*^«/^<«L— 7- ^„ . ->•.»% \ CONVERSATIONS OK IN WHICH THE ELEMENTS OF THAT SCIENCE ARE FAMILIARLY EXPLAINED, AND ADAPTED TO THE COMPREHENSION OF YOUNG PUPILS. ZZiI-VSTRATSB WZTH FZ.ATES. BT THE AUTHOR OF CONVERSATIONS ON CHEMISTRY, AND . CONVERSATIONS ON POLITICAL ECONOMY. IMPROVED BY APPROPRIATE QUESTIONS, FOR THE EXAMINATION OF SCHOLARS ; ALSO BY AND A DICTIONARY OF PHILOSOPHICAL TERMS. BY REV. J. L. BLAKE, A. M. Rector of St Matthew's Church, and Principal of a Literary Seminary, Boston, Mass. EIGHTH AMERICAN EDITION. fSonton : PRINTED AND PUBLISHED BY LINCOLN &. EDMANDS, No. 59, Washington-street, (53, Comhill.) STEREOTYPED BY T. H. CARTER & CQ. BOSTON. 1826. DISTRICT OF MASSACHUSETTS, fofot*.. District ClerVs Ofiet, BE IT REMEMBERED, that on the fourth day of December, A. D. 1824, in the forty-ninth year of the independence of the United States of Araericaj JOHN LAURIS BLAKE, of the said district, has deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : "Conversations on Natural Philosophy, in which the elements of that science •re familiarly explained, and adapted to the comprehension of young pupils. Illustrated with plates. By the author of Conversations on Chemistry, and Con- Tersations on Political Economy. Improved by appropriate Questions, for the examination of Scholars ; also by Illustrative Notes, and a Dictionary of Philoso- phical Terms. By J. L. BLAKE, A. M. Rector of St. Matthew's Church, and J*rincipal of a Literary Seminary, Boston, Mass." In Conformity to the Act of the Congress of the United States, entitled, " An Act for the encouragement of learning, by securing the copies 'of maps, charts^ and books, to the authors and proprietors of such copies during the times therein mentioned ;" and also to an Act, entitled " An Act supplementary to an Act, entitled An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during tha times therein mentioned; and extending the benefits thereof to the arts of de- sifoiog) engraving, and etehing historical, and other prints." TNO W nAVT<5 ^ Clerk of the District JNO. W. DAVIS, J of Massachusetts. PREFACE. The following work does not probably contain so much of th« science of Natural Philosophy as might be crowded into a volume of equal size, on some different plan. The author seems to have been influenced chiefly by other considerations ; and, in the opinion of the editor, with the most happy success. Mr^. Bryan did not profess to prepare a work suited to the highest stages of education. Her aim was to accommodate an important science to the literary taste and intellectual apprehensions of persons, within whose reach Natural Philosophy had not previously been placed — to accommo- date to the use of schools generally a science, wiiich had hitherto been considered too abstruse and uninteresting for any, whose minds had not been disciplined and invigorated by long and regu- lar habits of study. Instead of exhausting the intellectual ener- gies of youth in committing to memory definitions and roathemati- eal demonstrations, which would nat be understood, she proposed to illustrate the great principles of Natural Philosophy by compari- sons of the most familiar kind ; and, it is believed, Mrs. Bryan has done more, in this way, towards giving youth a taste for the study 0f philosophy than all others who have published treatises on the sub- ject. In her preface she remarks:*—" It is with increased diflSdence that the author offers this little work to the publick. The encou- raging reception which the Conversations on Chemistry and Politi- eal Economy have met with has induced her to venture on publish- ing a short course on Natural Philosophy. They are intended, in a course of elementary science, to precede the Conversations on Chemistry, and were actually written previous to either of her othef publications.** The Conversations on Natural Philosophy were introduced into the editor's Seminary about three years since, then at Concord, N. H.; but it was soon found that his pupils were often embar- rassed in not knowing to what particular parts they were chiefly to direct the attention, committing to memory what was not neces- sary and omitting what was, thereby causing great loss of time as well as of improvement. This induced him to prepare, as they were needed, day after day, Questions for their examination. When questions were thus prepared upon the whole work, it wa» judged expedient to hare them published in a pamphlet, which was accordingly done ; but being prepared in haste and without thought of their being published, they were of course imperfect j nor was there opportunity to revise them, when afterwards printed with notes in connexion with the work itself! But as successive f ditions were required, and as the demand is still increasing, he has been induced to revise and write them anew, placing them at the bottom of the several pages to which they relate ; and, also to in- •rease the number of Notes, and to add to the volume a Dictionary of Philosophical Terms. As the work is now presented to the publick, the Editor has full confidence in recommending it to Instructors, well persuaded it will lessen their own labour and facilitate the improvement of their pupils. It is perfectly obvious, that, instead of embodying, the questions at the close of the book, as in former impressions great convenience will be found, both by instructors and scholars, in having them printed on the pages from which they are to be an- swered ; nor is the 1? Jour of finding the answers to be given so les- sened, as to enable scholars to select those answers without read- ing and studying the whole book. . It has been thought best to place the Plates at the end of the volume. If interspersed throughout the work, as in former edi- tions, it is evident that no more than one page could face eack Plate, while a very considerable number of pages would have re- ference to it, BO that the object contemplated could only in a smali degree be accomplished. Besides, it is judged advisable by the editor, that the plates should not face the explanations in the Text if practicable. Many of the Questions are to be answered from the Plates ; but if the several Plates were placed opposite the different portions of the work to which they relate, the answers might be read from the explanations there given instead of being^^ recited from the figures as intended. J. L. BLA&E. Boston, December f 1824. CONTENTS- CONVERSATION L On General Properties of Bodies, Introduction ; General Properties of Bodies ; Impenetrability; Extension ; Figure ; Divisibility ; Inertia ; Attraction ; Attrac- tion of Cohesion ; Density ; Rarity ; Heat ; Attraction of Gra- vitation. Page 9. 