, it forms, you see, (fig. 1.) a right angle on either side. Angles containing more than 90 degrees are called obtuse angles ; (fig. 2.) and those containing less than 90 degrees are called acute angles, (fig. 3.)

Caroline. The angles of this square table are right angles, but those of the octagon table are obtuse an- gles ; and the angles of sharp-pointed instruments are acute angles.

Mrs. B. Very well. To retarn now to your ob- servation, that if a ball is thrown obliquely against the wall it will not rebound in the same direction ; tell me, have you ever played at billiards ?

Caroline, Yes, frequently ; and I have observed that when I push the ball perpendicularly against the cushion, it returns in the same direction ; but when I send it obliquely to the cushion, it rebounds ob- liquely, but on the opposite side ; the ball in this lat- ter case describes an angle, the point of which is at the cushion. I have observed too, that the more ob- liquely the ball is struck against the cushion, the more obliquely it rebounds on the opposite side, so that a billiard player can calculate with great accu- racy in what direction it will return.

Mrs. B. Very well. This figure (fig. 4. plate II.) represents a billiard table ; now if you draw a line A B from the point where the ball A strikes perpen- dicular to the cushion ; you will find that it will di- vide the angle which the ball describes into two parts, or two angles ; the one will show the obliquity of the direction of the ball in its passage towards the cush- ion, the other its obliquity in its passage back from the cushion. The first is called the angle of inci-

58 ON THE LAWS OF MOTION.

dence^ the other the angle of reflection, and these ao- gles are always equal.

Caroline. This then is the reason why, when I throw a ball obliquely against the wall, it rebounds in an opposite oblique direction, forming equal angles of incidence and of reflection.

Mrs, B. Certainly ; and you will find that the more obliquely you throw the ball, the more oblique- ly it will rebound.

We must now conclude ; but I shall have some further observations to make upon the laws of mo- tion, at our next meeting.

CONVERSATION IV.

ON COxMPOUND MOTION.

Compound Motion, the Result of two Opposite For- ces.— Of Circular Motion, the Result of two Forces, one of which confines the Body to a Fixed Point. — Centre of Motion, the Point at Rest while the other Parts of the Body move round it. — Centre of Magni- tude, the Middle of a Body. — Centripetal Force, that which confines a Body to a fixed Central Point. — Centrifugal Force, that which impels a Body to fly from the Centre. — Fall of Bodies in a Parabola. — Centre of Gravity, the Centre of Weight, or point about which the Parts balance each other,

MRS. B. I must explain to you the nature of com- pound motion. Let us suppose a body to be struck by two equal forces in opposite directions, how will it move ?

Emily. If the directions of the forces are in exact opposition to each other, I suppose the body would not move at all.

Mrs. B. You are perfectly right ; but if the for- ces, instead of acting on the body in opposition, strike it in two directions inclined to each other, at an angle of ninety degrees, if the ball A (fig. 6. plate II.) be struck by equal forces at X and at Y, will it not move ?

Emily. The force X would send it towards ,B, and the force Y towards C ; and since these forces are equal, I do not know how the body can obey one im^ pulse rather than the other, and yet I think the ball

60 ON COMPOUND MOTION.

would move, because, as the two forces do not act in direct opposition, they cannot entirely destroy the effect of each other.

Mrs, B, Very true ; the ball will therefore follow the direction of neither of the forces, but will move in a line between them, and will reach D in the same space of time, that the force X would have sent it to B, and the force Y would have sent it to C. Now, if you draw two lines from D, to join B and^, you will form a square, and the oblique line which the body describes is called the diagonal of the square.

Caroline. That is very clear, but supposing the two forces to be unequal, that the force X, for in* stance, be twice as great as the force Y ?

Mrs. B. Then the force X would drive the ball twice as far as the force Y, consequently you must draw the line A B (fig. 6.) twice as long as the line A C, the body will in this case move to D ; and if you draw lines from that point to B rand C, you will iind that the ball has moved in the diagonal of a rectangle.

Emily. Allow me to put another case ? Suppose the two forces are unequal, but do not act on the ball in the direction of a right angle, 'but in that of an acute angle, what will result ?

Mrs. B. Prolong the lines in the directions of the two forces, and you will soon discover which way the ball will be impelled ; it will move from A to D, in the diagonal of a parallelogram, (fig. 7.) Forces acting in the direction of lines forming an obtuse angle, will also produce motion in the diagonal of a parallel- ogram. For instance, if the body set out from B, instead of A, and was impelled by the forces X and Y, it would move in the dotted diagonal B C.

We may now proceed to circular motion : this is the result of two forces on a body, by one of which it is projected forward in a right line, whilst by the other it is confined to a fixed point. For instance, when 1 whirl this ball, which is fastened to ray hand with a string, the ball moves in a circular direction ;

ON COMPOUND MOTION. 01

because it is acted on by two forces, that which I give it, which represents the force of projection, and that of the string, which confines it to my hand. If during its motion you were suddenly to cut the string, the ball would fly off in a straight line ; being releas- ed from confinement to the fixed point, it would be acted on but by one force, and motion produced by one force, you know, is always in a right hne.

Caroline. This is a little more difficult to compre- hend than compound motion in straight hnes.

Mrs. B. You have seen a mop trundled, and have observed that the threads which compose the head -of the mop fly from the centre ; but being confined to it at one end, they cannot part from it ; whilst the water they contain, being unconfined, is thrown off in straight lines.

Emily. In the same way, the flyers of a windmill, when put in motion by the wind, would be driven straight forwards in a right line, were they not con- fined to a fixed point, round which they are compel- led to move.

Mrs. B. Very well. And observe, that the point to which the motion of a small body, such as the ball with the string, which may be considered as revolv- ing in one plane, is confined, becomes the centre of its motion. But when the bodies are not of a size or shape to allow of our considering every part of them as moving in the same plane, they in reality revolvje round a line, which line is called the axis of motion. In a top, for instance, when spinning on its point, the axis is the line which passes through the middle of it, perpendicularly to the floor.

Caroline. The axle of the flyers of the windmill is then the axis of its motion ; but is the centre of motion always in the middle of a body ?

Mrs. B. No, not always. The middle point of a body is called its centre of magnitude, or position, that is, the centre of its mass or bulk. Bodies have also another centre, called the centre of gravity, »y}iich I shall explain to you ; but at present, we must

62 ON COMPOUND MOTION.

confine ourselves to the axis of motion. This line you must observe remains at rest, whilst all the other parts of the body move around it ; when you spin a top the axis is stationary whilst every other part is in motion round it.

Caroline. But a top generally has a motion for- wards, besides its spinning motion ; and then no point within it can be at rest ?

Mrs. B. What i say of the axis of motion, relates only to circular motion ; that is to say, to motion round a line, and not to that which a body may have at the same time in any other direction. There is one circumstance in circular motion, which you must carefully attend to ; which is, that the further any part of a body is from the axis of motion, the greater is its velocity ; as you approach that line, the velo- city of the parts gradually diminishes till you reach the axis of motion, which is perfectly at rest.

Caroline. But, if every part of the same body did not move with the same velocity, that part which moved quickest must be separated from the rest of the body, and leave it behind ? ^

Mrs. B. You perplexyourself by confounding the idea of circular motion with that of motion in a right line : you must think only of the motion of a body round a fixed line, and you will find, that if the parts farthest from the centre had not the greatest velocity, those parts would not be able to keep up with the rest of the body, and would be left behind. Do not the extremities of the vanes of a windmill move over a much greater space, than the parts nearest the axis of motion ? (plate III. fig. 1.) the three dotted circles describe the paths in which three different parts of the vanes move, and though the circles are of diff'er- ent dimensions, the vanes describe each of them in the same space of time.

Caroline. Certainly they do ; and I now only won- der, that we neither of us ever made the observation before : and the same effect must take place in a so- lid body, like the top, in spinning ; the most bulging

%■ ^■

PLATE n

Fi^S.

Fi^.4

%• '^■

Fi^. S.

F^ 8

ON COxMPOUND MOTION. 63

part of the surface must move with the greatest rapi-

dfty.

Mrs. B. The force which confines a body to a centre round which it moves is called the centripetal force ; and that force, which impels a body to fly from the centre, is called the centrifugal force ; in circular motion, these two forces constantly balance each other : otherwise the revolving body would ei- ther approach the centre, or recede from it, accord- ing as the one or the other prevailed.

Caroline. When I see any body moving in a circle, I shall remember that it is acted on by two forces.

Mrs. B. Motion, either in a circle, an ellipsis, or any other curve-line, must be the result of the action of two forces ; for you know, that the impulse of one single force always produces motion in a right line.

Emily. And if any cause should destroy the cen- tripetal force, the centrifugal force would alone im- pel the body, and it would I suppose fly off in a straight line from the centre to which it had been confined.

Mrs. B. It would not fly off" in a right line from the centre ; but in a right line in the direction in which it was moving, at the instant of its release ; if a stone, whirled round in a sling, gets loose at the point A, (plate III. fig. 2.) it flies off in the direction A B ; this Hne is called a tangent, it touches the cir- cumference of the circle, and forms a right angle with a line drawn from that point of the circumfer- ence to the centre of the circle, C.

Emily. You say, that motion in a curve-line is owing to two forces acting upon a body ; but when 1 throw this ball in a horizontal direction, it describes a curve-line in falling ; and yet it is only acted upon by the force of projection ; there is no centripetal force to confine it, or produce compound motion.

Mrs. B. A ball thus thrown, is acted upon by no less than three forces ; the force of projection, which you communicated to it ; the resistance of the air through which it passes, which diminishes its veloci-

04 ON COMPOUND MOTION.

ty, without changing its direction ; and the force of gravit}^ which finally brings it to the ground. The power of gravity, and the resistance of the air, being always greater than any force of projection we can give a body, the lattdr is gradually overcome, and the body brought to the ground ; but the stronger the projectile force, the longer will these powers be in subduing it, and the further the body will go before it falls.

Caroline. A shot fired from a cannon, for instance, will go much further than a stone projected by the hand.

Mrs. B. Bodies thus projected, you observed, described a curve-line in their descent; can you ac- ' count for that?

Caroline. No ; I do not understand why it should not fall in the diagonal of a square.

Mrs. B. You must consider that the force of pro- jection is strongest when the ball is first thrown ; this force, as it proceeds, being weakened by the continued resistance of the air, the stone, therefore, begins by moving in a horizontal direction ; but as the strong- er powers prevail, the direction of the ball will gradu- ally change from a horizontal to a perpendicular line. Projection alone, would drive the ball A, to B, (fig. 3.) gravity would bring it to C ; therefore, when acted on in different directions, by these two forces, it moves between, gradually inclining more and more to the force of gravity, in proportion as this accumu- lates ; instead therefore of reaching the ground at D, as you supposed it would, it falls somewhere about E.

