^ 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, 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 soon fori^otten. Mrs. B. You supposed, then, that astronomers had been at the trouble of inventing a number uf lines to little purpose. It will be impossible for me to ex- plain to you the particular effects of the earth's mo- tion, without your having acquired a knowledge of these lines : in Plate Vlll. fig. 2. you will find them ail delineated : and you mu'^t learn them perfectly if you wish to make any proficiency in astronomy. Caroline. I was taught them at so early an age that I could not understand their meaning ; and I have often heard you say that the only use of words was to convey ideas. ON THE EARTH. lib Mrs. B. The names of these lines would have conveyed ideas of the tigures they were designed to express, though the use of these tigures might at that time have been too difficult for you to understand. Childhood is the season when impression*^ on the me- mory are most strongly and most easily made : it is the period at which a large stock of ideas should be treasured up, the application of which we may learn when the understanding is more developed. It is, I think, a very mistaken notion that children should be taught such things only as they can perfectly under- stand. Had you been early made acquainted with the terms which relate to figure and motion, how much it would have facilitated your progress in natural philo- sophy. I have been obliged to confine myself to the most common and familiar expressions, in explaining the laws of nature, though I am convinced that ap- propriate and scientific terms would have conveyed more precise and accurate ideas ; but 1 was afraid of not being understood. Emily. You may depend upon our learning the names of these lines thoroughly, Mrs. B. ; but, before we commit them to memory, will you have the good- ness to explain them to us ? Mrs. B. Most willingly. This globe, or sphere, represents the earth ; the line which passes through its centre, and on which it turns, is called its axis : and the two extremities of the axis, A and B, are the poles, distinguished by the names of the north and the south pole. The circle C D, which divides the globe into two equal parts between the poles, is called the equator, or equinoctial line ; that part of the globe to the north of the equator is the northern hemisphere ; that part to the south of the equator, the southern Iiemisphere. The small circle E F, which surrounds the north pole, is called the arctic circle ; that G H, which surrounds the south pole, the antarctic circle. There are two intermediate circles between, the polar circles and the equator; that to the north, I K, called the tropic of Cancer ; that to the souths 110 OJJ THE EARTfir. L M, called the tropic of Capricorn. Lastly, thi circle, L K, which divides the globe into two equal parts, crossing the equator and extending northward as far as the tropic of Cancer, and southward as far as the tropic of Capricorn, is called the ecliptic. The delineation of the ecliptic on the terrestrial globe is not without danger of conveying false ideas ; for the ecliptic (as I have before said) is an imagi- nary circle in the heavens passing through the mid- dle of the zodiac, and situated in the plane of the earth's orbit. Caroline. I do not understand the meaning of the plane of the earth's orbit. Mrs. D. A plane, or plain, is an even level sur- face. Let us suppose a smooth thin solid plain cut- ting the sun through the centre, extending out as far as the tixed stars, and terminating in a circle which passes through the middle of the zodiac ; in this plane the earth would move in its revolution round the sun ; it is therefore called the plane of the earth's orbit, and the circle in which this plane cuts the signs of the zodiac is the ecliptic. Let the fig. 1. Plate IX. represent such a plane, S the sun, E the earth with its orbit, and A B C D the ecliptic passing through the middle of the zodiac. Emily. If the ecliptic relates only to the heavens, why is it described upon the terrestrial globe ? Mrs. B. It is convenient for the demonstration of a variety of problems in the use of the globes ; and besides, the obliquity of this circle to the equator is rendered more conspicuous by its being described on the same globe ; and the obliquity of the ecliptic shows the inclination of the earth's axis to the plane of its orbit. But to return to fig. 2. Plate VIH. The spaces between the several parallel circles on the terrestrial globe are called zones ; that which is comprehended between the tropics is distinguished by the name of the torrid zone ; the spaces which ex- tend from the tropics to the polar circles, the north ON THE EARTH. 117 and south temperate zones ; and the spaces contain- ed within the polar circles, the frigid zones. . The several lines which, you observe, are drawn from one pole to ihe other, cutting the equator at right angles, are called meridians. When any one of these meridians is exactly opposite the sun it is mid- day, or twelve o'clock in the day, with all the places situated on that meridian ; and, with the places situa- ted on the opposite meridian, it is consequently mid- night. Emily. To places situated equally distant from these two meridians, it must then be six o'clock? Mrs. B. Yes ; if they are to the east of the sun's meridian it is six o'clock in the afternoon, because the sun will have previously passed over them ; if to the west, it is six o'clock in the morning, and the sun will be {)roceeding towards that meridian. Those circles which divide the globe into two equal parts, such as the equator and the ecliptic, are called greater circles ; to distinguish them from those which divide it into two unequal parts, as the tropics and polsyf circles, which are called lesser circles. All circles are divided into 360 equal parts, called de- grees, and degrees into 60 equal parts, called minutes. The diameter of a circle is a right line drawn across it, and passing through the centre ; for instance, the boundary of this sphere is a circle, and its axis the di- ameter of that circle ; the diameter is equal to a little less than one third of the circumference. Can you tell me nearly how many degrees it contains ? Caroline. It must be something less than one third of 360 degrees, or nearly 120 degrees. Mrs. B. Right ; now Emily you may tell me exactly how many degrees are contained in a meri- dian ? Emily. A meridian, reaching from one pole to the other, is half a circle, and must therefore contain 180 degrees. Mrs. B. Very well : and what number of degrees, are there from the equator to the poles ? 118 ON THE EARTH. Caroline. The equator being equally distant iVom either pole, that distance must be half ofa meridian, or a quarter of the circumference ofa circle, and con- tain 90 degrees. Mrs. B. Besides the usual division of circles into degrees, the ecliptic is divided into twelve equal parts, called signs, which bear the names of the constellations through which this circle passes in the heavens. The degrees measured on the meridians from north to south, or south to north, are called degrees of la- titude ; those measured from east to west on the equator, the ecliptic, or any of the lesser circles, are called degrees of longitude ; hence these circles bear the name of longitudinal circles ; they are also called parallels of latitude. Emily. The degrees of longitude must then vary in length according to the dimensions of the circle on which they are reckoned ; those, for instance, at the polar circles will be considerably smaller than those at the equator ? Mrs. B. Certainly ; since the degrees of circles of different dimensions do not vary in number, they must necessarily vary in length. The degrees of la- titude, you may observe, never vary in length ; for the meridians on which they are reckoned are all of the same dimensions. Emily. And of what length is a degree of latitude ? Airs. B. Sixty geographical miles, which is equal to 69i English statute miles. Emily. The degrees of longitude at the equator must then be of the same dimensions. Mrs. B. They would, were the earth a perfect sphere ; but its form is not exactly spherical, being somewhat protuberant about the equator, and flat- tened towards the poles. This form is supposed to proceed from the superior action of the centrifugal power at the equator. Caroline. I thought I had understood the centri- fugal force perfectly, but I do not comprehend its e£tect in this instance. ON THE EARTH. 119 Mrs. B. You know that the revolution of the earth on its axis must give every particle a tenden- cy to fly o£F from the centre, that this tendency is stronger or weaker in proportion to the velocity with which the particle moves ; now a particle situated near one of the polar circles makes one rotation in the same space of time as a particle at the equator ; the latter, therefore, having a much larger circle to describe, travels proportionally faster, consequently the centrifugal force is much stronger at the equator than at the polar circles : it gradually decreases as you leave the equator and approach the poles, where, as there is no rotatory motion, it entirely ceases. Supposing, therefore, the earth to have been origi- nally in u fluid state, the particles in the torrid zone would recede much farther from the centre than those in the frigid zones ; thus the polar regions would become flattened, and those about the equator elevated. Caroline. I did not consider that the particles in the neighbourhood of the equator move with greater velocity than those about the poles ; this was the reason I could not understand you. Mrs. B. You must be careful to remember, that those parts of a body which are farthest from the centre of motion must move with the greatest velo- city : the axis of the earth is the centre of its diur- nal motion, and the equatorial regions the parts most distant from the axis. Caroline. My head then moves faster than my feet ; and upon the summit of a mountain we are carried round quicker than in a valley ? Airs. B. Certainly, your head is more distant from the centre of motion than your feet ; the mountain- top than the valley : and the more distant any part of a body is from the centre of motion, the larger is the circle it will describe, and the greater therefore must be its velocity. Emily. I have been reflecting, that if the earth h not a perfect circle 120 ON THE EARTtt. Mrs. B. A sphere you mean, my dear ; a circle is a round line, every part of which is equally distant from the centre ; a sphere or globe is a round body, the surface of which is every where equally distant from the centre. Emily. If, then, the earth is not a perfect sphere, but prominent at the equator, and depressed at the poles, would not a body weigh heavier at the equa- tor than at the poles ; for the earth being thicker at the equator, the attraction of gravity perpendicu- larly downwards must be stronger. Mrs. B. Your reasoning has some plausibility, but I am sorry to, be obliged to add, that it is quite er- roneous ; for the nearer any part of the surface of a body is to the centre of attraction, the more strongly it is attracted ; because the most considerable quan- tity of matter is about that centre. In regard to its effects, you might consider the power of gravity as that of a magnet placed at the centre of attraction. Emily. But were you to penetrate deep into the earth, would gravity increase as you approached the centre ? Mrs. B. Certainly not ; 1 am referring only to any situation on the surface of the earth. Were you to penetrate into the interior, the attraction of the parts above you would counteract that of the parts Ijeneatli you, and consequently diminish the power of gravity in proportion as you approached the cen- tre ; and if you reached that point, being equally attracted by the parts all around you, gravity would cease, and you would b^ without weight. Emily. Bodies then should weigh less at the equator than at the poles, since they are more dis- tant from the centre of gravity in the former than in the latter situation ? Mrs. B. And this is really the case ; but the dif- ference of weight would be scarcely sensible, were it not augmented by another circumstance. Caroline. And what is this singular circumstance, which seems to disturb the laws of nature ? ON THE EARTH. 