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. Page 24. CONVERSATION III. On the haws of Motion, Of Motion ; Of the Inertia of Bodies ; Of Force to produce Mo- tion ; Direction of Motion ; Velocity, absolute and relative ; Uniform Motion ; Retarded Motion ; Accelerated Motion ; Ve- locity of Falling Bodies ; Momentum ; Action and Re-action equal; Elasticity of Bodies ; Porosity of Bodies ; Reflected Mo- tion ; Angles of Incidence and Reflection. Page 36. CONVERSATION IV. On Compound Motion. Compound Motion the result of two opposite forces; Of Circular Motion, the result of two forces, one of which confines the body to a fixed point ; Centre of Motion, the point at rest while the other parts of the body move round it ; Centre of Magnitude the middle of a body ; Centripetal Force, that which confines A body to a fixed central point ; Centrifugal Force,that v/hich im- pels 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. Page 51. I * yi CONTENTS. CONVERSATION V. On the Mechanical Powers, Of the Power of Machines ; Of the Lever in general ; Of the Le- ver of the first kind, having the Fulcrum betv/een 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, Pages 60, 68. 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. Page 7&. CONVERSATION VII. On the Planets. Of the Satellites or Moons ; Gravity diminishes as the square of the Distance; Of the Solar System; Of Comets; Constellations^ sjgne of the Zodiack ; Of Copernicus, Newton, &c. Page 9&, CONVERSATION VIII. On the Earth. Of the Terrestrial Globe ; Of the Figure of the Earth ; Of the pendulum ; Of the Variation of the Seasons j and of the Length of Days and Nights ; Of the causes of the Heat of Summer j Of Soikr^ Siderial, and Equal or Mean Time. Page 102. 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 Longi- tude ; Of the transits of the inferior Planets ; Of the Tides. Page 124. CONTENTS. VU CONVERSATION X. HYDROSTATICKS. 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 Equi- librium : Of their Pressure ; Of Specifick Gravity ; Of the Specifick Gravity of Bodies heavier than Water ; Of those of the same weight as Water ; Of those lighter than Water ; Of the Specifick Gravity of Fluids. Page 137. CONVERSATION XL Of Springs, Fountains^ 8^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. Page 159. CONVERSATION XIL PNEUMATICKS. 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 ; Descrip- tion of the Sucking Pump ; Description of the Forcing Pump. Page 158. CONVERSATION XIIL On Wind and Sound. Of Wind in General; Of the Trade Wind; Of the Periodical Trade Winds ; Of the Aerial Tides ; Of Sound in General ; Of Sonorous Bodies ; Of Musical Sounds ; Of Concord or Har- mony, and Melody. Page 170. CONVERSATION XIV. On Optics. Of Luminous, Transparent, and Opaque Bodies ; Of the Radiation of Light ; Of Shadows ; Of the Reflection of Light ; Opaque Bodies seen only by Reflected Light ; Vision Explained ; Ca- mera Obacura ; Image of Objects on the Retina. Page 183 ▼Ui CONTENTS. CONVERSATION XV. On the Angle of Vision, and Reflection of Mirrors. Angle of Vision ; Reflection of Plain Mirrors ; Reflection of Con- vex Mirrors ; Reflection of Concave Mirrors. Page 197. CONVERSATION XVI. On Refraction and Colours. Transmission of Light by Transparent Bodies ; Refraction ; Re- fraction of the Atmosphere ; Refraction of a Lens ; Refraction of the Prism ; Of the Colours of Rays of Light ; Of the Colours of Bodies. Page 211 CONVERSATION XVIL OPTICKS. On the Structure of the Eye, and Optical Instruments. Description of the Eye ; Of the Image on the Retina ; Refraction of the Humours of the Eye ; Of the Use of Spectacles ; Of the Single Microscope ; Of the Double Microscope ; Of the Solar Microscope ; Magick Lantern ; Refracting Telescope ; Reflect- ing Telescope. Page 229. A Dictionary of Philosophical Terms. Page IMl. Directitm to the Binder. The Plates, with the exception of the FrontispieGC, which is to face the Title Page, to be put at the close of the volume, in their order of being numbered. CONVERSATION L ON GENERAL PROPERTIES OF BODIES. Introduction ; General Properties of Bodies ; Impentf trability ; Extension ; Figure ; Divisibility ; Inertia ; Attraction; Attraction of Cohesion; Density; Rarity ; Heat ; Attraction of Gravitation* EMILY. I MUST request your assistance, my dear Mrs. B. in a charge which I have lately undertaken ; it is that of in- structing my youngest sister, a task, which 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 diffi- culty that occurs to her, and frequently asks me questions which I am at a loss to answer. This morning, for in- stance, when I had explained to her that the world was round like a ball, instead of being flat as she had suppos- ed, and that it was surrounded by the air, she asked me what supported it. I told her that it required no sup- port ; 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 unnatural it was that sjj heavy a body, bearing the weight of all other things, should be able to support itself. Mrs. J5. I make no doubt, my dear, but that I shall be able to explain this difficulty to you ; but I believe that it would be almost impossible to render it intelligible to the comprehension of so young a child as your sister Sophia. You, who are now in your thirteenth 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. 