Caroline. It is precisely so ; look, Emily, as I throw this ball directly upwards, how the resistance of the air and gravity conquers projection. Now I will throw it upwards obliquely ; see, the force of projection enables it, for an instant, to act in opposi- tion to that of gravity ; but it is soon brought down again.

Mrs. B. The curve-line which the ball has de- scribed, is called in geometry r parabola ; but when

ON COMPOUND MOTION. Qo

the ball is thrown perpendicularly upwards, it will descend perpendicularly ; because the force of pro- jection, and that of gravity, are in the same line of direction.

We have noticed the centres of magnitude, and of motion ; but I have not yet explained to you what is meant by the centre of gravity ; it is that point in a body, about which all the parts exactly balance each other ; if therefore that point is supported, the body will not fall. Do you understand this ?

Emily. I think so, if the parts round about this point have an equal tendency to fall, they will be in equilibrium, and as long as this point is supported, the body cannot fall.

Mrs. B. Caroline, what would be the effect, were any other point of the body alone supported ?

Caroline. The surrounding parts no longer balan- cing each other, the body, I suppose, would fall on the side at which the parts are heaviest.

Mrs. B. Infallibly; whenever the centre ofgra vity is unsupported the body must fall. This some- times happens with an overloaded wagon winding up a steep hill, one side of the road being more elevated than the other ; let us suppose it to slope as is de- scribed in this figure, (plate III. fig. 4.,) we will say, that the centre of gravity of this loaded wagon is at the point A. Now your eye will tell you, that a wa- gon thus situated will overset ; and the reason is, that the centre of gravity A, is not supported ; for if you draw a perpendicular line from it to the ground at C, it does not fall under the wagon within the wheels, and is therefore not supported by them.

Caroline. I understand that perfectly ; but what is the meaning of the other point B ?

Mre. B. Let us, in imagination, take off the upper part of the load ; the centre of gravity will then change its situation, and descend to B, as that will now be the point about which the parts of the less heavily laden wagon will balance each other. Will the wagon now be upset?

6*

G.6 ON COMPOUND MOTION.

Caroline. No, because a perpendicular line from that point falls within the wheels at D, and is support- ed by them ; and when the centre of gravity is sup- ported, the body will not fall.

Emily, Yet I should not much like to pass a wa- gon in that situation ; for, as you see, the point D is but just within the left wheel ; if the right wheel was merely raised, by passing over a stone, the point D would be thrown on the outside of the left wheel, and the wagon would upset.

Caroline. A wagon, or any carriage whatever, will then be most firmly supported, when the centre of gravity falls exactly between the wheels ; and that is the case in a level road.

Pray, whereabouts is the centre of gravity of the human body ?

Mrs. B. Between the hips ; and as long as we Stand upright, this point is supported by the feet ; if you lean on one side, you will find that you no longer stand firm. A rope-dancer performs all his feats of agility, by dexterously supporting his centre of gravi- ty ; whenever he finds that he is in danger of losing his balance, he shifts the heavy pole, which be holds in his hands, in order to throw the weight towards the side that is deficient ; and thus, by chang- ing the situation of the centre of gravity, he restores his equilibrium.

Caroline. When a stick is poised on the tip of the finger, is it not by supporting its centre of gravity ?

Mrs. B. Yes ; and it is because the centre of gra- vity is not supported that spherical bodies roll down aslope. A sphere, being perfectly round, can touch the slope but by a single point, and that point cannot be perpendicularly under the centre of gravity, and therefore cannot be supported, as you will perceive by examining this figure. (Fig. 5. plate III.)

Emily. So it appears ; yet I have seen a cylinder of wood roll up a slope ; how is that contrived ?

Mrs. B. It is done by plugging one side of the i^y Under with lead, as at B, (fig. 5» plate III.) the bo-

ON COMPOUND MOTION. 6?

dy being no longer of a uniform density, the centre of gravity is removed from the middle of the body to some point in the lead, as that substance is much hea- vier than wo«d ; now you may observe that in order that the cylinder may roll down the plane, as it is here situated, the centre of gravity must rise, which is impossible ; the centre of gravity must always de- scend in moving, and will descend by the nearest and readiest means, which will be by forcing the cylinder up the slope, until the centre of gravity is supported, and then it stops.

Caroline. The centre of gravity, therefore, is not always in the middle of a body ?

Mrs. B. No, that point we have called the centre of magnitude; when the body is of a uniform densi- ty, the centre of gravity is in the same point; but when one part of the body is composed of heavier materials than another part, the centre of gravity be- ing the centre of the weight of the body can no long- er correspond with the centre of magnitude. Thus you see the centre of gravity of this cylinder plugged with lead, cannot be in the same spot as the centre of magnitude.

Emily. Bodies, therefore, consisting but of one kind of substance, as wood, stone, or lead, and whose densities are consequently uniform, must stand more firmly, and be more difficult to overset, than bodies composed of a variety of substances^ of different den- sities, which may throw the centre of gravity on one side.

Mrs. B. Yes ; but there is another circumstance which more materially affects the firmness of their position, and that is their form. Bodies that have a narrow base are easily upset, for if they are the least inclined, their centre is no longer supported, as you may perceive in fig. 6.

Caroline. I have often observed with what diffi- culty a person carries a single pail of water ; it is owing, I suppose, to the centre of gravity being thrown on one side, and the opposite arm is stretched

68 ON COMPOUND MOTION.

out to endeavour to bring it back to it3 original situa- tion ; but a pail hanging on each arm is carried with- out difficulty, because they balance each other, and the centre of gravity remains supported by the feet.

Mrs. B. Very well ; 1 have but one more remark to make on the centre of gravity, which is, that when two bodies are fastened together, by a line, string, chain, or any power whatever, they are to be consi- dered as forming but one body ; if the two bodies be of equal weight, the centre of gravity will be in the middle of the line which unites them, (fig. 7.) but if one be heavier than the other, the centre of gravity will be proportionally nearer the heavy body than the light one. (fig. 8.) If you were to carry a rod or pole with an equal weight fastened at each end of it, you would hold it in the middle of the rod, in order that the weights should balance each other ; whilst if it had unequal weights at each end, you would hold it nearest the greater weight, to make them balance each other.

Emily. And in both cases we should support the centre of gravity ; and if one weight be very consi- derably larger than the other, the centre of gravity will be thrown out of the rod into the heaviest weight. (fig. 9.)

Mrs. B. Undoubtedlv.

CONVERSATION V.

ON THE MECHANICAL POWERS.

Of the Power of Machines. — Of the Lever in General. — Of the Lever of the First Kind, having the Fulcrum between the Power and the Weight. — Of the Lever of the Second Kind, having the Weight between the Pow- er and the Fulcrum. — Of the Lever of the Third Kindy having the Power between the Fulcrum and the Weight.

MRS. B. We may now proceed to examine the mechanical powers ; they are six in number, one or more of which enters into the composition of every machine. The lever, the pulley, the wheel, and axle^ the inclined plane, the wedge, and the screw.

In order to understand the power of a machine, there are four things to be considered. 1st. The power that acts : this consists in the effort of men or horses, of weights, springs, steam, &c.

2dly. The resistance which is to be overcome by the power ; this is generally a weight to be moved. The power must always be superior to the resist- ance, otherwise the machine could not be put in mo- tion.

Caroline. If for instance the resistance of a car- riage was greater than the strength of the horses employed to draw it, they would not be able to make it move.

Mrs, B, 3dly. We are to consider the centre of mo~

TO ON THE MECHANICAL POWERS.

tion, or, as it is termed in mechanics, the fulcrum; this you may recollect is the point about which all the parts of the body move; and, lastly, the respective velocities of the power, and of the resistance.

Emily. That must depend upon their respective distances from the axis of motion ; as we observed in the motion of the vanes of the windmill.

Mrs. B. We shall now examine the power of the lever. The lever is an inflexible rod or beam of any kind, that is to say, one which will not bend in any direction. For instance, the steel rod to which these scales are suspended is a lever, and the point in which it is supported the fulcrum, or centre of mo- tion ; now, can you tell me why the two scales are in equilibrium ?

Caroline. Being both empty, and of the same weight, they balance each other.

Emily. Or, more correctly speaking, because the centre of gravity common to both is supported.

Mrs. B. Very well ; and which is the centre of gravity of this pair of scales ? (fig. 1. plate III.)

Emily. You have told us that when two bodies of equal weight were fastened together, the centre of gravity was in the middle of the line that connected them ; the centre of gravity of the scales must there- fore be in the fulcrum F of the lever which unites the two scales ; and corresponds with the centre of motion.

Caroline. But if the scales contained different weights, the centre of gravity would no longer be in the fulcrum of the lever, but removed towards that scale which contained the heaviest weight ; and since that point would no longer be supported, the heavy scale would descend and outweigh the other.

Mrs. B. True ; but tell me, can you imagine any mode by which bodies of different weights can be made to balance each other, either in a pair of scales, or simply suspended to the extremities of the lever ? for the scales are not an essential part of the machine, they have no mechanical power, and are used merely

PLATu nr

ON THE MECHANICAL POWERS. 71

for the convenience of containing the substance to be weighed.

Caroline. What! make a light body balance a heavy one ? I cannot conceive that possible.

Mrs. B. The fulcrum of this pair of scales (fig. 2.) is moveable, you see ; I can take it ofif the prop, and fiisten it on again in another part ; this part is now become the fulcrum, but it is no longer in the centre of the lever.

Caroline. And the scales are no longer true ; for that which hangs on the longest side of the lever de- scends.

Mrs. B. The two parts of the lever divided by the fulcrum are called its arms, you should therefore say the longest arm, not the longest side of the lever. These arms are likewise frequently distinguished by the appellations of the acting and the resisting part of the lever.

Your observation is true that the balance is now destroyed ; but it will answer the purpose of en- abling you to comprehend the power of a lever when the fulcrum is not in the centre.

Emily. This would be an excellent contrivance for those who cheat in the weight of their goods ; by making the fulcrum a little on one side, and placing the goods in the scale which is suspended to the longest arm of the lever, they would 4ippear to weigh more than they do in reality.

Mrs. B. You do not consider how easily the fraud would be detected ; for on the scales being emptied they would not hang in equilibrium.

Emily. True ; I did not think of that circum- stance. But I do not understand why the longest arm of the lever should not be in equilibrium with the other ?