121 Mrs, B. One that you are well acquainted with, as conducing more to the preservation than the de- struction of order — the centrifugal force. This we have just observed to be stronger at the equator ; and as it tends to drive bodies from the centre, it is ne- cessarily opposed to, and must lessen the power of gravity, which attracts them towards the centre. We accordingly find that bodies weigh lightest at the equator, where the centrifugal force is greatest ; and heaviest at the poles, where this power is least. Carolinr. Has tlie experiment been made in these different situations ? Mrs. B, Lewis XIV., of France, sent philosophers both to the equator and to Lapland for this purpose : the severity of the climate, and obstruction of the ice, has hitherto rendered every attempt to reach the pole abortive ; but the difference of gravity at the equator and in Lapland is very perceptible. Caroline, Yet I do not comprehend, how the dif- ference of weight could be ascertained ; for if the body under trial decreased in weight, the weight which was opposed to it in the opposite scale must have diminished in the same proportion. For in- stance, if a pound of sugar did not weigh so heavy at the equator as at the poles, the leaden pound which served to weigh it would not be so heavy either ; therefore they would still balance each other, and the different force of gravity could not be ascertained by this means. Mrs, B, Your observation is perfectly just : the difference of gravity of bodies situated at the poles and at the equator cannot be ascertained by weigh- ing them ; a pendulum was therefore used for that purpose. Caroline, What, the pendulum of a clock ? how could that answer the purpose ? Mrs. B. A pendulum consists of a line, or rod, to one end of which a weight is attached, and it is sus- pended by the other to a fined point, about which it is made to vibrate. Without being put in motion, a 11 122 ©N THE EARTHr pendulum, like a plumb line, hangs perpendicular to the general surface of the earth, by which it is at- tracted ; but, if you raise a pendulum, gravity will bring it back to its perpendicular position. It will, however, not remain stationary there, for the veloci- ty it has received during its descent will impel it on- wards, and it will rise on the opposite side to an equal height ; from thence it is brought back by gravity, and again driven by the impulse of its velocity. Caroline. If so, the motion of a pendulum would be perpetual, and 1 thought you said, that there was no perpetual motion on the earth. Mrs. B. The motion of a pendulum is opposed by the resistance of the air in which it vibrates, and by the friction of the part by which it is suspended : were it possible to remove these obstacles, the mo- tion of a pendulum would be perpetual, and its vi- brations perfectly regular ; being of equal distances, and performed in equal times. Emily. That is the natural result of the uniformi- ty of the power which produces these vibrations, for the force of gravity being always the same, the veloci- ty of the pendulum must consequently be uniform. Caroline. No, Emily, you are mistaken ; the cause is not always uniform, and therefore the effect will not be so either. I have discovered it, Mrs. B. ; since the force of gravity is less at the equator than at the poles, the vibrations of the pendulum will be slower at the equfitor than at the poles. Mrs. B. You are perfectly right, Caroline ; it was by this means that the difference of gravity was discovered, and the true figure of the earth ascer- tained. Emily. But how do they contrive to regulate their time in the equatorial and polar regions ? for, since in this part of the earth the pendulum of a clock vibrates exactly once in a second, if it vibrates faster at the poles and slower at the equator, the inhabitants must regulate their clocks in a different manner frem ours. ON THE EARTH. 133 Mrs. B. The only alteration required is to length- en the pendulum in one case, and to shorten it in the other: for the velocity of the vibrations of a pendu- lum depends on its length ; and when it is said that a pendulum vibrates quicker at the pole than at the equator, it is supposing it to be of the same length. A pendulum which vibrates a second in this latitude is 36k inches long. In order to vibrate at the equa- tor in the same space of time, it must be lengthened by the addition of a few lines ; and at the poles, it must be proportionally shortened. I shall now, I think, be able to explain to you the variation of the seasons, and the difference of the length of the days and nights in those seasons ; both effects resulting from the same cause. In moving round the sun, the axis of the earth is not perpendicuhir to the plane of its orbit. Suppo- sing this round table to represent the plane of the earth's orbit, and this little globe, which has a wire passing through it, representing the axis and poles, we shall call the earth ; in moving round the table, the wire is not perpendicular to it, but oblique. Emily. Yes, I understand the earth does ftot go round the sun in an upright position, its axis is slant- ing or oblique. Mrs. B. All the lines, which you learnt in your last lesson, are delineated on this little globe ; you must consider the ecliptic as representing the plane of the earth's orbit; and the equator, which crosses the ecliptic in two places, shows the degree of obli- quity of the axis of the earth in that orbit, which is ex- actly 23| degrees. The points in which the ecliptic intersects the equator are called nodes. But I believe I shall make this clearer to you by revolving the little globe round a candle, which shall represent the sun. (Plate IX. 6g. 2.) As I now hold it, at A, you see it in the situation in which it is in the midst of summer, or what is called the summer solstice, which is on the Slst of June. 1:24 ON THE EARTH. Emily. You hold the wire awry, I suppose, in oi-- ier to show that the axis of the earth is not upright '{ Mrs. B. Yes ; in summer, the north pole is incli- ned towards the sun. In this season, therefore, the northern hemisphere enjoys much more of his rays than the southern. The sun, you see, now shines over the whole of the north frigid zone, and notwith- jstanding the earth's diurnal revolution, which I imi tate hy twirling the ball on the wire, it will continue to shine upon it as long as it remains in this situation, whilst the south frigid zone is at tlie same time com- pletely in obscurity. Caroline. That is very strange : I never before heard that there was constant day or night in any part of the world! Mow mucli happier the inhabitants of the north frigid zone must be than those of the south- ern ; the first enjoy uninterrupted day, while the last are involved in perpetual darkness. Mrs. B. You judge with too much precipitation ; examine a little further, and you will find, that the two frigid zones share an equal fate. We shall now make the earth set off from its posi- tion in the siimmer solstice, and carry it round the sun ; observe that the pole is always inclined in the same direction, and points to the same spot in the heavens. Tliere is a fixed star situated near that spot, which is hence called the North Polar star. Now let us stop the earth at B, and examine it in its present situation ; it has gone through one quarter of its orbit, and is arrived at that point at which the ecliptic cuts or crosses the equator, and which is call- ed the autumnal equinox. Emily. That is then one of the nodes. The sun now shines from one pole to the other, just as it would constantly do, if the axis of the earth were perpendicular to its orbit, Mrs. B. Because the inclination of the axis is now neither towards the sun nor in the contrary direction ; at this period ef the year, therefore, the days and nights are equal in every part of the earth. But the UN THE EARTH. 1.25 uext Step she takes in her orbit, you see, involves the north pole in darkness, whilst it illumines that of the south ; this change was gradually preparing as 1 mo- ved the earth from summer to autumn ; the arctic circle, which was at tirst entirely illumined, began to have short nights, which increased as the earth ap- proached the autumnal equinox; and the instant it passed that point, the long night of the north pole commences, and the south pole begins to enjoy the light of the sun. We shall now make the earth pro- ceed in its orbit, and you may observe that as it ad- vances, the days shorten, and the nights lengthen, throughout the northern hemisphere, until it arrives at the winter solstice^on the 21st of December, when the north frigid zone is entirely in darkness, and the southern has uninterrupted daylight. Caroline. Then, after all, the sun, which I thought so partial, confers his favours equally on all. Mrs. B. Not so neither ; the inhabitants of the torrid zone have much more heat than we have, aa the sun's rays fall perpendicularly on them, while they shine obliquely on the rest of the world, and al- most horizontally on the poles ; for during their long day of six months, the sun moves round their horizon without either rising or setting; the only observable difference is, that it is more elevated by a few de- grees at midday, than at midnight. Emily. To a person placed in the temperate zone, in the situation in which we are in England, the sun will shine neither so obliquely as it does on the poles, nor so vertically as at the equator ; but its rays will fall upon him more obliquely in autumn and winter, than in summer. Caroline. And, therefore, the inhabitants of the temperate zones will not have merely one day and one night in the year as happens at the poles, nor will they have equal days and equal nights as at the equa- tor ; but their days and nights will vary in length, at different times of the year, according as their respec- tive poles incline towards or from the sun, and the 11* JiG ON THE EARTH. difference will be greater in proportion to their dis- tance from the equator. Mrs. B, We shall now follow the earth through the other half of her orbit, and you will observe, that now, exactly the same effect takes place in the south- ern hemisphere, as what we have just remarked in the northern. Day commences at the south pole when night sets in at the north pole ; and in every other part of the southern hemisphere the days are longer than the nights, while, on the contrary, our eights are longer than our days. When the earth ar- rives at the vernal equinox, D, where the ecliptic again cuts the ei^uator, on the 26th of March, she is situated, with respect to the sun, exactly in the same position as in the autumnal equinox ; and the only difference with respect to the earth is, that it is now autumn in the southern hemisphere, whilst it is spring with us. Caroline. Then the days and nights are again every where equal ? Mrs. B. Yes, for the half of the globe which is enlightened extends exactly from one pole to the other ; the day breaks to the north pole, and the sun sets to the south pole ; but in every other part of the globe, the day and night is of twelve hours length, hence the word equinox, which. is derived from the Latin, meaning equal night. As the earth proceeds towards summer, the days lengthen in the northern hemisphere, and shorten in the southern, till the earth reaches the summer sol- stice, when the north frigid zone is entirely illumined, and the southern is in complete darkness ; and we have now brought the earth again to the spot from whence we tirst accompanied her. Emily. This is indeed a most satisf;\ctory expla- nation of the seasons ; and the more I learn, the more I admire the simplicity of means by which such wonderful effects are produced. Mrs. B. 1 know not which is most worthy of our admiration, the cause, or the effect of the earth's re» 6N THE EARTH. 127 Tolution round the sun. The mind can find no ob- ject of contemplation more sublime than the course of this magnificent globe, impelled by the combined powers of projection and attraction to roll in one in- variable course around the source of light and heat: and what can be more delightful than the beneficent effects of this vivifying power on its attendant planet. It is at once the grand principle which animates and fecundates nature. Emily. There is one circumstance in which this little ivory globe appears to me to differ from the earth ; it is not quite dark on that side of it which is turned from the candle, as is the case with the earth when neither moon nor stars are visible. Mrs, B. This is owing to the light of the candle being reflected by the walls of the room on every part of the globe, consequently that side of the globe on which the candle does not directly shine, is not in total darkness. Now the skies have no walls to re- flect the sun's light on that side of our earth which is in darkness. Caroline. I beg your pardon, Mrs. B., I think that the moon and stars answer the purpose of walls in reflecting the sun's light to us in the night. Mrs. B. Very well, Caroline ; that is to say, the moon and planets ; for the fixed stars, you know, shine by their own light. Emily. You say, that the superior heat of the equatorial parts of the earth arises from the rays falling perpendicularly on those regions, whilst they fall obliquely on these more northern regions ; now 1 do not understand why perpendicular rays should afford more heat than oblique rays. Caroline. You need only hold your hand perpen- dicularly over the candle, and then hold it sideways obliquely, to be sensible of the difference. Emily, I do not doubt the fact, but I wish to have it explained. Airs, B. You are quite right ; if Caroline had not been satisfied with ascertaining the fact, without u!>* 5:^B ON THE KAHTtf. derstanding it, she would not have brought forward the candle as an illustration j the reason why 3'ou feel so much more heat if you hold your hand per- pendicularly over the candle, than if you hold it aide- ways, is because a stream of heated vapour constantly ascends from the candle, or any other burning body, which being lighter than the air of the room, does not spread laterally but rises perpendicularly, and this led you to suppose that the rays were hotter in the latter direction. Had you reflected, you would have discovered that rays issuing from the candle sideways, are no less perpendicular to your hand when held opposite to them, than the rays which as- cend when your hand is held over them. The reason why the sun's rays afford less heat when in an oblique direction than when perpendicu- lar, is because fewer of them fall upon an equal por- tion of the earth ; this will be understood better by referring to Plate X. fig. 1, which represents two equal portions of the sun's rays, shining upon difl'er- ent parts of the earth. Here it is evident, that the same quantity of rays fall on the space A B, as fall on the space B C ; and as A B is less than B C, the heat and light will be much stronger in the former than in the latter; A B, you see, represents the equatorial regions, where the sun shines perpendicu- larly ; and B C, the temperate and frozen climates, where his rays fall more obliquely. Emily. This accounts not only for the greater heat of the equatorial regions, but for the greater heat of summer ; as the sun shines less obliquely ia summer than in winter. Airs. B. This you will see exemplified in figure -2, in which the earth is represented as it is situated *on the 21st of June, and England receives less oblique, and consequently a greater number of rays, than at any other season ; and figure 3, shows the situation of England on the 21st of December, when the rays *of the sun fall most obliquely upon her. But there -*#- ako another reasoa why ..oblique rays give le«s m. J. Tiif- 4. ON THE EARTH* 123 keat than perpendicular rays ; which i^, that they have a greater portion of the atmosphere to traverse ; and though it is true that the atmosphere i« itself a transparent body, freely admitting the passage of the sun's rays, yet it is always loaded more or less with dense and foggy vapour, which the rays of the sun cannot easily penetrate ; therefore the greater the quantity of atmosphere the sun's rays have to pass through in their way to the earth, the less heat they will retain when they reach it. 