10 GENERAL PROPERTIES OF BODIES. Mrs, B. Not whon familiarly explained ; if you have patience to attend, I will most willingly give you all the information in my power. You may perliaps find the f^ubject 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 ntady. Emily, I make no doubt of it, Mrs. B. ; and pray begin by explaining why the earth requires no support ; for that is the point which just now most strongly excites my curiosity. Mrs, B, My dear Emily, if I am to attempt to give yciW a general idea of the laws of nature, which is no less than to intro^ace you to a knowledge of the science of natural philosophy, it will be necessary for us to proceed with some de^rroe of regularity. I do not wish to confine you to the systematic order of a scientific treatise ; but if we were merely to examine every vague question that may chance to occur, our progress would be but very slow. Let us, therefore, begin by taking a short survey of the general properties of bodies, some of which must necessa- rily be explained before I can attempt to make you under- stand why 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 ge- neral term used to denote the substance, whatever its nature be, of which the different bodies are composed. Thus, wood is the matter of which this table is made ; water is the matter with which this glass is filled, &c. Emily, I am very glad you have explained the mean- ing of the word matter, as it has corrected an erroneous conception I had formed of it ; I thought that it was ap- plicable to solid bodies only. Mrs, B, There are certain properties which appear to be common to all bodies, and are hence called the e5- sential properties of bodies ; these are. Impenetrability, Extension^ Fi^ure^ Divisibility^ Inertia, and Attraction, These are called the general properties of bodies, as we do not suppose any body to exist without them. 1. What is to be understood by the term bodies, as used in phi- losophy ? 2. Wliat term is used to denote substances ? 3. What properties are common to all bodies ? 4. Why are these called general properties of bodies ? GENERAL PROPERTIES OF BODIES. 11 By impenetrahility ^ is meant the property which bodies have of occupying a certain space, so that, where one body is, another cannot be, without displacing the for- mer ; for two 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. I 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 ea- sily displaced. Mrs. B. The air is a fluid differing in its nature from liquids, but no less impenetrable. If I endeavour to fill this phial by plunging it into this bason 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 «xist together in the same space, any more than two hard bodies ; and if I reverse this goblet, and plunge it per- pendicularly into the water, so that the air will not be able to escape, the water will no longer be able to fill the goblet. Emily. But it rises a considerable way into the glass. Mrs. B. Becn.use 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 occu- py the same place. Emily. A difficulty has just occurred to me, with re- gard to the impenetrability of solid bodies ; if a nail is driven into a piece of trood, it penetrates it, and both the wood and the nail occupy the same space that the wood alone did before. 31rs. B. The nail penetrates between the particles of the wood, 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 wood is not increased in size by the addition of the nail, it is because wood is a porous substance, like sponge, the particles of 5. What is impenetrability ? 6. Can liquids occupy the same space of a solid body ?- 7. How can you prove that they cannot occupy the same space occupied by solids ? 8. Can hit quids and air occupy the same space in the same time ? 9. How would you prove that they cannot ? 12 GENERAL PROPERTIES OF BODIES. 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 of bodies, extension, A body which occupies a certain space must necessarily have extension ; that is to say, length, breadth, and depth ; these are called the dimen- sions of extension ; can you form an idea of any body without them ? Emily, No : certainly I cannot ; though these dimen- sions must, of course, vary extremely in different bodies. The length, breadth, and depth, of a box, or of a thimble, are very different from those of a walking-stick, 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 would have enabled me to discover that ; and breadth and width are also the same dimension. Mrs, B, Yes ; the limits of extension constitute fi- gure or shape. You conceive that a body having length, breadth, and depth, cannot be without form, either sym- metrical or irregular. Emily, Undoubtedly ; and this property admits of al- most an infinite variety. Mrs, B, Nature has assigned regular forms to her productions in general. The natural form of mineral sub- stances 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 natural history. The vege- table and animal creation appears less symmetrical, but is still more diversified in figure than the mineral kingdom. 10. What is meant by extension ? 11. What is the differ- ence between height and depth as applied to extension .'* 12 What is the figure of a body ? 13. What forms has nature, in general, given to her productions ^•^ 14. What is said of mine ral substances ? 15. How does the vecetable and animal ere ation compare with the mineral kingdom ? ffENERAL PROPERTIES OF BOIilES. 13 Manufactured substances assume the various arbitrary forms which the art of man designs for them ; and an in- finite number of irregular forms are produced by frac- tures, 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 eifect of torrents and other causes. The picturesque ef- fect of rock-scenery is in a great measure owing to acci- iiental irregularities of this kind. We may now proceed to dunsihiiitij ; tliat is to say, a susceptibility of being divided into an indefinite number of parts. Take any small quantity of matter, a grain of sand for instance, and cut it into tw^o parts ; these two parts might be again divided, had v/e instruments sufficiently fine for the purpose ; and if, by means of pounding, grind- ing and other similar methods, 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 destroyed, and the body will continue to exist, though in this altered state. The melting of a solid body in a liquid affords a very striking example of the extreme divisibility of matter ; when you sweeten a cup of tea, for instance, with what minuteness the sugar must be divided to be diffused throughout the whole of the liquid. 