Caroline. It is because it is heavier than the short- est arm ; the centre of gravity, therefore, is no long- er supported.

Mrs. B. You are right ; the fulcrum is no longer in the centre of gravity ; but if we can contrive to

72 ON THE MECHANICAL POWERS.

make the fulcrum in its present situation become the centre of gravity, the scales will again balance each other ; for you recollect that the centre of gravity is that point about which every part of the body is in equilibrium.

Emily. It has just occurred to me how this may be accomplished ; put a great weight into the scale suspended to the shortest arm of the lever, and a smaller one into that suspended to the longest arm. Yes, 1 have discovered it — look, Mrs. B., the scale on the shortest arm will carry 21bs., and that on the longest arm only one, to restore the balance, (tig. 3.)

Mrs. B. You see, therefore, that it is not so im- practicable as you imagined to make a heavy body balance a light one ; and this is in fact the means by which you thought an imposition in the weight of goods might.be effected, as a weight often or twelve ounces might thus be made to balance a pound of goods. Let us now take off the scales, that we may consider the lever simply ; and in this state you see that the fulcrum is no longer the centre of gravi- ty ; but it is, and must ever be, the centre of motion, as it is the only point which remains at rest, while the other parts move about it.

Caroline. It now resembles the two opposite vanes of a windmill, and the fulcrum the point round which they move.

Mrs. B. In describing the motion of those vanes, you may recollect our observing that the farther a body is from the axis of motion the greater is its velocity.

Caroline. That I remember and understood per- fectly.

Mrs. B. You comprehend then, that the extremi- ty of the longest arm of a lever must move with greater velocity than that of the shortest arm ?

Emily. No doubt, because it is farthest from the centre of motion. And pray, Mrs. B., when my brothers play at see-saw, is not the plank on which they ride a kind of lever ?

UN THE MECHANICAL POWERS. 73

Mrs, B. Certainly ; the log of wood which sup- ports it from the ground is the fulcrum, and those who ride represent the power and the resistance at each end of the lever. And have you not observed that when those who ride are of equal weight, the plank must be supported in the middle to make the two arms equal ; whilst, if the persons diifer in weight, the plank must be drawn a little further over the prop, .>, make the arms unequal, and the lightest person, who represents the resistance, must be placed at the extremity of the longest arm.

Caroline. That is always the case when I ride on a plank with my youngest brother; 1 have observed also that the lightest person has the best ride, as he moves both further and quicker ; and I now understand that it is because he is more distant from the centre of motion.

Mrs. B. The greater velocity with which your little brother moves, renders his momentum equal to yours.

Caroline. Yes ; I have the most gravity, he the greatest velocity ; so that upon the whole our mo- mentums are equal. — But you said, Mrs. B., that the power should be greater than the resistance to put the machine in motion ; how then can the plank move if the momentums of the persons who ride are equal.

Mrs. B. Because each person at his descent touches the ground with his feet ; the reaction of which gives him an impulse which increases his ve- locity ; this spring is requisite to destroy the equili- brium of the power and the resistance, otherwise, the plank would not move. Did you ever observe that a lever describes the arc of a circle in its motion?

Emily. No ; it appears to me to rise and descend perpendicularly ; at least I always thought so.

Mrs. B. I believe I must make a sketch of you and your brother riding on a plank, in order to con- vince you of your error, (fig. 4. pi. IV.) You may now observe that a lever can move only round the 7

74 ON THE MECHANICAL POWERS.

fulcrum, since that is the centre of motion ; it would, be impossible for you to rise perpendicularly to the point A, or for your brother to descend in a straight line to the point B ; yon must in rising and he in de- scending describe arcs of your respective circles. This drawing shows you also how much superior his velocity must be to yours ; for if you could swing quite round, you would each complete your respec- tive circles in the same time.

Caroline. My brother's circle being much the largest, he must undoubtedly move the quickest.

Mrs. B. Now tell me, do you think that your brother could raise you as easily without the aid of a lever?

Caroline. Oh no, he could not lift me off the ground.

Mrs. B. Then 1 think you require no further proof of the power of a lever, since you see what it enables your brother to perform.

Caroline, I now understand what you meant by saying, that in mechanics motion was opposed to mat- ter, for it is my brother's velocity w|iich overcomes my weight.

Mrs. B. You may easily imagine what enormous weights may be raised by levers of this description, for the longer the acting part of the lever in compari- son to the resisting part, the greater is the effect pro- duced by it ; because the greater is the velocity of the power compared to that of the weight.

There are three different kinds of levers; in the first the fulcrum is between the power and the weight.

Caroline. This kind then comprehends the seve- ral levers you have described.

Mrs. B. Yes, when in levers of the first kind, the fulcrum is equally between the power and the weight, as in the balance the power must be greater than the weight, in order to move it ; for nothing can in this case be gained by velocity ; the two arms of the le- ver being equal, the velocity of their extremities must be so likewise. The balance is therefore of no

ON THE MECHANICAL POWERS. iO

assistance as a mechanical power, but it is extremely tiseful to estimate the respective weights of bodies.

But when (fig. 6.) the fulcrum F of a lever is not equally distant from the power and the weight, and that the power P acts at the extremity of the longest arm, it may be less than the weight W, its deficiency being compensated by its superior velocity ; as we observed in the sce-saw.

Emily. Then when we want to lift a great weight, we must fasten it to the shortest arm of a lever, and apply our strength to the longest arm ?

Mrs. B. If the case will admit of your putting the end of the lever under the weight, no fastening will be required ; as you will perceive by stirring the fire.

Emily. Oh yes! the poker is a lever of the first kind, the point where it rests against the bars of the grate, whilst I am stirring the fire, is the fulcrum ; the short arm, or resisting part of the lever, is employed in lifting the weight, which is the coals, and my hand is the power applied to the longest arm, or acting part of the lever.

Mrs. B. Let me hear, Caroline, whether you can equally well explain this instrument, which is compos- ed of two levers, united in one common fulcrum.

Caroline. A pair of scissars !

Mrs. B. You are surprised, but if you examine their construction, you will discover that it is the power of the lever that assists us in cutting with scis- sars.

Caroline. Yes ; I now perceive that the point at which the two levers are screwed together, is the fulcrum ; the handles, to which the power of the fin- gers is applied, are the extremities of the acting part of the levers, and the cutting part of the scissars are the resisting parts of the levers : therefore, the long- er the handles and the shorter the points of the scis- sars, the more easily yon cut with them.

Emily. That I have often observed, for when I cut paste-board or any hard substance, I always make

76 ox THE MECHANICAL POWERS.

use of that part of the scissars nearest the screw or rivet, and J now understand why it increases the pow- er of cutting; hut I confess that I never should have discovered scissars to have been double levers ; and pray are not snuffers levers of a similar description ?

Mrs. B. Yes, and most kinds of pincers ; the great power of which consists in the resisting part of the lever being very short in comparison of the acting part.

Caroline. And of what nature are the two other kinds of levers ?

Mrs. B. In levers of the second kind, the weight, instead of being at one end, is situated between the power and the fulcrum, (fig. 6.)

Caroline. The weight and the fulcrum have here changed places ; and what advantage is gained by this kind of lever ?

Mrs. B. In moving it, the velocity of the power must necessarily be greater than that of the weight, as it is more distant from the centre of the motion. Have you ever seen your brother move a snow-ball by means of a strong stick, when it became too heavy for him to move without assistance ?

Caroline. Oh yes ; and this was a lever of the se- cond order ; (fig. 7.) the end of the stick, which he thrusts under the ball, and which rests on the ground, becomes the fulcrum ; the ball is the weight to be moved, and the power his hands applied to the other end of the lever. In this instance there is an immense difference in the length of the arms of the lever ; for the weight is almost close to the fulcrum.

Mrs. B. And the advantage gained is proportional to this difference. Fishermen's boats are by levers of this description raised from the ground to be launched into the sea, by means of slippery pieces of board which are thrust under the keel. The most common example that we have of levers of the second kind is in the doors of our apartments.

Emily. The hinges represent the fulcrum, oiir

ON THE MECHANICAL POWERS. 77

hands the power applied to the other end of the lever ; but where is the weight to be moved ?

Mrs. B. The door is the weight, and it conse- quently occupies the whole of the space between the power and the fulcrum. Nutcrackers are double le- vers of this kind : the hinge is the fulcrum, the nut the resistance, and the hands the power.

In levers of the third kind (fig. 8.), the fulcrum is again at one of the extremities, the weight or resist- ance at the other, and it is now the power which is applied between the fulcrum and the resistance.

Emily. The fulcrum, the weight, and the power, then, each in their turn, occupy some part of the middle of the lever between its extremities. But in this third kind of lever, the weight being farther from the centre of motion than the power, the difficulty of raising it seems increased rather than diminished.

Mrs. B. That is very true ; a lever of this kind is therefore never used, unless absolutely necessary, as is the case in lifting up a ladder perpendicularly in order to place it against a wall ; the man who raises it cannot place his hands on the upper part of the ladder, the power, therefore, is necessarily placed much nearer the fulcrum than the weight.

Caroline, Yes, the hands are the power, the ground the fulcrum, and the upper part of the ladder the weight.

Mrs. B. Nature employs this kind of lever in the structure of the human frame. In lifting a weight with the hand, the lower part of the arm becomes a lever of the third kind ; the elbow is the fulcrum, the muscles of the fleshy part of the arm the power ; and as these are nearer to the elbow than the hand, it is necessary that their power should exceed the weight to be raised.

Emily. Is it not surprising that nature should have furnished us with such disadvantageous levers ?

Mrs. B, The disadvantage, in respect to power, is more than counterbalanced by the convenience re- sulting from this structure of the arm j and it is no 7*.

78 ON THE MECHANICAL POWERS,

doubt that which is best adapted to enable it to per- form its various functions.

We have dwelt so long on the lever, that we must reserve the examination of the other mechanical pow- ers to our next interview.

^^'

Fich 2.

PLATE V.

Awrv^x

CONVERSATION VL

ON THE MECHANICAL POWERS.

Of the Pulley.^Of the Wheel arid Axle.— Of the In- clined Plane. — Of the Wedge. — Of the Screw.

MRS. B. The pulley is the second mechanical power we 'are to examine. You both, I suppose, have seen a pulley ?

Caroline. Yes, frequently : it is a circular and flat piece of wood or metal, with a string which runs in a groove round it ; by means of which a weight may be pulled up ; thus pulleys are used for drawing up curtains.