'J'his will be better \inderstood by rt^ferring to fig. 4. The dotted line round the earth describes the extent of the atmos- phere, and the lines which proceed from the sun to the earth the passage of two equal portions of the sun's rays to the equatorial and polar regions ; the latter, you see, from its greater obliquity passes through a greater extent of atmosphere. Caroline. And this, no doubt, is the reason why the sun in the morning and the evening gives so much less heat than at midday. Mrs. B. The diminution of heat, morning and evening, is certainly owing to the greater obliquity of the sun's rays ; and as such they are affected by both the causes which I have just explained to you ; the difficulty of passing through a foggy atmosphere is perhaps more particularly applicable to them, as mists and vapours are very prevalent about the time of sunrise and sunset. But the diminished obliquity of the sun's rays is not the sole cause of the heat of summer ; the length of the days greatly conduces to it ; for the longer the sun is above the horizon, the more heat he will communicate to the earth. Caroline. Both the longest days, and the most per- pendicular rays, are on the 21st of June ; and yet the greatest heat prevails in July and August. Mrs. B. Those parts of the earth which are once heated, retain the heat for some length of time, and the additional heat they receive, occasions an eleva- tion of temperature, although the days begin to short- en, and the sun's rays to fall more obliquely. For 130 ©N THE EARTH. the same reason, we have generally more heat ai three o'clock in the afternoon, than at twelve, when the sun is on the meridian. Emily. And pray, have the other planets the same vicissitudes of seasons as the earth ? - Mrs. B. Some of them more, some less, accord- ing as their axes deviate more or less from the per- pendicular to the plane of their orbits. The axis of Jupiter is nearly perpendicular to the plane of his or- bit ; the axes of Mars and of Saturn are each inclined at angles of about sixty degrees ; whilst the axis of Venus is believed to be elevated only fifteen or twenty degrees above her orbit ; the vicissitudes of her sea- sons must theretbre be considerably greater than ours. For further particulars respecting the planets, I shall refer you to Bonnycastle's Introduction to Astronomy. 1 have but one more observation to make to you relative to the earth's motion, which is, that although we have but 365 days and nights in the year, she per- forms 366 complete revolutions on her axis during that time. Caroline. How is that possible ? for every com- plete revolution must bring the same place back to the sun. It is^novv just twelve o'clock, the sun is, therefore, on our meridian ; in twenty-four hours will it not be returned to our meridian again, and will not the earth have made a complete rotation on its axis ? Mrs. B. If the earth had no progressive motion in its orbit whilst it revolves on its axis, this would be the case ; but as it advances almost a degree west- ward in its orbit, in the same time that it completes a revolution eastward on its axis, it must revolve nearly one degree more in order to bring the same meridian back to the sun. Caroline. Oh, yes ! it will require as much more of a second revolution to bring the same meridian back to the sun, as is equal to the space the earth ON THE EARTH. 131 has advanced in her orbit, that is, nearly a degree ; this difference is, however, very little. Mrs. B. These small daily portions of rotation are each equal to the three hundred and sixty-fifth part of a circle, which at the end of the year amounts to one complete rotation. Emily. That is extremely curious. If the earth, then, had no other than its diurnal motion, we should have 366 days in the year. Mrs B. We should have 366 days in the same period of time that we now have 365 : but if we did not revolve round the sun, we should have no na- tural means of computing years. You will be surprised to hear, that if lime is calcu- lated by the stars instead of the sun, the irregularity which we have just noticed does not occur, and that one complete rotation of the earth on its axis, brings the same meridian back to any fixed star. Emily. That seems quite unaccountable ; for the earth advances in her orbit with regard to the fixed stars, the same as with regard to the sun. Mrs. B. True, but then the distance of the fixed stars is so immense, that our solar system is in com- parison to it but a spot, and the whole extent of the earth's orbit but a point ; therefore, whether the earth remained stationary, or whether it revolved in its orbit durins; its rotation on its axis, no sensible dif- ference would be produced with regard to the fixed stars. One complete revolution brings the same meridian back to the same fixed star ; hence the fix- ed stars appear to go round the earth in a shorter time than the sun by three minutes fifty-six seconds of time. Caroline. These three minutes fifty-six seconds is the time which the earth takes to perform the addi- tional three hundred and sixty-fifth part of the circle, in order to bring the same meridian back to the sun. Mrs. B. Precisely. Hence the j^tars gain every N WIND AND SOUND. 18l every quarter. Those who live to the north of it ex- perience a north wind ; those to the south, a south wind ; — do you comprehend this ? Caroline Perfectly. But what sort of weather must those people have, who live on the spot where ihese winds meet and interfere ? Mrs. B. They have turbulent and boisterous weather, whirlwinds, hurricanes, rain, lightning, thunder, &c. This stormy weather occurs most fre- quently in the torrid zone, where the heat is greatest : the air being more rarefied there than m any other part of the ^lobe, is lighter, and consequently ascends ', whilst the air about the polar regions is continually flowing from the poles, to restore the equilibrium. Caroline. This motion of the air would produce a regular and constant north wind to the inhabitants of the northern hemisphere ; and a south wind to those of the southern hemisphere, and continual storms at the equator, where these two adverse winds would meet. Mrs. B. These winds do not meet, for they each change their direction before they reach the equator. The sun, in moving over the equatorial regions from east to west, rarefies the air as it passes, and causes the denser eastern air to flow westwards, in order to restore the equilibrium ; thus producing a regular east wind about the equator. Caroline. The air from the west, then, constantly goes to meet the sun, and repair the disturbance which his beams have produced in the equilibrium of the atmosphere. But 1 wonder how you will recon- cile these various winds, Mrs. B. : you first led me to suppose there was a constant struggle between op- posite winds at the equator, producing storm and tempest ; but now 1 hear of one regular invariable wind, which must naturally be attended by calm weather. Emily. I think I comprehend it : do not these winds from the north and south combine with the 16 182 ON WIND AND SOUND. easterly wind about the equator, and form what are called the trade-winds ? Mrs. B. Just so, my dear. The composition of the two winds nortli and east, produces a constant north-east wind ; and that of the two winds south and east, produces a regular south-east wind : these winds extend to about thirty degrees on each side of the equator, the regions further distant from it expe- riencing only their respective north and south winds. Caroline. But, Mrs. B., if the air is constantly flowing from the poles to the torrid zone, there must be a deficiency of air in the polar regions ? Mrs. B. The light air about the equator, which ex- pands and rises into the upper regions of the atmos- phere, ultimately flows from thence back to the poles to restore the equilibrium : if it were not for this re- source, the polar atmospheric regions would soon be exhausted by the stream of air, which, in the lower strata of the atmosphere, they are constantly sending towards the equator. Carolitie. There is then a sort of circulation of air in the atmosphere ; the air in the lower strata flowing from the poles towards the equator, and in the upper strata, flowing back from the equator to- wards the poles. Mrs. B. Exactly : I can show you an example of this circulation on a small scale. The air of this room being more rarefied than the external air, a wind or current of air is pouring in from the crevices of the windows and doors, to restore the equilibrium ; but the light air with which the room is filled must find some vent, in order to make way for the heavy air which enters. If you set the door a-jar, and hold a candle near the upper part of it, you will find that the flame will be blown outwards, showing that there is a current of air flowing out from the upper part of the room. — Now place the candle on the floor close by the door, and you will perceive, by the inclination of the flame, that there is also a current of air setting into the room. ON WIND AND SOUND. 183 Caroline. It is just so ; the upper current is the warm light air, which is driven out to make way for the stream of cold dense air which enters the room lower down. Emily. I have heard, Mrs. B., that the periodical winds are not so regular on land as at sea : what is the reason of that ? Mrs. B. The land reflects into the atmosphere a much greater quantity of the sun's rays than the wa- ter ; therefore, that part of the atmosphere which is over the land, is more heated and rarefied than that which is over the sea : this occasions the wind to set in upon the land, as we find that it regularly does on the coast of Guinea, and other countries in the torrid zone. Emily. I have heard much of the violent tempests occasioned by the breaking up of the monsoons ; are not they also regular trade-winds ? Mrs. B. They are called periodical trade-winds, as they change their course every half year. This variation is produced by the earth's annual course round the sun, when the north pole is inclined towards that luminary one half of the year, the south pole the other half. During the summer of the northern hemisphere, the countries of Arabia, Persia, India and China, are much heated, and reflect great quan- tities of the sun's rays into the atmosphere, by which it becomes extremely rarefied, and the equilibrium consequently destroyed. In order to restore it, the air from the equatorial southern regions, where it is colder, (as well as from the colder northern parts,) must necessarily have a motion towards those parts. The current of air from the equatorial regions pro- duces the trade-winds for the first six months, in all the seas between the heated continent of Asia, and the equator. The other six months, when it is summer in the southern hemisphere, the ocean and countries towards the southern tropic are most heated, and the air over those parts most rarefied : then the air about it84 ON WIND AND SOUND. flhe equator alters iis course, and flows exactly in an •pposite direction. Caroline. This explanation of the monsoons is very ourious ; but what does their breaking up mean ? Mrs, B. It is the name given by sailors to the shifting of the periodical winds ; they do not change their course suddenly, but by degrees, as the sun moves from one hemisphere to the other : this change is usually attended by storms and hurricanes, very dana^erous for shipping ; so that those seas are sel- dom navigated at the season of the equinox. Etniiy. 