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 laven- der water will be almost as instantaneously diffused throughout the room, if I take out the stopper. Emily, But in this case it is only the perfume of the la- vender, 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 by very minute particles or exhalations which escape from odoriferous bodies. It would be impossible that you should smell the lavender water, if particles of it did not come in actual contact with your nose. 16. What is divisibilitv in natural philosophy ? 17. What are instances of practical divisibility of matter to a ffreat ex- tent ? 18. On what principle is it that we can smell odorife- ^crus objects ? 2 14 GENERAL PROPERTIES OF BODIES. Emily, But when I smell a flower, I see no vapour rise from it ; and yet I can perceive the smell at a con- siderable 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 par- ticles of which did not come in contact with your tongue. Emihj, That is wonderful indeed ; the particles, then, which exhale from the flower and from the lavender 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 diminished ? Mrs, B, Undoubtedly ; and were you to leave the bottle open a sufl^cient length of time, the whole of the water would evaporate and disappear. But though so minutely subdivided as to be imperceptible to any of our senses, each particle would continue to exist ; for it is not within the power of man to destroy a single particle of matter : nor is there any reason to suppose that in na- ture an atom is ever annihilated. 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. Mrs, B. That part of the coals, which you sup)X)se to be destroyed, evaporates in the form of smoke and va- pour, 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 w hich it has been separated by combustion, continue in exist- ence, and retain all the essential properties of bodies. Emily, But that part of a burnt body which evapo- rates in smoke has no figure ; smoke, it is true, ascends 19. If we inhale particles of odoriferous objects, why cannot we see these particles ? 20. If the particles of fragrant liquid in a phial escape from the phial in order to perfume a room, why can we not see them epcape ? ^21. Is not the matter, of which wood is composed, destroyed or annihilated, when burnt to ashes •' GENERAL PROPERTIES OF BODIES. 15 in columns into the air, but it is soon so much diffused as to lose all form ; it becomes indeed invisible. Mrs. B, Invisible, I allow ; but we must not imagine 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 diffused 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 principle 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, Avhence, while living, they drew their support.* The next essential property of matter is called inertia ; this word expresses the resistance which inactive matter makes to a change of state. Bodies appear 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 in motion ; an exertion of strength is also requisite to stop a body which is already in motion. The resistance 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 '^ As a further illustration of the great practical divisi- bility of matter, it may be added, that a single grain of gold may be hammered by a gold-beater until it will cover fifty square inches. Each square inch may then be divided into two hundred strips, and each strip into two hundred parts, which may be seen with the naked eye ; consequently, a square inch contains forty thousand visible parts, which multiplied by 50, the number of square inches which a grain of gold will make, give two million parts, which may be seen with the naked eye. — It has also been calculated, that sixteen ounces of gold, which, in the form of a cube, would not measure one inch and a quarter in its side, will completely gild a quantity of silver wire sufficient to surround the globe. 22. Is it a principle in natural philosophy that no particle of matter can be destroyed ? 23. What is meant by the term inertia ^ ^24. What instances of great 'practice- divisibility of matter are given in tlie note ? 16 GENERAL PROPERTIES OF BODIES. 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 it- self, as it is of putting itself in 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 un- acquainted, we cannot at present investigate its effects. The last property which appears to be common to all bodies is attraction. All bodies consist of infinitely 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 ex- tends to so very small a distance around them that its effect is not sensible, unless 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 am so much accustomed to see bodies firm and solid, that it never occurred to me that any power w^as requisite to unite the particles of which they are composed. But the attraction of cohesion does not, I suppose, exist in liquids ; for the particles of liquids do not remain to- gether 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 my 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 attraction of solid bodies is much greater than that of fluids. The thinner and lighter a fluid is, the less is the cohesive attraction of its particles, because they are further apart ; and in elastic fluids, such as air, there is no cohesive attraction among the particles. 25. What would be the consequence, if a body were put in motion and no resistance should be offered ? 26. What is the property common to all bodies ? — ^27. Of what do all bodies consist? 28. What is the power called which binds thew^ small particles together ? 29. What would be the conse- quence if the power of cohesive attraction were destroyed ? 30. Does the power of cohesion exist also iil liquids .''- 31. How would 3^ou prove that it exists jn liqui^i> ? 32. Why are ^ome bodies liard and others soft .'* GENERAL PROPERTIES OP BOI>IES. 17 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 attraction ? 