Mrs. B. Yes ; but in that instance the pulleys are fixed, and do not increase the power to raise the weights, as you will perceive by this figure, (plate V. fig 1.) Observe that the fixed pulley is on the same principle as the lever of a pair of scales, in which the fulcrum F being in the centre of gravity, the power P and the weight W, are equally distant from it, and no advantage is gained.

Emily. Certainly ; if P represents the power em- ployed to raise" the weight W, the power must be greater than the weight in order to move it. But of what use then are pulleys in mechanics ?

Mrs. B. The next figure represents a pulley which is not fixed, (fig. 2.) and thus situated you will perceive that it affords us mechanical assistance. In order to raise the weight (W) one inch, P, the pow-

80 ON THE MECHANICAL POWERS.

er, must draw the strings B and C one inch each ; the whole string is therefore shortened two inches, while the weight is raised only one.

Emily. That I understand : if P drew the string but one inch, the weight would be raised only half an inch, because it would shorten the strings B and C half an inch each, and consequently the pulley, with the weight attached to it, can be raised only half an inch.

Caroline. I am ashamed of my stupidity ; but I confess that I do not understand this ; it appears to me that the weight would be raised as much as the string is shortened by the power.

Mrs. B. I will endeavour to explain it more clearly. I fasten this string to a chair and draw it towards me ; I have now shortened the string, by the act of drawing it, one yard.

Caroline. And the chair, as I supposed, has ad- vanced one yard.

Mrs. B. This exemplifies the nature of a single ^xed pulley only. Now unfasten the string, and re- place the chair where it stood before. In order to represent the moveable pulley, we must draw the chair forwards by putting the string round it ; one end of the string may be fastened to the leg of the table, and I shall draw the chair by the other end of the string. I have again shortened the string one yard ; how much has the chair advanced ?

Caroline. I now understand it ; the chair repre- sents the weight to which the moveable pulley is at- tached ; and it is very clear that the weight can be drawn only half the length you draw the string. I believe the circumstance that perplexed me was, that 1 did not observe the difference that results from the weight being attached to the pulley, instead of being fastened to the string, as is the case in the fixed pul- ley.

Emily. But I do not yet understand the advantage of pulleys ; they seem to me to increase rather than diminish the difficulty of raising weights, since you

ON THE MECHANICAL POWERS. 81

must draw the string double the length that you raise the weighty whilst with a single pulley, or without any pulley, the weight is raised as much as the string is shortened.

J^lrs. B. The advantage of a moveable pulley consists in dividing the difficulty ; we must draw, it is true, twice the length of the string, but then only half the strength is required that would be necessary to raise the weight without the assistance of a move- able pulley.

Emily. So that the difficulty is overcome in the same manner as it would be, by dividing the weight into two equal parts, and raising them successively.

Mrs. B. Exactly. You must observe, that with a moveable pulley the velocity of the power is double that of the weight, since the power P (fig. 2.) moves two inches whilst the weight W moves one inch ; therefore the power need not be more than half the weight to make their momentum^ equal.

Caroline. Pulleys act then on the same principle as the lever, the deficiency of strength of the power being compensated by its superior velocity.

Mrs. B. You will find, that all mechanical power is founded on the same principle.

Emily. But may it not be objected to pulleys, that a longer time is required to raise a weight by their aid than without it ; for what you gain in power you lose in time ?

Mrs. B. That, my dear, is the fundamental law in mechanics : it is the case with the lever, as well as the pulley ; and you will find it to be so with all the other mechanical powers.

Caroline. I do not see any advantage in the me- chanical powers then, if what we gain by them one way is lost another.

Mrs. B. Since we are not able to increase our natural strength, is not that science of wonderful utility, by means of which we may reduce the resist- ance or weight of any body to the level of our strength ? This the mechanical powers enable us to

82 ON THE MECHANICAL POWERS.

accomplish, by dividing the resistance of a body into parts which we can successively overcome. It is true, as you observe, that it requires a sacrifice of time to attain this end, but you must be sensible how very advantageously it is exchanged for power : the utmost exertion we can make adds but little to our natural strength, whilst we have a much more un- limited command of time. You can now understand, that the greater the number of pulleys connected by a string the more easily the weight is raised, as the difficulty is divided amongst the number of strings, or rather of parts into which the string is divided by the pulleys. Several pulleys thus connected, form what is called a system, or tackle of pulleys, (fig. 3.) You may have seen them suspended from cranes to raise goods into warehouses, and in ships to draw up the sails.

Emily. But since a fixed pulley affords us no me- chanical aid, why is it ever used ?

Mrs. B. Though it does not increase our power, it is frequently useful for altering its direction. A single pulley enables us to draw up a curtain by draw- ing dozvn the string connected with it ; and we should be much at u loss to accomplish this simple opera- tion without its assistance.

Caroline. There would certainly be some diffi- culty in ascending to the head of the curtain, in order to draw it up. Indeed, I now recollect having seen workmen raise small weights by this means, which seemed to answer a very useful purpose.

Mrs. B. In shipping, both the advantages of an increase of power and a change of direction, by means of pulleys, are united ; for the sails are raised up the masts by the sailors on deck, from the change of direction which the pulley effects, and the labour is facilitated by the mechanical power of a corbbina- tion of pulleys.

Emily. But the pulleys on ship-board do not ap- pear to me to be united in the manner you have shown us.

ON THE MECHANICAL POWERS. 83

Mrs. B. They are, I believe, generally connect- ed, as described in figure 4, both for nautical, and a variety of other purposes ; but in whatever manner pulleys are connected by a single string, the mecha- nical power is the same.

The third mechanical power is the wheel and axle. Let us suppose (plate VI. fig. 5.) tlie weight W to be a bucket of water in a well, which we raise by winding the rope, to which it is attached, round the axle ; if this be done without a wheel to turn the axle, no mechanical assistance is received. The axle without a wheel is as impotent as a single fixed pulley, or a lever, whose fulcrum is in the centre ; but add the wheel to the axle, and you will immediately find the bucket is raised with much less difficulty. The velocity of the circumference of the wheel is as much greater than that of the axle, as it is further from the centre of motion ; for the wheel describes a great circle in the same space of time that the axle describes a small one ; therefore the power is increas- ed in the same proportion as the circumference of the wheel is greater than that of the axle. If the velocity of the wheel is twelve times greater than that of the axle, a power nearly twelve times less than the weight of the bucket would be able to raise it.

Emily. The axle acts the part of the shorter arm of the lever, the wheel that of the longer arm.

Caroline. In raising water, there is commonly, I believe, instead of a wheel attached to the axle, on- ly a crooked handle, which answers the purpose of winding the rope round the axle, and thus raising the bucket.

Mrs. B. In this manner (fig. 6.) : now if you ob- serve the dotted circle which the handle describes in winding up the rope, you will perceive that the branch of the handle A, which is united to the axle, represents the spoke of a wheel, and answers the purpose of an entire wheel ; the other branch B af- fords no mechanical aid, merely serving as a handle to turn the wheel.

^4 ON TlTE MECHANICJAL POWERS.

Wheels are a very essential part of most ma- chines : they are employed in various ways ; but, when fixed to the axle, their mechanical power is always the same ; that is, as the circumference of the wheel exceeds that of the axle, so much will the energy of its power be increased.

Caroline. Then the larger the wheel the greater must be its effect.

Mrs. B. Certainly. If you have ever seen any considerable mills or manufactures, you must have admired the immense wheel, the revolution of which puts the whole of the machinery into motion ; and though so great an effect is produced by it, a horse or two has sufficient power to turn it ; sometimes a stream of water is used for that purpose, but of late years, a steam-engine has been found both the most powerful and the most convenient mode of turning the wheel.

Caroline. Do not the vanes of a windmill repre- sent a wheel, Mrs. B.

Mrs. B. Yes ; and in this instance we have the advantage of a gratuitous force, the wind, to turn the wheel. One of the great benefits resulting from the use of machinery is, that it gives us a sort of empire over the powers of nature, and enables us to make them perform the labour, which would otherwise fall to the lot of man. When a current of wind, a stream of water, or the expansive force of steam, performs our task, we have only to superintend and regulate their operations.

The fourth mechanical power is the inclined plane ; this is nothing more than a slope, or declivi- ty, frequently used to facilitate the drawing up of weights. It is not difficult to understand, that a weight may much more easily be drawn up a slope than it can be raised the same height perpendicu- larly. But in this, as well as the other mechanical powers, the facility is purchased by a loss of time (fig. 7 ) ; for the weight, instead of moving directly from A to C, must move from B to C, and as the

ON THE MECHANICAL POWERb. 86

length of the plane is to its height, so much is the resistance of the weight diminished.

Emily. Yes ; for the resistance, instead of being confined to the short line A C, is spread over the long line B C.

Mrs. B. The wedge, which is the next mechani- cal power, is composed of two inclined planes: (fig. 8.) you may have seen wood-cutters use it to cleave wood. The resistance consists in the cohesive at- traction of the wood, or any other body which the wedge is employed to separate ; and the advantage gained by this power is in the proportion of half its width to its length ; for while the wedge forces asun- der the coherent particles of the wood to A and B, it penetrates downwards as iar as C.

Emily. The wedge, then, is rather a compound than a distinct mechanical power, since it is compos- ed of two inclined planes.

Mrs. B. It is so. All cutting instruments are con- structed upon the principle of the inclined plane, or the wedge : those that have but one edge sloped, Uke the chisel, may be referred to the inclined plane : whilst the axe, the hatchet, and the knife (when used to split asunder) are used as wedges.

Caroline. But a knife cuts best when it is drawu across the substance it is to divide. We use it thus in cutting meat, we do not chop it to pieces.

Mrs. B. The reason of this is, that the edge of a knife is really a very fine saw, and therefore acts best when used Uke that instrument.

The screw, which is the last mechanical power, is more complicated than the others. You will see by this figure, (fig. 9.) that it is composed of two parts, the screw and the nut. The screw S is a cylinder, with a spiral protuberance coiled round it, called the thread ; the nut N is perforated to contain the screw, and the inside of the nut has a spiral groove, made to fit the spiral thread of the screw.

Caroline, It is just like this little box, the lid of

8

86 ON THE MECHANICAL POWERS'.

which screws on the box as you have described ; but what is this handle which projects from the nut ?

Mrs. B. It is a lever, which is attached to the nut, without which the screw is never used as a me- chanical power ; the nut with a lever L attached to it, is commonly called a winch. The power of the screw, complicated as it appears, is referable to one of the most simple of the mechanical powers ; which of them do yon think it is ?

Caroline. In appearance, it most resembles the wheel and axle.