1 think I understand the winds in the tor- rid zone perfectly well ; but what is it that occasions the great variety of winds which occur in the tempe- rate zones ? for, according to your theory, there should be only north and south winds in those cli- mates. Mrs. B. Since so large a portion of the atmos- phere as is over the torrid zone is in continued agi- tation, these agitations in an elastic fluid, which yields to the slightest impression, must extend every way to a great distance ; the air, therefore, in all climates, will suff"er more or less perturbation, according to the situation of the country, the position of mountains, val- leys, and a variety of other causes : hence it is easy to conceive, that almost every climate must be liable to variable winds. On the seashore, there is almost always a gentle sea-breeze setting in on the land on a summer's even- ing, to restore the equilibrium which has been dis- turbed by reflections from the heated surHice of the shore during the day ; and when night has cooled the land, and condensed the air, we generally find it, to- wards morning, flowing back towards the sea. Caroline. I have observed, that the wind, which- ever way it blows, almost always falls about sunset ? Mrs. B. Because the rarefaction of air in the par- ticular spot which produces the wind, diminishes as the sun declines, and consequently the velocity of the wind abates. ON WIND AND SOUND* 1 8^ Emily. Since the air is a gravitating fluid, is it not affected by the attraction of the moon and the sun, ia the same manner as the waters ? Mrs. B. Undoubtedly ; but the aerial tides are as much greater than those of water, as the density of water exceeds that of air, which, as you may recol- lect, we found to be about 800 to 1. Caroline. What a prodigious protuberance that must occasion! How much the weight of such a co- lumn of air must raise the mercury in the barometer? Emily. As this enormous tide of air is drawn up and supported, as it were, by the moon, its weight and pressure, I should suppose, would be rather di- minished than increased ? Mrs. B. The weight of the atmosphere is neither increased nor diminished by the aerial tides. The moon's attraction augments the bulk as much as it di- minishes the weight of the column of air ; these ef- fects, therefore, counterbalancing each other, the aerial tides do not affect the barometer. Caroline. I do not quite understand that. Mrs. B. Let us suppose that the additional bulk of air at high tide raises the barometer one inch ; and on the other hand, that the support which the moon's attraction affords the air diminishes its weight or pres- sure, so as to occasion the mercury to fall one inch ; under these circumstances the mercury must remain stationary. Thus you see, that we can never be sen- sible of aerial tides by the barometer, on account of the equality of pressure of the atmosphere, whatever be its height. The existence of aerial tides is not, however, hy- pothetical ; it is proved by the effect they produce on the apparent position of the heavenly bodies ; but this I cannot explain to you, till you understand the pro- perties of light. Emily. And when shall we learn them ? Mr. . B. 1 shall first explain to you the nature of sound, which is intimately connected with that of airj 16* 18C ON WIND AND SOUND. and I think at our next meeting we may enter upon the subject of optics. We have now considered the effects produced by the wide and extended agitation of the air ; but there is another kind of agitation of which the air is suscep- tible — a sort of vibratory trembling motion, which, striking on the drum of the ear, produces sound. Caroline. Is not sound produced by soHd bodies ? The voice of animals, the ringing of bells, musical instruments, are all solid bodies. I know of no sound "but that of the wind which is produced by the air. Mrs. B. Sound, I assure you, results from a tre- mulous motion of the air ; and the sonorous bodies you enumerate are merely the instruments by which that peculiar species of motion is communicated to the air. Caroline. What! when I ring this little bell, is it the air that sounds, and not the bell? Mrs. B. Both the bell and the air are concerned in the production of sound. But sound, strictly Speaking, is a perception excited in the mind by the motion of the air on the nerves of the ear ; the air, therefore, as well as the sonorous bodies which put it in motion, is only the cause of sound, the immediate effect is produced by the sense of hearing ; for, with- out this sense, there would be no sound. Emily. I can with difl&culty conceive that. A per- son born deaf, it is true, has no idea of sound, be- cause he hears none : yet that does not prevent the peal existence of sound, as all those who are not deaf can testify. Mrs. B. I do not doubt the existence of sound to all those who possess the sense of hearing ; but it exists neither in the sonorous body nor in the air, but in the mind of the person whose ear is struck by the vibratory motion of the air, produced by a sonorous body. To convince you that sound does not exist in sono- cous bodies, but that air or some other vehicle is ne- tressary to its production, endeavour to ring the little ON WIND AUD SOUND. 18^ bell, after I have suspended it under a receiver in the air-pump, from which I shall exhaust the air Caroline. This is indeed very strange : though I agitate it so violently, it does not produce the least sound. Mrs. B. By exhausting the receiver, 1 have cut off the communication between the air and the bell ; the latter, therefore, cannot impart its motion to the air. Caroline. Are you sure that it is not the glass, which covers the bell, that prevents our hearing it ? Mrs. B. That you may easily ascertain by letting the air into the receiver, and then ringing the bell. Caroline. Very true : I can hear it now almost as loud as if the glass did not cover it ; and I can no longer doubt but that air is necessary to the produc- tion of sound. Airs. B. Not absolutely necessary, though by far the most common vehicle of sound. Liquids, as well as air, are capable of conveying the vibratory motion of a sonorous body to the organ of hearing ; as sound can be heard under water. Solid bodies also convey sound, as I can soon convince you by a very simple experiment. I shall fasten this string by the middle round the poker ; now raise the poker from the ground by the two ends of the string, and hold one to each of your ears : — I shall now strike the poker with a ke}^ and you will find that the sound is conve3'ed to the ear by means of the strings, in a much more per- fect manner than if it had no other vehicle than the air. Caroline. That it is, certainly, for I am almost stunned by the noise. But what is a sonorous body, Mrs. B. ? for all bodies are capable of producing some kind of sound by the motion they communicate to the air. Mrs. B. Those bodies are called sonorous, which produce clear, distinct, regular, and durable sounds, such as a bell, a drum, musical strings, wind-instru- ments, &c. They owe this property to their elasti* 188 ©N WIND AND SOUND. city ; for an elastic body, after having been struck, not only returns to its former situation, but having acquired momentum by its velocity, like the pendu- lum, it springs out on the opposite side. If 1 draw the string A B, which is made fast at both ends to C, it will not only return to its original position, but pro- ceed onwards to D. This is its first vibration, at the end of which it will retain sufficient velocity to bring it to E, and back again to F, which constitutes its se- cond vibration ; the third vibration will carry it only to G and H, and so on, till the r^istance of the air destroys its motion. The vibration of a sonorous body gives a tremu- lous motion to the air around it, very similar to the motion communicated to smooth water when a stone is thrown into it. This first produces a small circu- lar wave around the spot in which the stone falls j the wave spreads, and gradually communicates its motion to the adjacent waters, producing similar waves to a considerable extent. The same kind of waves are produced in the air by the motion of a sonorous body, but with this difference, that as air is an elastic fluid, the motion does not consist of regu- larly extending waves, but of vibrations, and are com- posed of a motion forwards and backwards, similar to those of the sonorous body. They differ also in the one taking place in a plane, the other in all direc- tions. The aerial undulations being spherical. Emily. But if the air moves backwards as well as forwards, how can its motion extend so as to convey sound to a distance ? Mrs. B. The first sphere of undulations which are produced immediately around the sonorous body, by pressing against the contiguous air, condenses it. The condensed air, though impelled forward by the pressure, re-acts on the first set of undulations, dri- ving them back again. The second set of undula- tions which have been put in motion, in their turn communicate their motion, and are themselves driven back by re-action. Thus there is a succession of v>N WIx\D AND SOUNE». 18& waves in the air, corresponding with the succession ©f waves in the water. Caroline. The vibrations of sound must extend much further than the circular waves in water, since sound is conveyed to a great distance. Mrs. B. The air is a fluid so much less dense than water, that motion is more easily communicated to it. The report of a cannon produces vibrations of the air, which extend to several miles around. Emily. Distant sound takes some time to reach us, since it is produced at the moment the cannon is fired ; and we see the light of the flash long before we hear the report. Mrs. B. The air is immediately put in motion by the firing of a cannon ; but it requires time for the vibrations to extend to any distant spot. The veloci- ty of sound is computed to be at the rate of 1142 feet in a second. Caroline. With what astonishing rapidity the vi- brations must be communicated ! But the velocity of sound varies, I suppose, with that of the air which conveys it. If the wind sets towards us from the cannon, we must hear the report sooner that if it set the other waj'. Mrs. B. The direction of the wind makes less difl*er- ence in the velocity of sound than you would imagine, if the wind sets from us, it bears most of the aerial waves away, and renders the sound fainter ; but it is not very considerably longer in reaching the ear than if the wind blew towards us. This uniform velocity of sound enables us to determine the distance of the object trom which it proceeds ; as that of a vessel at sea firing a cannon, or that of a thunder cloud. If we do no not hear the thunder till half a minute after we see the lightning, we conclude the cloud to be at the distance of six miles and a half. Emily. Pray how is the sound of an echo pro- duced ? Mrs. B. When the aerial vibrations meet with an obstacle, having a hard and regular surface, such as a 190 ON WIND AND SOUND. wall, or rock, they are reflected back to the ear, and produce the same sound a second time ; but the sound will then appear to proceed from the object by which it is reflected. If the vibrations fall perpendicularly on the obstacle, they are reflected back in the same line ; if obliquely, the sound returns obliquely in the opposite direction, the angle of reflection being equal to the angle of incidence Caroline. Oh, then, Emily, I now understand why the echo of my voice behind our house is heard so much plainer by you than it is by me, when we stand at the opposite ends of the gravel walk. My voice, or rather, 1 should say, the vibrations of air it occa- sions, fall obliquely on the wall of the house, and are reflected by it to the opposite end of the gravel walk. Emily. Very true ; and we have observed, that when we stand in the middle of the walk, opposite the house, the echo returns to the person who spoke. Mrs. B. Speaking-trumpets are constructed on the principle of the reflection of sound. The voice, instead ofbeingdiff'usedinthe open air, is confined within the trumpet ; and the vibrations, which spread and fall against the sides of the instrument, are reflected ac- cording to the angle of incidence, and fall into the direc- tion of the vibrations which proceed straight forwards. The whole of the vibrations are thus collected into a focus ; and if the ear be situated in or near thkt spot, the sound is prodigiously increased. Figure 7. Plate XIV. will give you a clearer idea of the speaking- trumpet : the reflected rays are distinguished from those of incidence, by being dotted ; and they are brought to a focus at F. The trumpet used by deaf persons acts on the same principle ; but as the voice enters the trumpet at the large, instead of the small end of the instrument, it i? not so much confined, nor the sound so much increased. Emily. Are the trumpets used as musical instru- ments also constructed on this principle ? Mrs. B. So far as their form tends to increase the V ON WIND AND SOUNIK 191 sound, they are ; but, as a musical instrument, the trumpet becomes itself the sonorous body, which is made to vibrate by blowing into it, and communicates its vibrations to the air. I will attempt to give you, in a few words, some no- tion of the nature of musical sounds, which, as you are fond of music, must be interesting to you. if a sonorous body be struck in such a manner, that its vibrations are all performed in regular times, the vibrations of the air will correspond with them ; and striking in the same regular manner on the drum of the ear, will produce the same uniform sensation on the auditory nerve, and excite the same uniform idea in the mind ; or, in other words, we shall hear one musical tone. But if the vibrations of the sonorous body are irre- gular, there will necessarily follow a confusion of aeri- al vibrations ; for a second vibration may commence before the first is finished, to meet it half way on its return, interrupt it in its course, and produce harsh jarring sounds, which are called discords. Emily. But each set of these irregular vibrations, if repeated at equal intervals, would, 1 suppose, pro- duce a musical tone ? It is only their irregular suc- cession which makes them interfere, and occasions discord. Mrs B. Certainly. The quicker a sonorous bo- dy vibrates, the more acute, or sharp, is the sound produced. Caroline. But if I strike any one note of the piano- forte repeatedly, whether quickly or slowly, it al- ways gives the same tone. Mrs. B. Because the vibrations of the same string at the same degree of tension, are always of a similar duration. The quickness or slowness of the vibrations relate to the single tones, not to the vari- ous sounds which they may compose by succeeding each other. Striking the note in quick succession, produces a more frequent repetition of the tone, but does not increase tlie velocity of the vibrations of the 192 ONT WIND AND 30UND. string. The duration of the vibrations of strings or chords, depends upon their length, their thickness or weight, and their degree of tension : thus, you find, the low bass notes are produced by long, thick, loose strings ; and the high treble notes by short, small, and tight strings. Caroline. Then the different length and size of the strings of musical instruments, serves to vary the duration of the vibrations, and consequently, the acuteness or gravity of the notes ? Mrs. B. Yes. Among the variety of tones, there are some which, sounded together, please the ear, producing what we call harmony, or concord. This arises from the agreement of the vibrations of the two sonorous bodies ; so that some of the vibrations of each strike upon the ear at the same time. Thus, if the vibrations of two strings are performed in equal times, the same tone is produced by both, and they are said to be in unison. Emily. Now, then, I understand why, when I tune my harp in unison with the piano-forte, I draw the strings tighter if it is too low, or loosen them if it is at too high a pitch ; it is in order to bring them to vibrate, in equal times, with the strings of the piano- forte. J\Jrs. B. But concord, you know, is not confined to unison ; for two different tones harmonize in a va- riety of cases. If the vibrations of one string (or sonorous body whatever) vibrate in double the time of another, the second vibration of the latter will strike upon the ear at the same instant as the first vi- bration of the former ; and this is the concord of an octave. If the vibrations of two strings are as two to three, the second vibration of the first corresponds with the third vibration of the latter, producing the harmony called a fifth. Caroline. So, then, when I strike the key-note with its fifth, I hear every second vibration of one, and every third of the other at the same time ? ON WIND AND SOUN». 