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 utmost efforts of human art have proved ineffectual in the attempt to com- press 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 composi- tion of liquid and solid bodies, in which state we have a proof of their attraction. Emily. It is then, I suppose, owing to the different degrees of attraction of different substances, that they are hard or soft ; and that liquids are thick or thin ? Mrs, B. Yes ; but you would express your meaning better by the term density, which denotes the degree of closeness and compactness of the particles of a body : thus you may say, both of solids, and of liquids, that the stronger the cohesive attraction the greater is the den- sity of the body. In philosophical language, density is said to be that property of bodies by which they ccm- tain a certain quantity of matter, under a certain bulk .or magnitude. Rarity is the contrary of density ; it denotes the thinness and subtlety 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 ? 33. Does the attraction of cohesion exist in the air ? — 34. But are the particles of the air actually under the influence of this attraction.^ 35. Why are they not, if attraction belong to them .'' 36. How do we know that attraction does belon;^ to the air if no influence is exerted upon it ? 37. What is meant by the term density ? 38. What is meant by the term rarity ^ 2 * 18 GENERAL PROPERTIES OF DOrHEr-. Mrs, 15. By the weight : under the same bulk bodies are said to be dense in proportion as they are heavy .. Emily, Then we may say tliat 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 gradually augment in density, till it was im- possible 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 consequence of the in- creasing attraction of their particles, as hard as iron ? Mrs, B, In such bodies as cork and sponge, the parti- cles which come in contact are so few as to produce but a slight degree of cohesion ; they are porous bodies, which, owing to the peculiar arrangement 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 tliere is another fluid much more subtle than air, which pervades all bodies, this is heat. Heat insinuates itself more or less be- tween the particles of all bodies, and forces them asunder ; you may therefore consider heat and the attraction of co- hesion, as constantly acting in opposition 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 contend- ing forces of heat and attraction, which prevents the ex- treme 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 39. How are we to judge of the quantity of matter in bodies? 40. In what proportion are bodies dense of the same bulk ? 41. What bodies are usually said to be dense ? 42. What ones are said to be rare ? 43. Why are not sponge and cork and other similar substances hard, since their particles come in contact ? 44. What fluid is named more subtle than air .' 45. What effect has heat on bodies ? 40. What two forces are said to act always on bodies in opposition to each otlier .'* • 47. In what cases may we see the effect of heat in the ex par? - eion of bodies, or in the separation of their particles ? GENERAL PROPERTIES OF BODIES. 19 the attraction of cohesion is so far diminished that the par^ tides separate, and the butter becomes liquid. A 'similar effect is produced by' heat on metals, and all bodi^ sus- ceptible of being melted. Liquids, you know, are made to boil by the application of heat : the attraction of cohe- sion then yields entirely to the expansive j|)ovver ; the particles are totally separated and converted into steam or vapour. But the agency of heat is in no body more seiv sible than in air, which dilates and contracts by its in- crease or diminution in a very remarkable degree.* 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 con- nected with chemistry, that you must allow me to defer the investigation of its properties till you become ac- quainted with that science. To return to its antagonist, the attraction of cohesion ; it is this power which restores to vapour its liquid form, which unites it into drops when it falls to the earth in a shower of rain, which gathers the dew into brilliant gems pn the blades of grass. Einily, And I have often observed that after a shower, the water collects into large drops on the leaves of plants ; but I cannot say that I perfectly understand how the attraction of cohesion produces this effect. 3Irs, B, Rain does not fall from the clouds in the form of drops, but in that of mist or rapour, which is composed of very small watery particles ; these in their descent, mutually attract each other, and those that are sufficient- ly near in consequence unite and form a drop, and thus * The expansive power of heat produces some of the most in- teresting phenomena in nature. The boiling of liquids, is the im- mediate result of this power ; and the operation, although simple, is peculiarly worthy of notice. As the numerous particles become expanded or rarified, they are continually rising to, and escaping from the surface, which occasions an agitation of the liquid, pro- portioned, in its violence, to the degree of heat operating on it. — And on exposing our hands or other limbs to the fire, the internal fluid becomes expanded, which causes them to appear swollen ; whereas, when exposed to the cold, the abstraction af the heat causes them to be compressed. AQ. How arc liquids made to boil by heat ; or hoio is the mo- tion or acritation of boiling liquids produced ? 49. Why are our hands and fingers swollen or larger on being held near the fire, than ichen exposed to the cold ? 50. In what state does rain fall from the clouds^? 51, What collects this mist or vapour into drops ? 