Mrs. B. The lever, it is true, has the effect of a wheel, as it is the means by which you wind the nut round ; but the lever is not considered as composing a part of the screw, though it is true, that it is neces- sarily attached to it. But observe, that the lever, considered as a wheel, is not fastened to the axle or screw, but moves round it, and in so doing, the nut either rises or descends, according to the way in which you turn it.

Emily. The spiral thread of the screw resembles, I think, an inclined plane : it is a sort of slope, by means of wliich the nut ascends more easily than it would do if raised perpendicularly ; and it serves to support it when at rest.

Mrs. B. Very well ; if you cut a slip of paper in the form of an inclined plane, and wind it round your pencil, which will represent the cylinder, you will find that it makes a spiral line, corresponding to the spiral protuberance of the screw. (Fig. 10.)

Emily. Very true ; the nut then ascends an in- clined plane, but ascends it in a spiral, instead of a straight line ; the closer the thread of the screw, the more easy the ascent ; it is like having shallow in- stead of steep steps to ascend.

Mrs. B. Yes ; excepting that the nut takes no steps, it gradually winds up or down ; then observe, that the closer the threads of the screw, the greater the number of revolutions the winch must make : so

ON THE MECHANICAL POWERS. 87

that we return to the old principle — what is saved in power is lost in time.

Emily. Cannot the power of the screw be in- creased also, by lengthening the lever attached to the nut ?

Mrs. B. Certainly. The screw with the addition of the lever, forms a very powerful machine, employ- ed either for compression or to raise heavy weights. It is used by book-binders, to press the leaves of books together ; it is used also in cider and wine pres- ses, in coining, and for a variety of other purposes.

All machines are composed of one or more of these six mechanical powers we have examined : I have but one more remark to make to you, relative to them, which is, that friction in a considerable degree diminishes their force, allowance must therefore al- ways be made for it in the construction of machinc-

Caroline. By friction do you mean one part of the machine rubbing against another part contiguous to it?

Mrs. B. Yes ; friction is the resistance which bodies meet with in rubbing against each other ; there is no such thing as perfect smoothness or even- ness in nature : polished metals, though they wear that appearance more than any other bodies, are far from really possessing it ; and their inequalities may frequently be perceived through a good magnifying glass. When, therefore, the surfaces of the two bodies come into contact, the prominent parts of the one will often fall into the hollow parts of the other, and occasion more or less resistance to motion.

Caroline. But if a machine is made of polished metal, as a watch for instance, the friction must be very trifling ?

Mrs. B. In proportion as the surfaces of bodies are well polished, the friction is doubtless diminish- ed ; but it is always considerable, and it is usually computed to destroy one third of the power of a ma- chine. Oil or grease is used to lessen friction :

o8 ON THE MECHANICAL POWERS.

it acts as a polish by filling up the cavities of the rub- bing surfaces, and thus making them slide more easily over each other.

Caroline. Is it for this reason that wheels are greased, and the locks and hinges of doors oiled ?

Mrs. B. Yes ; in these instances the contact of the rubbing surfaces is so close, and the rubbing so continual, that notwithstanding their being polished and oiled, a considerable degree of friction is pro- duced.

There are two kinds of friction ; the one occasion- ed by the sliding of the flat surface of a body, the other by the rolling of a circular body : the friction resulting from the first is much the most considera- ble, for great force is required to enable the sliding body to overcome the resistance which the asperities of the surfices in contact oppose to its motion, and it must be either lifted over, or break through them ; whilst in the other kind of friction, the rough parts roll over each other with comparative facility ; hence it is, that wheels are often used for the sole purpose of diminisliing the resistance of friction.

Emily. This is one of the advantages of carriage- wheels ; is it not ?

Mrs. B. Yes ; and the larger the circumference of the wheel the more readily it can overcome any considerable obstacles, such as stones, or inequalities in the road. When, in descending a steep hill, we fasten one of the wheels, we decrease the velocity of the carriage, by increasing the friction.

Caroline. That is to say, by converting the roll- ing friction into the dragging friction. And when you had casters put to the legs of the table, in order to move it more easily, you changed the dragging in- to the rolling friction.

Mrs. B. There is another circumstance which we have already noticed, as diminishing the motiop of bodies, and which greatly affects the power of machines. This is the resistance of the medium in which a machine is worked. All fluids, whether

ON THE MECHANICAL POWERS. 89

of the nature of air or of water, are called me- diums ; and their resistance is proportioned to their density ; for the more matter a body contains, the greater the resistance it will oppose to the motion of another body striking against it.

Emily. It would then be much more difficult to work a machine under water than in the air ?

Mrs. B. Certainly, if a machine could be worked in vacuo, and without friction, it would be perfect ; but this is unattainable ; a considerable reduction of power must therefore be allowed for the resistance of the air.

We shall here conclude our observations on the mechanical powers. At our next meeting I shall en- deavour to give you an explanation of the motion of the heavenly bodies.

S*

CONVERSATION VI.

CAUSES OF THE EARTH'S ANNUAL MOTION.

Of the Planets, and their Motion — Of the Diurnal Mo' Hon of the Earth and Planets.

CAROLINE. I am come to you to-day quite elated with the spirit of opposition, Mrs. B. ; for I have discovered such a powerful objection to your theory of attraction, that I doubt whether even your conjuror Newton, with his magic wand of attraction, will be able to dispel it.

Mrs. B. Well, my dear, pray what is this weighty objection ?

Caroline. You say that bodies attract in propor- tion to the quantity of matter they contain, now we all know the sun to be much larger than the earth : why, therefore, does it not attract the earth ; you will not, I suppose, pretend to say that we are fall- ing towards the sun ?

Emily. FJowever plausible your objection ap- pears, Caroline, 1 think you place too much reliance upon it : when any one has given such convincing proofs of sagacity and wisdom as Sir Isaac Newton, when we find that his opinions are universally re- ceived and adopted, is it to be expected that any ob- jection we can advance should overturn them ?

Caroline. Yet I confess that I am not inclined to yield implicit faith even to opinions of the great

Fi^.l.

FLATS VI.

CAUSES, Arc. 91

Newton ; for what purpose are we endowed with reason, if we are denied the privilege of making use of it, by judging for ourselves ?

Mrs. B. It is reason itself which teaches us, that when we, novices in science, start objections to the- ories established by men of acknowledged wisdom, we should be diffident rather of our own than of their opinion. I am far from wishing to lay the least restraint on your questions; j^ou cannot be better convinced of the truth of a system, than by finding that it resists all your attacks, but I would advise you not to advance your objections with so much con- fidence, in order that the discovery of their fallacy may be attended with less mortification. In answer to that you have just proposed, I can only say, that the earth really is attracted by the sun.

Caroline. Take care at least that we are not con- sumed by him, Mrs. B.

Mrs. B. We are in no danger : but our magician Newton, as you are pleased to call him, cannot extricate himself from this difficulty without the aid of some cabilistical figures, which I must draw for liim.

Let us suppose the earth, at its creation, to have been projected forwards into universal space ; we know that if no obstacle impeded its course, it would proceed in the same direction, and with a uniform velocity for ever. In fig. 1. plate VI., A represents the earth, and S the sun. We shall suppose the earth to be arrived at the point in which it is repre- sented in the figure, having a velocity which would carry it on to B in the space of one month ; whilst the sun's attraction would bring it to C in the same space of time. Observe that the two fi^rces of pro- jection and attraction do not act in opposition, but perpendicularly, or at a right angle to each other. Can you tell me now, how the earth will move ?

Emily. I recollect your teaching us that a body acted upon by two forces perpendicular to each other would move in the diagonal of a parallelogram ; if,

92 CAUSES or the

therefore, I complete the parallelogram by drawing the lines CD, B D, the earth will move in the dia- gonal A D.

Mrs. B. A ball struck by two forces acting per- pendiciilarl}"^ to each other, it is true, moves in the diagonal of a parallelogram ; but you must observe that the force of attraction is continually acting upon our terrestrial ball, and producing an incessant devi- ation from its course in a right line, which converts it into that of a curved line ; every point of which may be considered as constituting the diagonal of an infinitely small parallelogram.

Let us detain the earth a moment at the point D, and consider how it will be affected by the combined action of the two forces in its new situation. It still retains its tendency to fly off in a straight line ; but a straight line would now carry it away to F, whilst the sun would attract it in the direction D S ; how then will it proceed ?

Emily. It will go on in a curve line in a direction between that of the two forces.

Mrs. B. In order to know exactly what course the earth will follow, draw another parallelogram similar to the first, in which the line D F describes the force of projection, and the line D S, that of attraction ; and you will find that the earth will proceed in the curve line D G.

Caroline. You must now allow me to draw a pa- rallelogram, Mrs. B. Let me consider in what direc- tion will the force of projection now impel the earth.

Mrs. B. First draw a line from the earth to the sun, representing the force of attraction ; then de- scribe the force of projection at a right angle to it.

Caroline. The earth will then move in the curve G I, of the parallelogram G li 1 K.

Mrs. B. You recollect that a body acted upon by two forces, moves through a diagonal in the same time that it would have moved through one of the sides of the parallelogram, were it acted upon by one force only. The earth has passed through the diago-

earth's annual motion. 93

nals of these three parallelograms in the space of three months, and has performed one quarter of a circle ; and on the same principle it will go on till it has completed the whole of the circle. It will then recommence a course, which it has pursued ever since it first issued from the hand of its Creator, and which there is every reason to suppose it will conti- nue to follow, as long as it remains in existence.

Emily. What a grand and beautiful effect, result- ing from so simple a cause !

Caroline. It affords an example, on a magnificent «cale, of the circular motion which you tau2;ht us in mechanics. The attraction of the sun is the centri- petal force, which confines the earth to a centre ; and the impulse of projection the centrifugal force, which impels the earth to quit the sun and fly off in a tangent.

Mrs. B. Exactly so. A simple mode of illustra- ting the effect of these combined forces on the earth, is to cut a slip of card in the form of a right angle, (fig. 2. plate VI.) to describe a small circle at the an- gular point representing the earth, and to fasten the extremity of one of the legs of the angle to a fixed point, which we shall consider as the sun. Thus si- tuated, the angle will represent both the centrifugal and centripetal forces ; and if you draw it round the fixed point, you will see how the direction of the cen- trifugal force varies, constantly forming a tangent to the circle in which the earth moves, as it is constant- ly at a right angle with the centripetal force.

Emily. The earth, then, gravitates towards the sun without the slightest danger either of approach- ing nearer or receding further from it. How admi- rably this is contrived! If the two forces which pro- duce this circular motion had not been so accurately adjusted, one would ultimately have prevailed over the other, and we should either have approached so near the sun as to have been burnt, or have receded so far from it as to have been frozen.