10^ Mrs. B. Yes ; and the key-note struck with the fourth is likewise a concord, hecause the vibrations are as three to four. The vibrations of a major third with the key-note, are as four to tive ; and those of a minor third, as five to six. There are other tones which, though they cannot be struck together without producing discord, if struck successively give us the pleasure which is call- ed melody. Upon these general principles the sci- ence of music is founded ; but I am not sufliciently acquainted with it to enter any further into it. We shall now, therefore, take leave of the subject of sound ; and, at our next interview, enter upon that of optics, in which we shall consider the nature of vision, light, and colours. 17 CONVERSATION XIV, ON OPTICS. Of Luminous, Transparent, and Opaque Bodies. — Of the Radiation of Light. — Of Shadows. — Of the Re- flection of Light. — Opaque Bodies seen only by Re- fleeted Light. — Vision Explained. — Camera ObscU' ra. — Image of Objects on the Retina. CAROLINE. I long to begin our lesson to day, Mrs. B., for 1 expect that it will be very entertaining. Mrs. B. Optics is certainly one of the most in- teresting branches of Natural Philosophy, but not one of the easiest to understand ; I must therefore beg that you will give me the whole of your attention. I shall first inquire, whether you comprehend the meaning of a luminous body, an opaque body, and a transparent body. Caroline. A luminous body is one that shines ; an opaque . . . Mrs. B. Do not proceed to the second, until we have agreed upon the definition of the first. All bo- dies that shine are not luminous ; for a luminous body is one that shines by its own light, as the sun, the fire, a candle, &c. Emily. Polished metal then, when it shines with so much brilliancy, is not a luminous body ? Mrs. B. No, for it wouM be dark if it did not re- ceive light from a luminous body ; it belongs, there- fore, to the class of opaque or dark bodies, which Fig. 1. fzatJ^ ^ ^^ ON OPTICS. 195 comprehend all such as are neither luminous nor will admit the light to pass through them. Emily. And transparent bodies are those which admit the light to pass through them ; such as glass and water ? Mrs. B» You are right. Transparent or pellucid bodies are frequently called mediums ; and the rays of light which pass through them are said to be transmitted by them. Light, when emanated from the sun, or any other luminous body, is projected forwards in straight lines in every possible direction : so that the luminous body is not only the general centre from whence all the rays proceed ; but every point of it may be con- sidered as a centre which radiates light in every di- rection. (Fig. 1. Plate XV.) Emily. But do not the rays which are projected in different directions, and cross each other, interfere and impede each other's course ? Mrs. B. Not at all. The particles of light are so extremely minute, that they are never known to in- terfere with each other. A ray of light is a single line of light projected from a luminous body ; and a pencil of rays is a collection of rays proceeding from any one point of a luminous body, as fig. 2. Caroline. Is light then a substance composed of particles like other bodies ? Mrs. B. That is a disputed point upon which I cannot pretend to decide. In some respects, light is obedient to the laws which govern bodies ; in others, it appears to be independent of them ; thus, though its course is guided by the laws of motion, it does not seem to be influenced by those of gravity. It has never been discovered to have weight, though a variety of interesting experiments have been made with a view of ascertaining that point ; but we are so ignorant of the intimate nature of light, that an at- tempt to investigate it would lead us into a labyrinth of perplexity, if not of error ; we shall therefore 196 ON OPTICS. i5onfine our attention to those properties of light which are well ascertained. Let us return to the examination of the effects of the radiation of light from a luminous body. Since the rays of light are projected in straight lines, when they meet with an opaque body through which they are unable to pass, they are stopped short in their course ; for they cannot move in a curve line round the body. Caroline. No, certainly ; for it would require some other force besides that of projection to pro- duce motion in a curve line. Mrs. B. The interruption of the rays of light, by the opaque body, produces, therefore, darkness on the opposite side of it ; and if this darkness fall upon a wall, a sheet of paper, or any object whatever, it forms a shadow. Emily. A shadow then, is nothing more than darkness produced by the intervention of an opaque body, which prevents the rays of light from reaching an object behind the opaque body. Caroline. Why then are shadows of different de- grees of darkness ; for I should have supposed from your definition of a shadow, that it would have been perfectly black ? Mrs. B. It frequently happens that a shadow is produced by an opaque body interrupting the course of the rays from one luminous body, while light from another reaches the space where the shadow is formed, in which case the shadow is proportionally fainter. This happens if the opaque body be lighted by two candles : if you extinguish one of them, the shadow will be both deeper and more distinct. Caroline. But yet it will not be perfectly dark. Mrs. B. Because it is still slightly illumined by light reflected from the walls of the room, and other surrounding objects. You must observe, also, that when a shadow is produced by the interruption of rays from a single ON OPTICS. 197 luminous body, the darkness is proportional to the intensity of the light. Emily. I should have supposed the contrary ; for as the light reflected from surrounding objects on the shadow, must be in proportion to the intensity of the light, the stronger tlie light the more the shadow will be illumined. Mrs. B. Your remark is perfectly just ; but as we have no means of estimating the degrees of light and of darkness but by comparison, the strongest light will appear to produce the deepest shadow. — Hence a total eclipse of the sun occasions a more sen- sible darkness than midnight, as it is immediately contrasted with the strong light of noonday. Caroline. The re-appearance of the sun after an eclipse must, by the same contrast, be remarkably brilliant. Mrs. B. Certainly. There are several things to be observed in regard to the form and extent of sha- dows. If the luminous body A (fig. 3.) is larger than the opaque body B, the shadow will gradually di- minish in size, till it terminate in a point. Caroline. This is the case with the shadows of the earth and the moon, as the sun which illumines them is larger than either of those bodies. And why is it not the case with the shadows of terrestrial objects, which are equally illumined by tffe sun ? but their shadows, far from diminishing, are always larger than the object, and increase with the dis- tance from it. Mrs. B. In estimating the effect of shadows, we must consider the apparent not the real dimensions of the luminous body ; and in this point of view, the sun is a small object compared with the generality of the terrestrial bodies which it illumines : and when the luminous body is less than the opaque body, the shadow will increase with the distance to infinity. All objects, therefore, which are apparently larger than the sun, cast a maccnified shadow. This will 17* 198 ON OPTICA. be best exemplified, by observing the shadow oi au object lighted by a candle. Emily. I have often noticed, that the shadow of my figure against the wall, grows larger as it is more distant from me, which is owing, no doubt, to the can- dle that shines on me being much smaller than my- self? Mrs. B. Yes. The shadow of a figure A, (fig. 4,) varies in size, according to the distance of the several surfaces B C D E, on which it is described. Caroline. 1 have observed, that two candles pro- duce two shadows from the same object ; whilst it would appear, from what you said, that they should rather produce only half a shadow, that is to say, a very faint one. Mrs. B. The number of lights (in different direc- tions) while it decreases the intensity of the sha- dow, increases their number, which always corres- ponds with that of the lights ; for each light makes the opaque body cast a different shadow, as illustrated by figure 5. It represents a ball A, lighted by three candles B, C, D, and you observe the light B pro- duces the shadow 6, the light C the shadow c, and the light D the shadow d. Emily. I think we now understand the nature of shadows very well ; but pray what becomes of the rays oi^ light which opaque bodies arrest in their course, and the interruption of which is the occasion of shadows ? Mrs. B. Your question leads to a very important property of light. Reflection. When rays of light encounter an opaque body, which they cannot tra- verse, part of them are absorbed by it, and part are leflected, and rebound just as an elastic ball which is struck against a wall. Emily. And is light in its reflection governed by the same laws as solid elastic bodies ? Mrs. B. Exactly. If a ray of light fall perpendi- eularly on an opaque body, it is reflected back in the same line, towards the point whence it proceeded. ON OPTICSi 191* If it fall obliquely, it is reflected obliquely, but in the opposite direction ; the angle of incidence being equal to the angle of reflection. You recollect that law in mechanics ? Emily. Oh yes, perfectly, Mrs. B. If you will shut the shutters, we shall admit a ray of the sun's light through a very small aperture, and I can show you how it is reflected, i now hold this mirror, so that the ray shall fall per- pendicularly upon it. Caroline. I see the ray which falls upon the mir- ror, but not that which is reflected by it. Mrs. B. Because its reflection is directly retro- grade. The ray of incidence and that of reflection both being in ti»e same line, though in opposite direc- tions, are confounded together. Emily. The ray then which appears to us single, is really double, and is composed of the incident ray proceeding to the mirror, and of the reflected ray re- turning from the mirror. Mrs. B. Exactly so. We shall now separate them, by holding the mirror M, (fig. 6,) in such a manner, that the incident ray A B shall fall obliquely upon it — you see the reflected ray B C, is marching off" in another direction. If we draw a line from the point of incidence B, perpendicular to the mirror, it will divide the angle of incidence from the angle of re- flection, and you will see that they are equal. Emily. Exactly ; and now that you hold the mir- ror so, that the ray falls more obliquely on it, it is also reflected more obliquely, preserving the equality of the angles of incidence and reflection. Mrs. B. It is by reflected rays only that we see opaque objects. Luminous bodies send rays of light immediately to our eyes, but the rays which they send to other bodies are invisible to us, and are seen only when they are reflected or transmitted by those bodies to our eyes. Emily. But have we not just seen the ray of light in its passage from the sua to the mirror^ and its re- 200 ON OPTICS. flection ? yet in neither case were those rays in a di- rection to enter our eyes. Mrs. B. No. What you saw was the light reflect- ed to your eyes by small particles of dust floating in the air, and on which the ray shone in its passage to and from the mirror. Caroline. Yet I see the sun shining on that house yonder, as clearly as possible. Mrs. B. Indeed you cannot sec a single ray which passes from the sun to the house ; you see no rays but those whicli enter your eyes ; therefore it is the rays which are reflected by the house to you, and not those which proceed from tlie sun to the house, that are visible to you. Caroline. Why then does one side of the house appear to be in sunshine, and the other in the shade ? for if I cannot see the sun shine upon it, the whole of the house should appear in the shade. Mrs. B. That side of the house which the sun shines upon, reflects more vivid and luminous rays than the side which is in shadow, for the latter is illu- mined only by rays reflected upon it by other objects, these rays are therefore twice reflected before they reach your sight ; and as light is more or less absorb- ed by the bodies it strikes upon, every time a ray is reflected its intensity is diminished. Caroline. Still I cannot reconcile myself to the idea, that we do not see the sun's rays shining on ob- jects, but only those which objects reflect to us. Mrs. B. I do not, however, despair of convincing you of it. Look at that large sheet of water, can you tell me why the sun appears to shine on one part of it only ? Caroline. No, indeed ; for the whole of it is equal- ly exposed to the sun. This partial brilliancy of wa- ter has often excited my wonder ; but it has struck me more particularly by moonlight. I have fre- quently observed a vivid streak of moonshine on the sea, while the rest of the water remained in deep obscurity, and yet there was no apparent obstacle to ON OPTICS. 