2D GENERAL PROPERTIES OF BODIES. the mist is transformed into a shower. The dew also was originally in a state of vapour, but is, by the mutual at- traction of the particles, formed into small globules on the blades of grass : in a similar manner the rain upon the leaf collects into 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 almost bewildered with surprise aiKl admiration at the number of new ideas I have already acquired. Mrs. B, Every step that you advance in the pursuit of natural science, will fill your mind with admiration and gratitude towards its Divine Author. In the study of natural philosophy, we must consider ourselves as read- ing 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 eftect of the attraction of co- hesion 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 li- quids ascend within them, from the cohesive attraction between the particles of the liquid and the interiour sur- face 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 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 dif- ferent sizes, you will see it rise to different heights in ■each of them. In making this experiment, 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 water, the 52. What causes the dew on leaves and blades of grass to collect into drops ? 53. Why will liquids rise above their level in capillary tubes ? 54. On what principle -do sponge, and other porous subs^^mces absorb liquids ? GENERAL PROPERTIES OF BODIES. 2^1 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 acquainted with the at- traction of cohesion, I must endeavour to explain to you that of Gravitation, which is a modification g^ the same power ; the first is perceptible only in very minute parti- cles, 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 whether it does not attract other bodies. What is it that occasions the fall of this book, when I no longer support 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 at- traction 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 have to fall results from the earth's attractive power, the earth itself can have no such tendency, since it cannot attract itself, and therefore it requires no support to prevent it from falling. Yet the idea that bodies do 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 myself to it. Mrs, B, When you are accustomed to consider the fall of bodies as depending on this cause, it will appear to you as natural, and surely much more satisfactory, 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 quan- tity of matter they contain. Emily, I do not perceive any difference between the attraction of cohesion and that of gravitation : is it not be- 55. What is the difference between cohesive attraction and gravitation ? 56. What causes bodies to fall to the earth ? 57. In what proportion do bodies gravitate towards or at ^ract each other ? 22 GENERAL PROPERTIES OF BODIES. cause every particle of matter is endowed with an attrac- tive power, that large bodies, consisting of a great num- ber of particles, are so strongly attractive ? Mrs. B. True. There is, however, this difference 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 whicli 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 opposition 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.* * The power of gravitation is greatest at the surface of the earth, whence it decreases both upwards and downwards ; but not in the same proportion. The force of gravity upwards is as the square of the distance from the centre. That is, gravity at the surface of the earth, which is about 4000 miles from the cen- tre, is four times more powerful than it would be at double that distance, or 8000 miles from the centre. Gravity arid weight may be taken, in particular circumstances, as synonymous terms. We «ay, a piece of lead weighs a pound, or sixteen ounces ; but if by any means it could be carried 4000 miles above the surface of the earth, it would weigh only one fourth of a pound, or four ounces ; and if it could be transported to 8000 miles above the earth, which is three times the distance from the centre that the surface is, it would weigh only one ninth of a pound, or something less than two ounces. And it is demonstrated, that the force of gravity downwards de- creases, as the distance from the surface increases, so that at one half the distance from the centre to the surface, the same weight- 58. What example is given to show that cohesive attraction is stronger than gravitation ? 59. Why must the bore of capil- iary tubes be exceedingly small for water to rise in them .** GO. What would be the effect of gravitation on bodies, were it not for cohesive attraction ? 61 . Where is the power of gravity greatest ? G2. In what proportion does gravity decrease from the surface of the earth upwards 9 63. in what proportion does it decrease doionwards f GENERAL PROPERTIES OF BODIES. 23 Emily. And some solid bodies appear to be of this nature, as sand and powder for instance : there is no at- traction of cohesion between their particles 1 Mrs. B, Every grain of powder or sand is composed of a great number of other more minute particles, firmly united by the attraction of cohesion ; but amongst the separate grains there is no sensible attraction, because they are not in sufficiently close contact. E?niL Yet they actually touch each other ? Mrs. B. Tiie surface of bodies is in general so rough and uneven, that when in actual contact, they touch each other only by a few points. Thus, if I lay upon the table this book, the binding of which appears perfectly smooth; yet so few of the particles of its under surface come in contact with the table, that no sensible degree of cohesive attraction takes place ; for you see, that it does not stick, or cohere to the table, and I find no difficulty in lifting it off. It is only when surfaces perfectly flat and well polished are placed in contact, that the particles approach in suffi- cient number, and closely enough, to produce a sensible degree of cohesive attraction. Here are two hemispheres of polished metal, I press their flat surfaces together, hav- ing previously interposed a few drops of oil, to fill up every little porous vacancy. Now try to separate them. already described would weigh only one half of a pound, and so on — Thus, a piece of metal weighing, on the surface of the earth, one pound, will At the centre weigh - - - 1000 miles from the centre, 1-4 pound. 2000 1-2 3000 3-4 4000 1 8000 1-4 12,000 1-9 And at the distance of the moon from the earth which is 240,000 miles, it would weigh only the 3, GOOth part of a pound, because the distance is 60 times further from the centre of the earth than the surface. 64. If a hodif weigh one pound at the surface of the earthy what will he its'iceight at the centre — at 1000— ai 2000— ai 3000 -^at 4000— rti BOOO^anrf at 12,000 miles from the centre of it ? 