Mrs. B. What will you say, my dear, when I tell

94 CAUSES OF THE

you, that these two forces are not, in fact, so pro- portioned as to produce circular motion in the earth?

Caroline. You must explain to us, at least, in what manner we avoid the threatened destruction.

Mrs. B. Let us suppose that when the earth is at A, (fig. 3.) its projectile force should not have given it a velocity sufficient to counterbalance that of gra- vity, so as to enable these powers conjointly to carry it round the sun in a circle ; the earth, instead of de- scribing the line A C, as in the former figure, vvill approach nearer the sun in the line A B.

Caroline. Under these circumstances, I see not what is to prevent our approaching nearer and nearer the sun till we fall into it ; for its attraction increases as we advance towards it, and produces an accelerated velocity in the earth, which increases the danger.

Mrs. B. And there is yet another danger, of which you are not aware. Observe, that as the earth approaches the sun, the direction of its projec- tile force is no longer perpendicular to that of attrac- tion, but inclines more nearly to it. When the earth reaches that part of its orbit at B, the force of projec- tion would carry it to D, which brings it nearer the sun instead of bearing it away from it.

Emily. If, then, we are driven by one power and drawn by the other to this centre of destruction, how is it possible for us to escape ?

Mrs. B. A little patience, and you will find that we are not without resource. The earth continues approaching the sun with a uniformly increasing ac- celerated motion, till it reaches the point E ; in what direction will the projectile force now impel it?

Emily. In the direction E F. Here then the two forces act perpendicularly to each other, and the earth is situated just as it was in the preceding figure ; therefore, from this point, it should revolve round the sun in a circle.

Mrs. B. No, all the circumstances do not agree. In motion round a centre, you recollect that the cen- trifugal force increases with the velocity of the body.

earth's annual motion. 95

or, in other words, the quicker it moves the stronger is its tendency to fly ofl' in a right line. When the earth, therefore, arrives at E, its accelerated motion will have so far increased its velocity, and consequent- ly its .centrifugal force, that the latter will prevail over the force of attraction, and drag the earth away from the sun till it reaches G.

Caroline. It is thus, then, that we escape from the dangerous vicinity of the sun ; and in proportion as we recede from it, the force of its attraction, and, consequently, the velocity of the earth's motion, are diminished.

Mrs. B. Yes. From G the direction of projection is towards H, that of attraction towards S, and the earth proceeds between them with a uniformly re- tarded motion, till it has completed its revolution. Thus you see, that the earth travels round the sun, not in a circle, but an ellipsis, of which the sun occupies one of the foci; and that in its course the earth alternately approaches and recedes from it, without any danger of being either swallowed up, or of being entirely carried away from it.

Caroline. And 1 observe, that what I apprehended to be a dangerous irregularity, is the means by which the most perfect order and harmony are produced !

Emily. The earth travels, then, at a very unequal rate, its velocity being accelerated as it approaches the sun, and retarded as it recedes from it.

Mrs. B. It is mathematically demonstrable, that, in moving round a point towards which it is attracted, a body passes over equal areas in equal times. The whole of the space contained within the earth's orbit, is, in fig. 4, divided into a number of areas, or spaces, 1, 2, 3, 4, &.C. all of which are of equal dimensions, though of very different forms ; some of them, you see, are long and narrow, others broad and short ; but they each of them contain an equal quantity of space. An imaginary line drawn from the centre of the earth to that of the sun, and keeping pace with the earth in its revolution, passes over equal areas in equal

96 CAUSES OF THE

times ; that is to say, if it is a month going from A to B, it will be a month going from B to C, and another from C to E, and so on.

Caroline. What long journeys the earth has to perform in the course of a month, in one part of her orbit, and how short they are in the other part!

Mrs. B. The inequality is not so considerable as appears in this figure ; for the earth's orbit is not so eccentric as it is there described ; and, in reality, differs but little from a circle : that part of the earth's orbit nearest the sun is called its perihelion, that part most distant from the sun its aphelion; and the earth is above three millions of miles nearer the sun at its perihelion than at its aphelion.

Emily. I think I can trace a consequence from these different situations of the earth ; is it not the cause of summer and winter?

Mrs. B. On the contrary ; during the height of summer, the earth is in that part of its orbit which is most distant from the sun, and it is during the severity of winter that it approaches nearest to it.

Emily. That is very extraordinary; and how then do you account for the heat being greatest when we are most distant from the sun ?

Mrs. B. The difference of the earth's distance from the sun in summer and winter, when compared with its total distance from the sun, is but inconsidera- ble. The earth, it is true, is above three millions of miles nearer the sun in winter than in summer ; but that distance, however great it at first appears, sinks into insignificance in comparison of 95 millions of miles, which is our mean distance from the sun. The change of temperature, arising from this difference, would scarcely be sensible ; were it not completely overpowered by other causes which produce the va- riations of the seasons ; but these I shall defer explain- ing, till we have made some further observations on the heavenly bodies.

Caroline. And should not the sun appear smaller in summer, when it is so much further from us ?

earth's annual motion. 97

Mrs. B. It actually does, when accurately mea- sured ; but the apparent difference in size is, I be- lieve, not perceptible to the naked eye.

Emily. Then, since the earth moves with greatest velocity in that part of its orbit nearest the sun, it must have completed its journey through one half of its orbit in a shorter time than the other half?

Mrs. B. Yes, it is about seven days longer per- forming the summer half of its orbit than the winter half.

The revolution of all the planets round the sun is the result of the same causes, and is performed in the same manner as that of the earth.

Caroline. Pray what are the planets ?

Mrs. B. They are those celestial bodies, which -revolve like our earth about the sun ; they are sup- posed to resemble the earth also in many other re- spects ; and we are led by analogy to suppose them to be inhabited worlds.

Caroline. I have heard so ; but do you not think such an opinion too great u stretch of the imagina- tion ?

Mrs. B. Some of the planets are proved to be larger than the earth ; it is only their immense dis- tance from us, which renders their apparent dimen- sions so small. Now, if we consider them as enor- mous globes, instead of small twinkling spots, we shall be led to suppose, that the Almighty would not have created them merely for the purpose of giving us a little light in the night, as it was formerly ima- gined, and we should find it more consistent with our ideas of the Divine wisdom and beneficence, to suppose that these celestial bodies should be created for the habitation of beings, who are, like us, bless- ed by His providence. Both in a moral as well as a physical point of view, it appears to me more ra- tional to consider the planets as worlds revolving round the sun ; and the fixed stars as other suns, each of them attended by their respective system of planets, to which they impart theif influence ? We 9

98 CAUSES OF THE

have brought our telescopes to such a degree of per- fection, that from the appearances which the moon exhibits when seen through them, we have very good reason to conclude, that it is a habitable globe, for though it is true, that we cannot discern its towns and people, we can plainly perceive its mountains and valleys ; and some astronomers have gone so far as to imagine they discovered volcanos.

Emily. If the fixed stars are suns, with planets revolving round them, why should we not see those planets as well as their suns ?

Mrs. B. In the first place, we conclude that the planets of other systems, (like those of our own,) are much smaller than the suns which give them light ; therefore at so great a distance as to make the suns appear like fixed stars, the planets would be quite invisible. Secondly, the light of the planets being only reflected light, is much more feeble than that of the fixed stars. There is exactly the same difference as between the light of the sun and that of the moon; the first being a fixed star, the second a planet.

Emily. But if the planets are worlds like our earth, they are dark bodies ; and instead of shining by night, we should see them only by daylight. — And why do we not see the fixed stars also by day-

light?"

Mrs. B. Both for the same reason ; — their light is so faint, compared to that of our sun reflected by the atmosphere, that it is entirely eff'aced by it : the light emitted by the fixed stars may probably be as strong as that of our sun, at an equal distance ; but being so much more remote, it is difl'used over a greater space, and is consequently proportionally ■weakened.

Caroline. True ; I can see much better by the light of a candle that is near me, than by that of one at a great distance. But I do not understand what makes the planets shine ?

Mrs. B. What is it that makes the steel buttons on your brother's coat shine ?

earth's annual M0TI0I7. 99

Caroline. The sun. But if it was the sun which made the planets shine, we should see them in the day-time, when the sun shone upon them ; or if the fjiintness of their light prevented our seeing them in the day, we should not see them at all, for the sun cannot shine upon them in the night.

Mrs. B. There you are in error. But in order to explain this to you, I must first make you acquainted with the various motions of the planets.

You know, that according to the laws of attraction, the planets belonging to our system all gravitate to- wards the sun : and that this force combined with that of projection, will occasion their revolution round the sun, in orbits more or less elliptical, ac- cording to the proportion which these two forces bear to each other.

But the planets have also another motion : they revolve upon their axes. The axis of a planet is an imaginary line which passes through its centre, and on which it turns ; and it is this motion which pro- duces day and night. With that side of the planet facing the sun, it is day ; and with the opposite side, which remains in darkness, it is night. Our earth, which we consider as a planet, is 24 hours in per- forming one revolution on its axis : in that period of time, therefore, we have a day and a niglit ; hence this revolution is called the earth's diurnal or daily motion ; and it is this revolution of the earth from west to east which produces an apparent motion of the sun, moon and stars in a contrary direction.

Let us now suppose ourselves to be beings, inde- pendent of any planet, travelling in the skies, and looking upon the earth in the same point of view as upon the other planets.

Caroline. It is not flattering to us, its inhabitants, to see it make so insignificant an appearance.

Mrs. B. To those who are accustomed to contem- plate it in this light, it never appears more glorious. We are taught by science to distrust appearances ; and instead of considering the planets as little stars,

100 CAUSES OF THE

we look np6n them either as hrilliant suns or habitable worlds, and we consider the whole together as form- ing one vast and magnificent system, worthy of the Divine hand b}' which it was created.

Emily. I can scarcely conceive the idea of this immensity of creation ;Mt seems too sublime for our imagination : — and to think that the goodness of Pro- vidence extends over millions of worlds throughout a boundless universe — Ah ! Mrs. B., it is we only who become trifling and insignificant beings in so magni- iScent a creation !

Mrs. B. This idea should teach us humility, but without producing despondency. The same Almighty })and which guides these countless worlds in their un- deviating course, conducts with equal perfection the ])lood as it circulates through the veins of a fly, and opens the eye of the insect to behold His wonders. Notwithstanding this immense scale of creation, therefore, we need not fear to be disregarded or for- gotten.