201 prevent the moon from shining on every part of the water equally. Mrs. B. By moonlight the effect is more remark- able, on account of the deep obscurity of the other parts of the water ; while by the sun's light the ef- fect is too strong for the eye to be able to contem*- plate it. Caroline, But if the sun really shines on every part of that sheet of water, why does not every part of it reflect rays to my eyes ? Mrs. B. The reflected rays are not attracted out of their natural course by your eyes. The direction of a reflected ray, you know, depends on that of the incident ray ; the sun's rays, therefore, which fall with various degrees of obliquity upon the water, are reflected in directions equally various ; some of these will meet your eyes, and you will see them, but those which fall elsewhere are invisible to you. Caroline. The streak of sunshine, then, which we now see upon the water, is composed of those rays which by their reflection happen to fall upon my eyes ? Mrs. B. Precisely. Emily. But is that side of the house yonder, which appears to be in shadow, really illumined by the sun, and its rays reflected another way ? Mrs. B. No ; that is a diff'erent case from the sheet of water. That side of the house is really in shadow ; it is the west side, which the sun cannot shine upon till the afternoon. Emily. Those objects, then, which are illumined by reflected rays, and those which receive direct rays from the sun, but which do not reflect those rays to- wards us, appear equally in shadow ? Mrs. B. Certainly ; for we see them both illu- mined by reflected rays. That part of the sheet of water, over which the trees cast a shadow, by what light do you see it ? Emily. Since it is not by the sun's direct rays, it 202 ON OPTICS. must be by those reflected on it from other objects, and which it again reflects to us. Caroline. But if we see all terrestrial objects by reflected light, (as we do the moon,) why do they ap- pear so bright and luminous ? 1 should have suppos- ed that reflected rays would have been dull and faint, like those of the moon. Mrs. B. The moon reflects the sun's light with as much vividness as any terrestrial object. If you look at it on a clear night, it will appear as bright as a sheet of water, the walls of a house, or any object seen by daylight, and on which the sun shines. The rays of the moon are doubtless feeble, when compar- ed with those of the sun ; but that would not be a fair comparison, for the former are incident, the lat- ter reflected rays. Caroline. True ; and when we see terrestrial ob- jects by moonlight, the light has been twice reflected, and is consequently proportionally fainter. Mrs. B. In traversing the atmosphere, the rays, both of the sun and moon, lose some of their light. ^ For though the pure air is a transparent medium, which transmits the rays of light freely, we have ob- served, that near the surface of the earth it is loaded with vapours and exhalations, by which some portion of them are absorbed. Caroline. I have often noticed, that an object oq the summit of a hill appears more distinct than one at an equal distance in a valley, or on a plain ; which is owing, I suppose, to the air being more free from va- pours in an elevated situation, and the reflected rays being consequently brighter. Mrs. B. That may have some sensible effect ; but when an object on the summit of a hill has a back ground of light sky, the contrast with the object makes its outline more distinct. Caroline. I now feel well satisfied, that we see opaque objects only by reflected rays ; but I do not understand how these rays show us the objects from which they proceed ? ON OPTICS. 203 Mrs, B. The rays of li^ht enter at the pupil of the eye, and proceed to the retina, or optic nerve, which is situated at the back part of the eye-ball ; and there they describe the (isjure, colour, and (ex- cepting size) form a perfect representation of the ob- ject from which they proceed. We shall again dose the shutters, and admit the light through the small aperture, and yo ; will see a picture on the wall, op- posite the ap«*rture, similar to that which is delinea- ted on the retina of the eye. Caroline. Oh, how wonderful! There is an exact picture in miniature of the garden, the gardener at work, the trees blown about by the wind. The landscape would be perfect, if it were not reversed ; the ground being ab )ve. and the sky beneath. Mrs. B. Is it not enough to admire, you must un- derstand this phenomenon, which is called a camera obscura, from the necessity of darkening the room, in order to exhibit it. This picture is produced by the rays of light re- flected from the various objects in the garden, and which are admitted through the hole in the window- shutter. The rays from the glittering weathercock at the top of the alcove A, (Plate XVI. fig. 1.) represent it in this spot a; for the weathercock being much higher than the aperture in the shutter, only a few of the rays, which are reflected by it in an obliquely de- scending direction, can find entrance there. The rays of light, you know, always move in straight lines ; those, therefore, which enter the room in a descending direction, will continue their course in the same direction, and will, consequently, fall upon the lower part of the wall opposite the aperture, and represent the weathercock reversed in that spot, in- stead of erect in the uppermost part of the landscape. Emily. And the rays of light from the steps (B) of the alcove, in entering the aperture, ascend, and will describe those steps in the highest instead of the lowest part of the landscape. 204 ©N OPTICS. Mrs. B. Observe, too, that the rays coming from the alcove, which is to our left, describe it on the wall to the right ; while those which are reflected by the walnut-tree C D, to our right, delineate its figure in the picture to the left, c d. Thus the rays, cona- ing in different directions, and proceeding always in right lines, cross each other at their entrance through the aperture: those which come above proceed be- low, those from the right go to the left, those from the left towards the right ; thus every object is re- presented in tlie picture, as occupying a situation the very reverse of that which it does m nature. Caroline. Excepting the flower-pot E F, which, though its position is reversed, has not changed its situation in the landscape. Mrs. B. The flower-pot is directly in front of the aperture ; so that its rays fall perpendicularly upon it, and, consequently, proceed perpendicularly to the wall, where they delineate the object directly behind the aperture. Emily. And is it thus that the picture of objects is painted on the retina of the eye ? Mrs. B. Precisely. The pupil of the eye, through wliich the rays of light enter, represents the aperture in the window-shutter ; and the image deli-r neated on the retina, is exactly similar to the picture on the wall. Caroline. You do not mean to say, that we see only the representation of the object which is painted oq the retina, and not the object itself? Mrs. B. If, by sight, you understand that sense by which the presence of objects is perceived by the mind, through the means of the eyes, we certainly see only the image of those objects painted on the retina. Caroline. This appears to me quite incredible. Mrs. B. The nerves are the only part of our frame capable of sensation : they appear, therefore^ to be the instruments which the mind employs in its perceptions : for a sensation always conveys an idea J'LATE. JCVI. /h A / ^ H \ \ ON OPTICS. 205 to the mind. Now it is known, that our nerves can be affected only by contact ; and for this reason the organs of sense cannot act at a distance : for instance, we are capable of smelling only particles which are actually in contact with the nerves of the nose. We have already observed, that the odour of a flower consists in etfluvia, composed of very minute particles, which penetrate the nostrils, and strike upon the ol- factory nerves, which instantly convey the idea of smell to the mind. Emily. And sound, though it is said to be heard at a distance, is, in fact, heard only when the vibrations of the air, which convey it to our ears, strike upon the auditory nerve. Caroline. There is no explanation required, to prove that the senses of feeling and of tasting are ex- cited only by contact. Mrs. B. And I hope to convince you, that the sense of sight is so likewise. The nerves, which constitute the sense of sight, are not different in their nature from those of the other organs ; they are merely instruments which convey ideas to the mind, and can be affected only on contact. Now, since real objects cannot be brought to touch the optic nerve, the image of them is conveyed thither by the rays of light proceeding from real objects, which actually strike upon the optic nerve, and form that image which the mind perceives. Caroline. While I listen to your reasoning, I feel convinced ; but when I look upon the objects around, and think that I do not see them, but merely their image painted in my eyes, my belief is again stagger- ed. I cannot reconcile myself to the idea, that 1 do not really see this book which I hold in my hand, nor the words which I read in it. Mrs. B. Did it ever occur to you as extraordina- ry, that you never beheld your own face ? Caroline. No ; because I so frequently see an ex- act representation of it in the looking-glass. v¥r ON THE ANGLE OF VISION. "213 pear to have moved with equal velocity : because they will both have gone through an equal number of degrees, though over a very unequal length of ground. Sight is an cxtremel}^ useful sense no doubt, but it cannot always be relied on, it deceives us both in regard to the size and the distance of objects ; in- deed our senses would be very liable to lead us into error, if experience did not set us right. Emily. Between the two, I think that we contrive to acquire a tolerably accurate idea of objects. Mrs. B. At least sufliciently so for the general purposes of life. To convince you how requisite experience is to correct the errors of sight, 1 shall relate to you the case of a young man who was blind from his infancy, and who recovered his sight at the age of fourteen, by the operation of couching. At first, he had no idea either of the size or distance of objects, but imagined that every thing he saw tough- ed his eyes ; and it was not till after having repeated- ly felt them, and walked from one object to another» that he acquired an idea of their respective dimen- sions, their relative situations, and their distances. Carolina/, The idea that objects touched his eyeS is, however, not so absurd as it at first appears ; for if we consider that we see only the image of objects, this image actually touches our eyes. Mrs. B. That is doubtless the reason of the opi- nion he formed, before the sense of touch had cor- rected his judgment. Caroline. But since an image must be formed on the retina of each of our eyes, why do we not see objects double ? Mrs. B. The action of the rays on the optic nerve of each eye is so perfectly similar, that they produce but a single sensation, the mind therefore receives the same idea, from the retina of both eyes, and conceives the object to be single. Caroline. This is difficult to comprehend, and, I should think, can be but conjectural. Mrs. B. I can easily convince you, that you have 214 ON THE ANGLE er VISION. a distinct image of an object formed on the retina of each eye. Look at the bell-rope, and tell me, do you see it to the right or the left of the pole of the fire- skreen ? Caroline. A little to the right of it. Mrs. B. Then shut your right eye, and you will see it to the left of the pole. Caroline. That is true indeed ! Mrs. B. There are evidently two representations of the bell-rope in different situations, which must be owing to an image of it being formed on both eyes ; if the action of the rays therefore on each retina were not so perfectly similar as to produce but one sensa- tion, we should see double, and we tind that to be the case with many persons who are afflicted with a dis- ease in one eye, which prevents the rays of light from affecting it in the same manner as the other. Emily' Pray, JMrs. B., when we see the image of an object in a looking-glass, why is it not inverted as in the camera obscura, and on the retina of the eye ? Mrs. B. Because the rays do not enter the mirror by a small aperture, and cross each other, as they do at the orifice of a camera obscura, or the pupil of the eye. When you view yourself in a mirror, the rayS from your eyes fall perpendicularly upon it, and are reflected in the same line ; the image is therefore described behind the glass, and is situated in the same manner as the object before it. Emily. Yes, I see tiiat it is ; but the looking-glass is not nearly so tall as I am, how is it therefore that I can see the whole of my figure in it ? Mrs. B. It is not necessary that the mirror should be more than half your height, in order that you may 8ee the whole of your person in it, (fig. 3.) The ray of light C D from your eye, which falls perpen- dicularly on the mirror B D, will be reflected back in the same line ; but the ray from your feet will fall obliquely on the mirror, for it must ascend in or- der to reach it j it will therefore be reflected in the ON THE ANGLE GF VISION. . 