65. What is the reason that cohesive attraction does not ope- rate on different bodies brought into contact, as well as on the particles of the same body ? ^^- When will the surfaces of different bodies adhere to each other by the force of cohesivQ attraction .- 24 ON THE ATTRACTION OF GRAVITY. Emily, It requires an effort beyond my strengtli, though there are handles for the purpose of pulling them asunder. Is the firm adhesion of the two hemispheres, merely owing to the attraction of cohesion ? Mrs, B, There is no force more powerful, since it is by this tnat the particles of the hardest bodies are held together. It would require a weight of several pounds, to separate these hemispheres. Emily, In making a kaleidoscope, I recollect that the two plates of glass, w hich were to serve as mirrors, stuck so fast together, that I imagined some of the gum I had been using had by chance been interposed between them ; but now I make no doubt but that it was their own natu- ral cohesive attraction which produced this effect. Mrs, B, Very probably it was so ; for plate-glass has an extremely smooth, flat surface, admitting of the con- tact of a great number of particles, between two plates, laid one over the other. Emily, But, Mrs. B. the cohesive attraction of some bodies is much greater than that of others ; thus, glue, gum, and paste, cohere with singular tenacity. Mrs, B, That is owing to the peculiar chemical pro- perties of those bodies, independently of their cohesive at- traction. There are some other kinds of modifications of attrac- tion peculiar to certain bodies ; namely, that of magnet- ism, and of electricity ; but we shall confine our attention merely to the attraction of cohesion and of gravity ; the examination of the latter we shall resume at our next meeting. CONVERSATION IL 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, EMILY. I HAVE related to my sister Caroline all that you have taught me of natural philosophy, and she has been so much delighted by it, that she hopes you will have the goodness to admit her to your lessons. ON THE ATTRACTION OF GRAVITY. 25 Mrs, B. Very willingly ; but I did not think you had any taste for studies of this nature, Caroline ? Caroline. I confess, Mrs. B., that hitherto I had form- ed no very agreeable idea, either of philosophy, or philo- sophers ; but what Emily has told me, has excited my curi- osity so much, that I shall be highly pleased if you will allow me to become one of your pupils. Mrs, B, I fear that I shall not find you so tractable a scholar as Emily ; I know that you are much biassed in favour of your own opinions. Caroline, Then you will have the greater merit in re- forming them, Mrs. B. ; and after all the wonders that Emily has related to me, I think I stand but little chance against you and your attractions. Mrs. B, You will, I doubt not, advance a number of objections ; but these I shall willingly admit, as they will be a means of elucidating the subject. Emily, do you recollect the names of the general properties of bodies ? Emily, Impenetrability, extension, figure, divisibility, inertia, and attraction. Mrs, B, Very well. You must remember that these are properties common to all bodies, and of which they cannot be deprived ; all other properties of bodies are called accidental, because they depend on the relation or connexion of one body to another. Caroline, Yet surely, Mrs. B., there are other proper- ties which are essential to bodies, besides those you have enumerated. Colour and weight, for instance, are com- mon to all bodies, and do not arise from their connexion with each other, but exist in the bodies themselves ; these, therefore, cannot be accidental qualities. Mrs. B, I beg your pardon ; these properties do not exist in bodies independently of their connexion with other bodies. Caroline, What ! have bodies no weight ? Does not this table weigh heavier than this book ; and, if one thing weighs heavier than another, must there not be such a thing as weight ? Mrs, B, No doubt : but this property does not appear to be essential to bodies ; it depends upon their connex- 67. What were the names of the common or general properties of bodies given in the first Conversation ? 63. What are called the accidental properties of bodies ? 69. Are colour and weight common or accidental properties ? ' '- 3 26 ON THE ATTRACTION OF GRAVITY. ion with each other. Weight is an effect of the power of attraction, without which the table and the book would have no weight whatever. Eniihj. I think I understand you ; is it not the at- traction of gravity, which makes bodies heavy ? Mrs, i?. You are right. I told you that the attrac- tion of gravity was proportioned to the quantity of matter which bodies contained : now the earth consisting of a much greater quantity of matter than any body upon its surface, the force of its attraction must necessarily be greatest, and must draw every thing towards it ; in con- sequence of which, bodies that are unsupported fall to the ground, whilst those that are supported press upon the object which prevents their fall, with a weight equal to the force with which they gravitate towards the earth. Caroline, The same cause then which occasions the fall of bodies produces also their weight. It was very dull in me not to understand this before, as it is the na- tural and necessary consequence of attraction ; but the idea that bodies were not really heavy of themselves ap- peared to me quite incomprehensible. But, Mrs. B., if attraction is a property essential to matter, weight must be so likewise ; for how can one exist without the other ? Mrs, B, Suppose there were but one body existing in universal space, what would its weight be I Caroline, That would depend upon its size ; or, more accurately speaking, upon the quantity of matter it con- tained. Emily, No, no ; the body w^ould have no weight, whatever were its size ; because nothing would attract it. Am I not right, Mrs. B.? Mrs, B, You are : you must allow, therefore, that it would be possible for attraction to exist without weight ; for each of the particles of which the body was composed, would possess the power of attraction ; but they could exert it only amongst themselves ; the whole mass, hav- ing nothing to attract, or to be attracted by, w^ould have no weight. Caroline, I am now well satisfied that weight is not essential to the existence of bodies ; but what have you 70. What is weight, or of what is it th'^ effect? 