But to return to our station in the skies. We were, if you recollect, viewing the earth at a great distance, in appearance a little star, one side illumin- ed by the sun, the other in obscurity. But would you believe it, Caroline, many of the inhabitants of this little star imagine that when that part which they inhabit is turned from the sun, darkness prevails throughout the universe, merely because it is night with them ; whilst, in reality, the sun never ceases to shine upon every planet. When, therefore, these little igno- rant beings look around them during their night, and behold all the stars shining, they cannot ima- gine why the planets, which are dark bodies, should shine, concluding, that since the sun docs not illu- mine themselves, the whole universe must be in darkness.

Caroline, I confess that I was one of these igno- rant people ; but I am now very sensible of the ab- surdity of such an idea. To the inhabitants of the other planets, then, we must appear as a little star ?

earth's annual motion. 101

Mrs. B. Yes, to those which rerolve round our sun ; for since those which may belong to other systems, (and whose existence is only hypothetical,) are invisible to us, it is probable, that we also are invisible to them.

Emily. But they may see our sun as we do theirs, ip appearance a fixed star ?

Mrs. B. No doubt ; if the beings who inhabit those planets are endowed with senses similar to ours. By the same rule, we must appear as a moon to the inhabitants of our moon ; but on a larger scale, as the surface of the earth is about thirteen times as large as that of the moon.

Emily. The moon, Mrs. B., appears to move in a different direction, and in a different manner from the stars ?

Mrs. B. I shall defer the explanation of the mo- tion of the moon, till our next interview, as it would prolong our present lesson too much.

9*

CONVERSATION VIL

ON THE PLANETS.

Of the Satellites or Moons. — Gravity diminishes as the Square of the Distance. — Of the Solar System. — Of Comets — Constellations, Signs of the Zodiac. — Of Copernicus, Newton, 4'C.

MRS. B. The planets are distinguished into pri- mary and secondary. Those which revolve immedi- ately about the sun are called primary. Many of these are attended in their course by smaller planets, which revolve around them : these are called secondary planets, satellites, or moons. Such is our moon, which accompanies the earth, and is carried with it round the sun.

Emily. How then can you reconcile the motion of the secondary planets to the laws of gravitation ; for the sun is much larger than any of the primary planets ; and is not the power of gravity proportion- al to the quantity of matter ?

Caroline. Perhaps the sun, though much larger, may be less dense than the planets. Fire you know is very light, and it may contain but little matter, though of great magnitude.

Mrs. B. We do not knOw of what kind of matter the sun is made ; but we may be certain, that since it is the general centre of attraction of our system of planets, it must be the body which contains the great- est quantity of matter in that system.

Yoa must recollect, that the force of attraction i*

ON THE PLANETS. 10^

not only proportional to the quantity of matter, but to the degree of proximity of the attractive body : this power is weakened by being diflfused, and diminishes as the squares of the distances increase. The square is the product of a number multiplied by itself; so that a planet situated at twice the distance at which we are from the sun would gravitate four times less than we do ; for the product of two multiplied by it- self is four.

Caroline. Then the more distant planets move slower in their orbits ; for their projectile force must be proportioned to that of attraction ? But I do not see how this accounts for the motion of the secondary round the primary planets, in preference to the sun ?

Emily. Is it not because the vicinity of the pri- mary planets renders their attraction stronger than that of the sun ?

Mrs. B. Exactly so. But since the attraction be- tween bodies is mutual, the primary planets are also attracted by the satellites, which revolve round them. The moon attracts the earth, as well as the earth the moon ; but as the latter is the smaller body, her at- traction is proportionally less ; therefore neither the earth revolves round the moon, nor the moon round the earth ; but they both revolve round a point, which is their common centre of gravity, and which is as much nearer the earth than the moon, as the gra- vity of the former exceeds that of the latter.

Emily. Yes, I recollect your saying, that if two bodies were fastened together by a wire or bar, their common centre of gravity would be in the middle of the bar, provided the bodies were of equal weight ; and if they differed in weight, it would be nearer the larger body. If then the earth and moon had no pro- jectile force which prevented their mutual attraction from bringing them together, they would meet at their common centre of gravity.

Caroline. The earth then has a great variety of motions : it revolves round the sun, upon its axis, and round the point towards which the moon attracts it.

104 ON THE PLANETS.

Mrs. B. Just so; and this is the case with every planet which is attended by satelhtes. The compli- cated effect of this variety of motions, produces cer- tain irregularities, which, however, it is not necessa- ry to notice at present.

The planets act on the sun in the same manner as they are themselves acted on by their satellites ; for attraction, you must remember, is always mutual ; but the gravity 0/ the planets (even when taken collec- tively) is so trifling compared with that of the sun, that they do not cause the latter to move so much as one half of his diameter. The planets do not, there- fore, revolve round the centre of the sun, but round a point at a small distance from its centre, about which the sun also revolves.

Emily. I thought the sun had no motion?

Mrs. B. You were mistaken ; for, besides that which I have just mentioned, which is indeed very inconsiderable, he revolves on his axis ; this motion is ascertained by observing certain spots which disap- pear, and re-appear regularly at stated times.

Caroline. A planet has frequently been pointed out to me in the heavens ; but I could not perceive that its motion differed from that of the fixed stars, which only appear to move.

Mrs. B. The great distance of the planets renders their motion apparently so slow, that the eye is not sensible of their progress in their orbit, unless we watch them for some considerable length of time : in different seasons they appear in different parts of the heavens. The most accurate idea 1 can give you of the situation and motion of the planets, will be by the examination of this diagram, (Plate VII. fig. 1.) repre- senting the solar system, in which you will find every planet with its orbit delineated.

Emily. But the orbits here are all circular, and you said that they were elliptical. The planets ap- pear, too, to be moving round the centre of the sun ; whilst you told us, that they moved round a point at a little distance from thence.

PLATE Vn.

Fi^.

Ft^. 2.

Mars yemis Forth

^'-y "o o o

Moon

Hertchel

n

t)N THE PLACETS. 105

Mrs. B. The orbits of the planets nre so nearly circular, and the common centre of gravity of the so- lar system so near the centre of the sun, that these deviations are scarcely worth observing. The di- mensions of the planets, in their true proportions, you will find delineated in fig. 2.

Mercury is the planet nearest the sun ; his orbit is consequently contained within ours ; but his vicinity to the sun, occasions his being nearly lost in the bril- liancy of his rays ; and when we see the sun, he is so dazzling, that very accurate observations cannot be made upon Mercury. He performs his revolution round the sun in about 87 days, which is consequent- ly the length of his year. The time of his ro- tation on his axis is not known ; his distance from the sun is computed to be 37 millions of miles, and his diameter 3180 miles. The heat of this planet is so great, that water cannot exist there, but in a state of vapour, and metals would be liquified.

Caroli7ie. Oh, what a dreadful climate!

Mrs. B. Though we could not live there, it may be perfectly adapted to other beings destined to inha- bit it.

Venus, the next in the order of planets, is 68 mil- lions of miles from the sun : she revolves about her axis in 23 hours and 21 minutes, and goes round the sun in 244 days 17 hours. The orbit of Venus is also within ours ; during one half of her course in it, we see her before sunrise, and she is called the morning star ; in the other part of her orbit, she rises later than the sun.

Caroline. In that case, we cannot see her, for she must rise in the day time ?

Mrs. B. True ; but when she rises later than the sun, she also sets later ; so that we perceive her ap- proaching the horizon after sunset : she is then call- ed Hesperus, or the evening star. Do you recollect those beautiful lines of Milton :

Now came still evening on, and twilight grav Had in her sober livery all things clad;.

f

106 ON THE PLANETS.

Silence accompanied ; for beast and bird, They to their grassy couch, these to their nests Were slunk, all but the wakeful nightingale ; She all night long her amorous descant sung; Silence was pleas'd : now glowed the firmament With living saphirs: Hesperus, that led The starry host, rode brightest, till the m6on Rising in clouded majesty, at length Apparent queen unveil'd her peerless light, And o'er the dark her silver mantle threw.

The planet next to Venus is the Earth, of which we shall soon speak at full length. At present I shall only observe that we are 95 millions of miles distant from the sun, that we perform our annual revolution in 365 days 5 hours and 49 minutes ; and are attend- ed in our course by a single moon.

Next follows Mars. He can never come between us and the sun, like I\rercury and Venus ; his motion is, however, very perceptible, as he may be traced to different situations in the heavens ; his distance from the sun is 144 millions of miles ; he turns rounds his axis in 24 hours and 39 minutes ; and he performs his annual revolution, in about 687 of our days : his diameter is 4120 miles.. Then follow four very small planets, Juno, Ceres, Pallas, and Vesta, which have been recently discovered, but whose di- mensions and distances from the sun have not been very accurately ascertained.

Jupiter is next in order : this is the largest of all the planets. He is about 490 millions of miles from the sun, and completes his annual period in nearly twelve of our years. He turns round his axis in about ten hours. He is above 1200 times as big as our earth ; his diameter being 86,000 miles. The respective proportions of the planets cannot, there- fore, you see, be conveniently delineated in a dia- gram. He is attended by four moons.

The next planet is Saturn, whose distance from the sun is about 900 millions of miles ; his diurnal rota- tion is performed in 10 hours and a quarter : — his an- nual revolution in nearly 30 of our years. His dia-

ON THE PLANETS. 107

meter is 79,000 miles. This planet is surrounded hy a luminous ring, the nature of which, astronomers are much at a loss to conjecture ; he has seven moons. Lastly, we observe the Georgium Sidus, disco- vered by Dr. Herschel, and which is attended by six moons.

Caroline. How charming; it must be in the distant planets, to see several moons shining at the eame time ; I think I should like to be an inhabitant of Ju- piter or Saturn.

Mrs. B. Not long, I believe. Consider what ex- treme cold must prevail in a planet, situated as Saturn is, at nearly ten times the distance at which we are from the sun. Then his numerous moons are far from making so splendid an appearance as ours ; for they can reflect only the light which they receive from the sun ; and both light and heat decrease in the same ratio or proportion to the distances as gravity. Caa you tell me now how much more light we enjoy than Saturn ?

Caroline. The square of ten is a hundred ; there- fore, Saturn has a hundred times less — or to answer your question exactly, we have a hundred times more light and heat than Saturn — this certainly does not increase my wish to become one of tbe poor wretches who inhabit that planet.

Mrs. B. May not the inhabitants of Mercury, with equal plausibility, pity us, for the insupportable coldness of our situation ; and those of Jupiter and Saturn for our intolerable heat ? The x'Mmighty Pow- er which created these planets, and placed them in their several orbits, has no doubt peopled them with beings whose bodies are adapted to the various tem- peratures and elements in which they are situated. If we judge from the analogy of our own earth, or from that of the great and universal beneficence of Providence, we must conclude this to be the case.