21i5 line D A : and since we view objects in the direc- tion of the reflected rays, which reach the eye, and that the image appears at the same distance behind the mirror that the object is before it, we must con- tinue the line A D to E, and the line C D to F, at the termination of which the image will be represented. Emily. Then I do not understand why I should not see the whole of my person in a much smaller mirror, for a ray of light from my feet would always reach it, though more obliquely. Mrs, B. True ; but the more obliquely the ray falls on the mirror, the more obliquely it will be re- flected ; the ray would therefore be reflected above your head, and yon could not see it. This is shown by the dotted line (fig. 3.) Now stand a little to the right of the mirror, so that the rays of light from your figure may fall ob- liquely on it Emily. There is no image formed of me in the glass now. Mrs. B. I beg your pardon, there is ; but you cannot see it, because the incident rays falling ob- liquely on the mirror will be reflected obliquely in the opposite direction, the angles of incidence and of reflection being equal. Caroline, place yourself in the direction of the reflected rays, and tell me whe- ther you do not see Emily's image in the glass ? Caroline. Let me consider. — In order to look v». the direction of the reflected rays, I must place n^^ ' self as much to the left of the glass as Emily stanusto the right of it. — Now 1 see her image, but it is not straight before me, but before her ; and appears at the same distance behind the glass, as she is in front of it. Mrs. B. You must recollect, that we always see objects in the direction of the last rays which reach our eyes. Figure 4. represents an eye looking at the image of a vase, reflected by a mirror ; it must see it in the direction of the ray A B, as that is the raj" 216 ON THE ANGLE OF VISION. which brings the image to the eye ; prolong the ray to C, and in that spot will the image appear. Caroline, I do not understand why a looking-glass reflects the rays of light ; for glass is a transparent body, which should transmit them ? J\irs. B. It is not the glass that reflects the rays which form the image you behold, but the mercury behind it. The glass acts chiefly as a transparent case, through which the rays find an easy passage. Caroline, Why then should not mirrors be made simply of mercury ? Mrs. B, Because mercury is a fluid. By amal- gamating it with tin-foil, it becomes of the consistence of paste, attaches itself to the glass, and forms in fact a mercurial mirror, which would be much more perfect without its glass cover, for the purest glass is never perfectly transparent : some of the rays therefore are lost during their passage through it, by being either absorbed, or irregularly reflected. This imperfection of glass mirrors has introduced the use of metallic mirrors, for optical purposes. Emily. But since all opaque bodies reflect the rays of light, I do not understand why they are not all mirrors ? Caroline. A curious idea indeed, sister ; it would be very gratifying.to see one's self in every object at which one looked. Mrs. B, It is very true that all opaque objects re- S*\^t light ; but the surface of bodies in general is so rough and uneven, that their reflection is extremely irregular, which prevents the rays from forming an image on the retina. This you will be able to under- "stand better, when I shall explain to you the nature of vision, and the structure of the eye. You may easily conceive the variety of directions in which rays would be reflected by a nutmeg-grater, on account of the inequality of its surface, and the number of holes with which it is pierced. All solid bodies resemble the nutmeg-grater in these respects, more or less ; and it is only those which are suscep- PLATE, xvnr. ON THE ANGLE OF VISION. S"! 7 tible of receiving a polish, that can be made to reflect the rays with regularity. As hard bodies are of the closest texture, the least porous, and capable of taking the highest polish, they make the best mirrors ; none, therefore, are so well calculated for this pur- pose as metals. Caroline. But the property of regular reflection is not confined to this class of bodies ; for 1 have of- ten seen myself in a highly polished mahogany table. Mrs. B. Certainly ; but as that substance is less durable, and its reflection less perfect, than that of metals, 1 believe it would seldom be chosen for the purpose of a mirror. There are three kinds of mirrors used in optics ; the plain or flat, which are the common mirrors we have just mentioned ; convex mirrors ; and concave mirrors. The reflection of the two latter is very dif- ferent from that of the former. The plain mirror, we have seen, does not alter the direction of the re- flected rays, and forms an image behind the glass exactly similar to the object before it. A convex mirror has the peculiar property of making the re- flected rays diverge, by which means it diminishes the image ; and a concave mirror makes the rays con- verge, and, under certain circumstances, magnifies the image. Eiriily. We have a convex mirror in the drawing room which forms a beautiful miniature picture of the objects in the room ; and I have often amused myself with looking at my magnified face in a concave mirror. But 1 hope you will explain to us why the one enlarges, while the other diminishes the objects it reflects. Airs. B. Let us begin by examining the reflection of a convex mirror. This is formed of a portion of the exterior surface of a sphere. When several pa- rallel rays fall upon it, that ray only which, if pro- longed, would pass through the centre or axis of the mirror, is perpendicular to it. In order to avoid con- fusion, 1 have, in fig. 1. Plat6 XVUl., drawn only 19 218 ON THE ANGLE OF VISION. three parallel lines, A B, C D, E F, to represent rays falling on the convex mirror M N ; the middle ray, you will observe, is perpendicular to the mirror, the others fall on it obliquely. Caroline. As the three rays are parallel, why are they not all perpendicular to the mirror ? Mrs. B. They would be so to a flat mirror ; but as this is spherical, no ray can fall perpendicularly upon it which is not directed towards the centre of the sphere. Emily. Just as a weight falls perpendicularly to the earth when gravity attracts it towards the centre. Mrs. B. In order, therefore, that rays may fldl perpendicularly to the mirror at B and F, the rays must be in the direction of the dotted lines, which, you may observe, meet at the centre O of the sphere, of which the mirror forms a portion. Now can you tell me in what direction the three rays, A B, C D, E F, will be reflected ? Emily. Yes, I think so; the middle ray falling perpendicularly on the mirror, will be reflected in the same line: the two others falling obliquely, will be reflected obliquely to G H ; for the dotted lines you have drawn are perpendiculars, which divide their angles of incidence and reflection. Mrs. B. Extremely well, Emily : and since we see objects in the direction of the reflected ray, we shall see the image at L, which is the point at which the reflected rays, if continued through the mirror, would unite and form an image. The point is equally distant from the surface and centre of the sphere, and is called the imaginary focus of the mirror. Caroline. Pray, what is the meaning of focus ? Mrs. B. A point at which converging rays unite. And it is in this case called an imaginary focus ; be- cause the rays do not really unite at that point, but only appear to do so : for the rays do not pass through the mirror, since they are reflected by it. Emily. I do not yet understand why an object ap- pears smaller when viewed in a convex mirror. O-V THE ANGLE OF TISION. 219 J\Irs. B. It is owing to the divergence of the re- flected rays. You Avdve seen that a convex mirror converts, by reflection, parallel rays into divergent rays ; rays that fall upon the mirror divergent, are rendered still more so by reflection, and convergent rays are reflected either parallel, or less convergent. If then an object be placed before any part of a con- vex mirror, as the vase A B, fig. 2. for instance, the two rays from its extremities, falling convergent on the mirror, will be reflected less convergent, and will not come to a locus till they arrive at C ; then an eye placed in the direction of the reflected rays will see the image formed in (or rather behind) the mirror at a b. Caroline. But the reflected rays do not appear to me to converge less than the incident rays. I should have supposed that, on the contrary, they converged more, since they meet in a point ? Mrs. B. They would unite sooner than they actu- ally do, if they were not less convergent than the in- cident rays : for observe, that if the incident rays, ia- Etead of being reflected by the mirror, continued their course in their original direction, they would come to a focus at D, which is considerably nearer to the mirror than at C ; the image is therefore seen under a smaller angle than the object ; and the more dis- tant the latter is from the mirror, the less is the image reflected by it. You wiH now easily understand the nature of the reflection of concave mirrors. These are formed of a portion of the internal surface of a hollow sphere, and their peculiar property is to converge the rays ©flight. Can you discover, Caroline, in what direction the three parallel rays, A B, C D, EF, which fall on the concave mirror M N, (fig. 3.) are reflected ? Caroline. I believe I can. The middle ray is sent back in the same line, as it is in the direction of the axis of the mirror ; and the two others will be reflected obliquely, as they fall obhquely on the mir- ^20 ON THE ANGLE OF VISION. ror. I must now draw two dotted lines perpendicu- lar to their points of incidence, which will divide their angles of incidence and reflection ; and in order that those angles may be equal, the two oblique rays must be reflected to L, where they will unite with the middle ray. Mrs, B. Very well explained. Thus you see, that when any number of parallel rays fall on a con- cave mirror, they are all reflected to a focus : for, in proportion as the rays are more distant from the axis af the mirror, they fall more obliquely upon it, and are more obliquely reflected ; in consequence of which they come to a focus in the direction of the axis of the mirror, at a point equally distant from the centre and the surface of the sphere, and this point is not an imaginary focus, as happens with the convex mirror, but is the true focus at which the rays unite. Emily. Can a mirror form more than one focus by reflecting rays ? Mrs. B. Yes. If rays fall convergent on a con- cave mirror, (fig. 4.) they are sooner brought to a focus, L, than parallel rays ; their focus is therefore nearer to the mirror M N. Divergent rays are brought to a more distant focus than parallel rays, as in figure 5, where the focus is at L ; but the true fo- cus of mirrors, either convex or concave, is that of parallel rays, which is equally distant from the cen- tre, and the surface of the sphere. I shall now show you the reflection of real rays of light, by a metallic concave mirror. This is one made of polished tin, which I expose to the sun, and fts it shines bright, we shall be able to collect the rays into a very brilliant focus. I hold a piece of paper where 1 imagine the focus to be situated ; you may see by the vivid spot of light on the paper, how much the rays converge : but it is not yet exactly in the focus ; as 1 approach the paper to that point, observe how the brightness of the spot of light increases, while its size diminishes. Caroline. That must be occasioned by the rays ON THE ANGLE OF VISION. 221 becoming closer together. I think ^-ou hold the pa- per just in the focus now, the light is so small and dazzling — Oh, Mrs. B., the paper has taken fire! Airs. B. The rays of light cannot be concentra- ted, without, at the same time, accumulating a propor- tional quantity of heat: hence concave mirrors have obtained the name of burning-mirrors. Emily. I have often heard of the surprising etfects of burning-mirrors, and I am quite dehghted to understand their nature. Caroline. It cannot be the true focus of the mir- ror at which the rays of the sun unite, for as they proceed from a point, they must fall divergent upon the mirror. Mrs. B. Strictly speaking, they certainly do. But when rays come from such an immense distance as the sun, their divergence is so trifling, as to be im- perceptible ; and they may be considered as parallel : their point of union is, therefore, the true focus of the mirror, and there the image of the object is re- presented. Now that I have removed the mirror out of the in- fluence of the sun's rays, if I place a burning taper in. the focus, how will its light be reflected ? (Fig. 6.) Caroline. That, I confess, I cannot say. Mrs. B. The ray which falls in the direction of the axis of the mirror, is reflected back in the same line ; but let us draw two other rays from the focus, falling on the mirror at B and F ; the dotted lines are perpendicular to those points, and the two rays will therefore be reflected to A and E. Caroline. Oh, now I understand it clearly. The rays which proceed from a light placed in the focus of a concave mirror fall div^ergent upon it, and are reflected parallel. It is exactly the reverse of the former experiment, in which the sun's rays fell pa- rallel on the mirror, and were reflected^ to a focus. Mrs. B. Yes : when the incident rays are paral- lel, the reflected rays converge to a focus ; when, odl the contrary, the incident rays proceed from the fo« 19* 222 ON THE ANGLE OF VISION* cus, they are reflected parallel. This is an impor- tant law of optics, and since you are now acquainted with the principles on which it is founded, I hope that you will not forget it. Caroline. I am sure that we shall not. But, Mrs. B., you said that the image was formed in the focus of a concave mirror ; yet I have frequently seen glass concave mirrors, where the object has been repre- sented within the mirror, in the same manner as in a convex mirror. Mrs. B. That is the case only when the object is placed between the mirror and its focus ; the image then appears magnified behind, or, as you call it, nvithin the mirror. Caroline. I do not understand why the image should be larger than the object. Mrs. B. It proceeds from the convergent properr ty of the concave mirror. If an object, A B, (fig. 7.) be placed between the mirror and its focus, the rays from its extremities fall divergent on the mirror, and on being reflected, become less divergent, as if they proceeded from C : to an eye placed in that situation the image will appear magnified behind the mirror ^t a b, since it is seen under a larger angle than the object. . You now, I hope, understand the reflection of light by opaque bodies. At our next meeting we shall enter upon another property of light, no less interest* ing, which is called refraction. CONVERSATION XVl: ON REFRACTION AND COLOURS. Transmission of Light by Transparent Bodies. — Re- fraction. — Refraction of the Atmosphere. — Refrac- tion of a Lens. — Refraction of the Prism. — Of the Colours of Rays of Light. — Of the Colours of Bodies. MRS. B. The refraction of light will furnish the •subject of to-day's lesson. Caroline. That is a property of which I have not the faintest idea. Mrs. B. It is the effect which transparent me- diums produce on light in its passage through them. Opaque bodies, you know, reflect the rays, and trans- parent bodies transmit them; but it is found, that if a ray, in passing from one medium into another of dif- ferent density, fall obliquely, it is turned out of its course. Caroline. It must then be acted on by some new- power, otherwise it would not deviate from its first direction. Mrs. B. The power which causes the deviation of the ray appears to be the attraction of the denser medium. Let us suppose the two mediums to be air and water ; if a ray of light passes from air into wa- ter, it is more strongly attracted by the latter on ac- count of its superior density. Emily, in what direction does the water attract- the ray ? Mrs. B. It must attract it perpendicularly towards it, Id the same manner as gravity acts on bodies. 224 THE REFRACTION OF LIGHT. If then a ray A B, (fig. 1. Plate XIX.) fall perpen- dicularly on water, the attraction of the water acts in the same direction as the course of the ray ; it will not therefore cause a deviation, and the ray will pro- ceed straight on to E. But if it fall obliquely, as the ray C B, the water will attract it out of its course. Let us suppose the ray to have approached the surface of a denser medium, and that it there begins to be af- fected by its attraction ; this attraction, if not counter- acted by some other power, would draw it perpen- dicularly to the water, at B ; but it is also impelled by its projectile force, which the attraction of the denser medium cannot overcome ; the ray, therefore, acted on by both these powers, moves in a direction between them, and instead of pursuing its original course to D, or being implicitly guided by the water to E, proceeds towards F, so that the ray appears bent or broken. Caroline, I understand that very well ; and is not this the reason that oars appear bent in water? Ah's. B. It is owing to the refraction of the rays reflected by the oar ; but this is in passing from a dense to a rave medium, for you know that the rays, by means of which you see the oar, pass from water into air. Emily. But I do not understand why a refraction takes place when a ray passes from a dense into a rare medium ; I should suppose that it would be ra- ther less, than more, attracted by the latter. Mrs, B. And it is precisely on that account that the ray is refracted. C B, fig. 2. represents a ray passing obliquely from glass into water : glass being the denser medium, the ray will be more strongly at- tracted by that which it leaves than by that which it enters. The attraction of the glass acts in the direc- tion A B, while the impulse of projection would carry the ray to F ; it moves, therefore, between these di- rections towards D. Emily. So that a contrary refraction takes place when a ray passes from a dense into a rare mediunk. a i a JHT a^lVTd T •%■ THE REFRACTION OF LIGHT. 22j Caroline. But does not the attraction of the denser medium affect the ray before it touches it ? Mrs. B. The distance at which the attraction of the denser medium acts upon a ray is so small as to be insensible ; it appears therefore to be refracted only at the point at which it passes from one medium to the other. Now that you understand the principle of refrac* tion, I will show you the refraction of a real ray of light. Do you see the flower painted at the bottom of the inside of this tea-cup ? (Fig. 3.) Emily. Yes. — But now you have moved it just out of sight, the rim of the cup hides it. Mrs. B. Do not stir. I will fill the cup with wa- ter, and you will see the flower again. Emily. I do indeed ! Let me try to explain this : when you draw the cup from me so «as to conceal the tiower, the rays reflected by it no longer met my eyes, but were directed above them ; but now that you have filled the cup with water, they are refracted by the attraction of the water, and bent downwards, so as again to enter my eyes. Mrs. B. You have explained it perfectly : fig. 3. will help to imprint it on your memory. You must observe that when the flower becomes visible by the refraction of the ray, you do not see it in the situation which it really occupies, but an image of the flower higher in the cup ; for as objects always appear to be situated in the direction of the rays which enter the eye, the flower will be seen in the direction of the reflected ray at B. Emily. Then, when we see the bottom of a clear stream, of water, the rays which it reflects being re- fracted in their passage from the water into the air, will make the bottom appear higher than it really is. Mrs. B. And the water will consequently appear more shallow. Accidents have frequently been oc- casioned by this circumstance ; and boys who are in the habit of bathing should be cautioned not to trust to the apparent shallowness of water, as it will always 226 THE REFRACTION OF LIGHT. prove deeper than it appears ; unless, indeed, they view it from a boat on the water, which will enable them to look perpendicularly upon it ; when the rays from the bottom passing perpendicularly, no refrac- tion will take place. The retraction of light prevents our seeing the heavenly bodies in their real situation : the light they send to us being refracted in passing into the atmos- phere, we see the sun and stars in the direction of the refracted ray ; as described in tig. 4. Plate XIX., the dotted line represents the extent of the atmos- phere, above a portion of the earth, E B E : a ray of light coming from the sun S, falls obliquely on it at A, and is refracted to B ; then, since we see the ob- ject in the direction of the refracted ray, a spectator at B will see an image of the sun at C, instead of the real object at S. Eiuily. But if the sun were immediately over our heads, its Fays, falling perpendicularly on the atmos- phere, would not be refracted, and we should then see the real sun in its true situation. Mrs. B. You must recollect that the sun is verti- cal only to the inhabitants of the torrid zone ; its rays, therefore, are always refracted in these cli- mates. There is also another obstacle to our seeing the heavenly bodies in their real situations : light, though it moves with extreme velocity, is about eight minutes and a half in its passage from the sun to the earth : therefore, when the rays reach us, the sun must have quitted the spot he occupied on their de- parture ; yet we see him in the direction of those rays, and consequently in a situation which he had abandoned eight minutes and a half before. Emily. When you speak of the sun's motion, you mean, I suppose, his apparent motion, produced by the diurnal motion of the earth. Mrs. B. No doubt; the effect being the same, whether it is our earth, or the heavenly bodies which move : it is more easy to represent things as they ap- pear to be, than as they really are. THE REFRACTION OF LIGHTS 227 Caroline. During the morning, then, when the sun is rising towards the meridian, we must rfrom the length of time the light is in reaching us) see an image of the sun below that spot which it really oc- cupies. Emily. But the refraction of the atmosphere coun- teracting this effect, we may perhaps, between the two, see the sun in its real situation. Caroline. And in the afternoon, when the sun is sinking in the west, refraction and the length of time which the light is in reaching the earth, will conspire to render the image of the sun higher than it really is* Mrs. B. The refraction of the sun's rays by the atmosphere prolongs our days, as it occasions our seeing an image of the sun, both before he rises and after he sets; for below the horizon, he still shines upon the atmosphere, and his rays are thence refract- ed to the earth. So likewise we see an image of the sun before he rises, the rays that previously fall upon the atmosphere being reflected to the earth. Caroline. On the other hand, we must recollect that light is eight minutes and a half on its journey ; so that, by the time it reaches the earth, the sun may perhaps be risen above the horizon. Emily. Pray do not glass windows refract the light. Mrs. B. They do ; but this refraction is not per- ceptible, because, in passing through a pane of glass the rays suffer two refractions, which being in contra- ry directions, produce the same effect as if no refrac- tion had taken place. Emily. I do not understand that. Mrs. B. Fig. b. Plate XIX. will make it clear to you : A A represents a thick pane of glass seen edge- ways. When the ray B approaches the glass at C, it is refracted by it ; and instead of continuing its course in the same direction, as the dotted line describes, it passes through the pane to D ; at that point returning into the air, it is again refracted by the glad's, but in a contrarv direction t© the first refraction, and in conse- 228 THE REFRACTION OF LIGHT. quence proceeds to E. Now you must observe that the ray B C and the ray D E being parallel, the ii^ht does not appear to have suffered any refraction. Emily So that the effect which takes place on the ray entering the glass, is undone on i s quitting it. Or, to express myself more scientifically, when a ray of light passes from one medium into another, an^^^ through that into the first again, the two refractiorfs being equal and in opposite directions, no sensible effect is produced. Mrs. B. Thi^ is the case when the two surfaces of the refracting medium are parallel to each other; if they are not, the two refractions may be made in the same direction, as 1 shall show you. When parallel rays (fig. 6.) fall on a piece of glass having a double convex surface, and wl)ich is called a Lens, that only which f tils in the direction of the axis of the lens is perpentlicular to the surface ; the other rays falling obliquely are refracted towards the axis, and will meet at a point beyond the lens, called its focus. Of the three rays, A B C, which fdl on the lens D E, the rays A and C are refracted in their passage through it, to a, and r, and on quitting the lens they undergo a second refraction in the same direction, which unites them with the ray B, at the focus F. Einilij. And what is the distance of the focus from the surface of the lens ? Mrs. B. The focal distance depends both upon the form of the lens, and of the refractive power of the substance of which it is made : in a glaes lens, both sides of wliich are equally convex, the focus is situated nearly at the centre of the sphere of which the sur- fiice of the lens forms a portion ; it is at the distance, therefore, of the radius of the sphere. There are lenses of various forms, as you will find described in fig. 1. Plate XX. The property of those which have a convex surface is to collect the rays of light to a focus ; and of those which have a concave surface, on the contrary, to disperse them. For the rays -%• ^■ PLATE. XT. m THE REFRACTION OF LIOHT# ' 2^ A C falling on the concave lens X Y, (fig. 7. Plate XIX.) instead of converging towards the ray B, wliicK falls on the axis of the lens, will each be attracted to- wards the thick edges of the lens, both on entering and quitting it, and will, therefore, by the first re- fraction, be made to diverge to a, c, and by the second to