Caroline. Are not comets also supposed to be planets ?

Mrs. B. Yes, they are ; for by the re-appear-

108 ON THE PLANETS.

ance of some of them, at stated times, they are known to revolve round the sun, but in orbits so ex- tremely eccentric, that they disappear for a great number of years. If they are inhabited, it must be by a species of beings very different, not only from the inhabitants of this, but from those of any of the other planets, as they must experience the greatest vicissitudes of heat and cold ; one part of their orbit being so near the sun, that their heat, when there, is computed to be greater than that of red-hot iron ; in this part of its orbit, the comet emits a luminous vapour, called the tail, which it gradually loses as it recedes from the sun ; and the comet itself totally disappears from our sight, in the more distant parts of its orbit, which extends considerably beyond that of the furthest planet.

The number of comets belonging to our system cannot be ascertained, as some of them are whole centuries before they make their re-appearance. The number that are known by their regular re-ap- pearance is only three.

Emily. Pray, Mrs. B., what are the constellations?

Mrs. B. They are the fixed stars, which the an- cients, in order to recognise them, formed into groups, and gave the names of the figures which you find delineated on the celestial globe. In order to show their proper situations in the heavens, they should be painted on the internal surface of a hollow sphere, from the centre of which you should view them ; you would then behold them, as they appear to be situated in the heavens. The twelve constel- lations, called the signs of the zodiac, are those which are so situated, that the earth in its annual revolution passes directly between them and the sun. Their names are Aries, Taurus, Gemini, Cancer, Leo, Vir- go, Libra, Scorpio, Sagittarius, Capricornus, Aquari- us, Pisces ; the whole occupj'ing a complete circle, or broad belt, in the heavens, called the zodiac. (Plate VIIl. fig. 1.) Hence a right line drawn from the earth, and passing through the sun, would reach

TLATE vm.

ON THE PLANETS. 109

one of these constellations, and the sun is said to be in that constellation at which the line terminates: thus, when the earth is at A, the sun would appear to be in the constellation or sign Aries ; when the earth is at B, the sun would appear in Cancer ; when the earth was at C, the sun would be in Libra ; and when the earth was at D, the sun would be in Capricorn. This circle, in which the sun thus appears to move, and which passes through the middle of the zodiac, is called the ecliptic.

Caroline. But many of the stars in these constel- lations appear beyond the zodiac.

Mrs. B. We have no means of ascertaining the distance of the fixed stars. When, therefore, they are said to be in the zodiac, it is merely implied, that they are situated in that direction, and that they shine upon us through that portion of the heavens which we call the zodiac.

Emily. But are not those large bright stars, which are called stars of the first magnitude, nearei* to us than those small ones which we can scarcely discern?

Mrs. B. It may be so ; or the difference of hze and brilliancy of the stars may proceed from their difference of dimensions ; this is a point which as- tronomers are not enabled to determine. Consider- ing them as suns, I see no reason why different suns should not vary in dimensions, as well as the planets belonging to them.

Emily. What a wonderful and beautiful system this is, and how astonishing to think that every fixed star ma/ probably be attended by a similar train of planets I

Caroline. You will accuse me of being very in- credulous, but I cannot help still entertaining some doubts, and fearing that there is more beauty than truth in this system. It certainly may be so ; but there does not appear to me to be sufficient evidence to prove it. It seems so plain and obvious that the earth is motionless, and that the sun and stars revolve round it ; — your solar system, you must allow, is di- rectly in opposition to the evidence of our senses. 10

110 ON THE PLANETS.

Mrs. J5. Our senses so often mislead us, that we should not place implicit reliance upon them.

Caroline. On what then can we rely, for do we not receive all our ideas through the medium of our senses ?

Mrs. B. It is true, that they are our primary source of knowledge ; but the mind has the power of reflecting, judging, and deciding upon the ideas received by the organs of sense. This faculty, which we call reason, has frequently proved to us, that our senses are liable to err. If you have ever sailed on the water, with a very steady breeze, you must have seen the houses, trees and every object move while you were sailing.

Caroline. I remember thinking so, when I was very young : but I now know that their motion is only apparent. It is true that my reason, in this case, corrects the error of my sight.

Mrs. B. It teaclies you, that the apparent motion of the objects on shore, proceeds from your being yourself moving, and that you are not sensible of yqpr own motion, because you meet with no resist- ance. It is only when some obstacle impedes our motion, that we are conscious of moving; and if you were to close your eyes when you were sailing on calm water, with a steady wind, you woujd not per- ceive that you moved, for you could not feel it, and you could see it only by observing the change of place of the objects on shore. So it is with the mo- tion of the earth ; every thing on its surface, and the air that surrounds it, accompanies it in its revolution ; it meets with no resistance ; therefore, like the crew of a vessel sailing with a fair wind, in a calm sea, we arc insensible of our motion.

Caroline. But the principal reason why the crew of a vessel in a calm sea do not perceive the motion, is, because they move exceedingly slowly ; while the earth, you say, revolves with great velocit3^

Mrs^ B. It is not because they move slowly, but because they move steadily, and meet with no ir-

ON THE I'LAXETS. HI

regular resistances, that the crew of a vessel do no! perceive their motion ; for they would be equally insensible to it, with the strongest wind, provided it were steady, that they sailed with it, and that it did not agitate the water ; but this last condition, you know, is not possible, for the wind will always pro- duce waves, which offer more or less resistance to the vessel, and then the motion becomes sensible because it is unequal.

Caroline. But, granting this, the crew of a vessel have a proof of their motion, though insensible, which the inhabitants of the earth cannot have — the apparent motion of the objects on shore.

Mrs. B. Have we not a similar proof of the earth's motion, in the apparent motion of the sun and stars. Imagine the earth to be sailing round its axis, and successively passing by every star, which, like the objects on land, we suppose to be moving instead of ourselves. 1 have heard it observed by an aerial traveller in a balloon, that the earth appears, to sink beneath the balloon, instead of the balloon rising above the earth.

It is a law which we discover throughout nature, and worthy of its great Author, that all its purposes are accomplished by the most simple means ; and what reason have we to suppose this law infringed, in or- der that we may remain at rest, while the sun and stars move round us ; their regular motions, which are explained by the laws of attraction on the first supposition, would be unintelligible on the last, and the order and harmony of the universe be destroyed. Think what an immense circuit the sun and stars would make daily, were their apparent motions real. We know many of them to be bodies more consider- able than our earth ; for our eyes vainly endeavour to persuade us, that they are little brilliants spark- ling in the heavens, while science teaches us that they are immense spheres, whose apparent dimen- sions are diminished by distance. Why then should these enormous globes daily traverse -such a prodi-

112 ON THE PLANETS.

gions space, merely to prevent the necessity of our earth's revolving on its axis ?

Caroline. I think I must now be convinced. But 3'ou vpill, I hope, allow me a little time to familiarize m^'^self to an idea so diirerent from that which 1 have been accustomed to entertain. And pray, at what rate do we move ?

Mrs. B. The motion produced by the revolution of the earth on its axis, is about eleven miles a mi- nute, to an inhabitant of London.

Emily. But docs not every part of the earth move with the same velocity ?

Mrs. B. A moment's reflection would convince you of the contrary ; a person at the equator must move quicker than one situated near the poles, since they both perform a revolution in 24 hours.

Emily. True, the equator is farthest from the axis of motion. But in the earth's revolution round the sun, every part must move with equal velocity ?

Mrs. B. Yes, about a thousand miles a minute.

Caroline. How astonishing! — and that it should be possible for us to be insensible of such a rapid mo- tion. You would not tell me this sooner, Mrs. B., for fear of increasing my incredulity.

Before the time of Newton, was not the earth sup- posed to be in the centre of the system, and the sun, moon, and stars to revolve round it ?

Mrs. B. This was the system of Ptolemy in an- cient times ; but as long ago as the beginning of the sixteenth century it was discarded, and the solar sys- tem, such as I have shown you, was established by the celebrated astronomer Copernicus, and is hence called the Copernican system. But the theory of gravitation, the source from which this beautiful and harmonious arrangement flows, we owe to the pow- erful genius of Newton, who lived at a much later period.

Emily. It appears, indeed, fiir less diflicult to trace by observation the motion of the planets, than to di- vine by what power they are impelled and guided. I

ON THE PLANETS. 113

wonder how the idea of gravitation could first have occurred to Sir Isaac Newton ?

Mrs. B. It is said to have been occasioned by a circumstance from which one should little have ex- pected so grand a theory to have arisen. During the prevalence of the plague in the year 1665, New- ton retired into the country to avoid the contagion : when sitting one day in his orchard, he observed an apple fall from a tree, and was led to consider what could be the cause which brought it to the ground.

Caroline. If I dared to confess it, Mrs. B., I should say that such an inquiry indicated rather a deficiency than a superiority of intellect. I do not understand how any one can wonder at what is so natural and so common.

Mrs. B. It is the mark of superior genius to find matter for wonder, observation, and research, in cir- cumstances which, to the ordinary mind, appear tri- vial, because they are common, and with which they are satisfied, because they are natural, without re- flecting that nature is our grand field of observation, that within it is contained our whole store of know- ledge ; in a word, that to study the works of nature, is to learn to appreciate and admire the wisdom of God. Thus, it was the simple circumstance of the fall of an apple, which led to the discovery of the laws upon whigh the Copernican system is founded ; and whatever credit this system had obtained before, it now rests upon a basis from which, it cannot be shaken.

Emily. This was a most fortunate apple, and more worthy to be commemorated than all those that have been sung by the poets. The apple of discord for which the goddesses contended ; the golden apples by which Atalanta won the race; nay, even the applQ which William Tell shot from the head of his son cannot be compared to this !

10*

CONVERSATION Vllf.

ON THE EARTH.

Of the Terrestrial Globe.— Of the Figure of the Earth, — Of the Pendulum. — Of the Variation of the Sea- sons, and of the Length of Days and JVights. — Of the causes of the Heat of Summer. — Of Solar, Side- rial, and Equal or Mean Time,

MRS. B. As the earth is the planet in wliich we are the most particuhirly interested, it is my intention. this mornina;, to explain to you the effects resulting li'om its annual and diurnal njotions ; but for this pur- pose it will bo necessary to make you acquainted with the terrestrial globe : you have not either of you, I conclude, learnt the use of the g;h:)bes ?

Carnline. No ; I once indeed loarnt by heart the names of the lines marked on the globe, but as 1 was informed they were only imaginary divisions, they did not appear to me worthy of much attention, and were