71. If there were but one body in the universe, would there be any such thing as weight t Tl. Can cohesive attraction exist where there is no weight ? ON THE ATTRACTION OF GRAVlTy. 27 to object to colours, Mrs. B. ? You will not, I think, deny that they really exist in the bodies themselves. 3Irs, B, When we come to treat of the subject of co- lours, I trust that I shall be able to convince you, that co- lours are likewise accidental qualities, quite distinct from the bodies to which they appear to belong. Caroline, Oh do pray explain it to us now, I am so very curious to know how that is possible. Mrs. B. Unless we proceed with some degree of or- der and method, you will in the end find yourself but lit- tle the wiser for all you learn. Let us therefore go on regularly, and make ourselves well acquainted with the general properties of bodies, before we proceed further. Emily, To return, then, to attraction, (which appears to me by far the most interesting of them, since it belongs equally to all kinds of matter,) it must be mutual between two bodies ; and if so, when a stone falls to the earth, the earth should rise part of the way to meet the stone ? Mrs, B. Certainly ; but you must recollect that the force of attraction is proportioned to the quantity of mat- ter which bodies contain, and if you consider the differ- ence there is in that respect, between a stone and the earth, you will not be surprised that you do not perceive the earth rise to meet the stone ; for though it is true that a mutual attraction takes place between the earth and the stone, that of the latter is so very small in comparison to to that of the former, as to render its effect insensible. Emily, But since attraction is proportioned to the quantity of matter which bodies contain, why do not the hills attract the houses and churches towards them ? Caroline. You surprise me, Emily ; what an idea ! How can the houses and churches be moved, when they are so firmly fixed in the ground ? Mrs. B. Emily's question is not absurd, and your answer, Caroline, is perfectly just ; but can you tell us why the houses and churches are so firmly fixed in the ground. Caroline. I am afraid I have ansv/ered right by mere chance ; for I begin to suspect that bricklayers and car- penters could give but little stability to their buildings, without the aid of attraction. 73. If the attraction of gravitation is mutual between bodies, why do we not see the earth rise part way to meet the stone '^hich ig falling towards it ? 28 ON THE ATTRACTION OP GRAVITY. Mrs. B. It is certainly the cohesive attraction between the bricks and the mortar which enables them to build walls, and these are so strongly attracted hjr the earth, as to resist every other impulse ; otherwise they would ne- cessarily move towards the hills and the mountains ; but the lesser force must yield to the greater. There are, how- ever, some circumstances iQ which the attraction of a large body has sensibly counteracted that of the earth. If, whilst standing on the declivity of a mountain, you hold a plumb-line in your hand, the weight will not fall perpen- dicular to the earth, but incline a little towards the moun- tain ; and this is owing to the lateral, or sideways attrac- tion of the mountain, interfering with the perpendicular attraction of the earth. Emily. But the size of a mountain is very trifling compared to the whole earth ? Mrs. B. Attraction, you must recollect, diminishes with distance ; and in the example of the plumb-line, the weight suspended is considerably nearer to the mountain than to the centre of the earth 1 Caroline. Pray, Mrs. B., do the two scales of a ba- lance hang parallel to each other 1 Mrs. B. You mean, I suppose, in other words, to in- quire whether two lines which are perpendicular to the earthy are parallel to each other ? I believe I guess the reason of your question ; but I wish you would endeavour to answer it without my assistance. Caroline. I was thinking that such lines must both tend by gravity to the same point, the centre of the earth ; now lines tending to the same point cannot be parallel, as parallel lines are always at an equal distance from each Other, and would never meet. Mrs. B. Very well explained ; you see now the use of your knowledge of parallel lines : had you been igno- rant of their properties, you could not have drawn such a conclusion. This may enable you to form an idea of the great advantage to be derived even from a slight knowledge of geometry in the study of natural philoso- phy ; and if, after I have made you acquainted with the first elements, you should be tempted to pursue the study, 74. And why are not houses and other objects at the side of a mountain attracted or drawn away from their foundations towards it ? 75. How can it be shown that mountains possess a side- ways attraction ? 76. Would two lines suspended by weio-hts be parallel to each other ' ON THE ATTRACTION OP GRAVITY. 29 I would advise you to prepare yourselves by acquiring some knowledge of geometry. This science would teach you that lines which fall perpendicular to the surface of a sphere cannot be parallel, because they would all meet, if prolonged to the centre of the sphere ; while lines that fall pel-pendicular to a plane or fiat surface, are always parallel, because, if prolonged, they v/ould never meet. Emily. And yet a pair of scales, hanging perpendicu- lar to the earth, appear parallel ? 3Irs. B. Because the sphere is so large, and the scales consequently converge so little, that their inclination is not perceptible to our senses ; if we could construct a pair of scales whose beam would extend several degrees, their convergence would be very obvious ; but as this cannot be accomplished, let us draw a small figure of the earth, and then we may make a pair of scales of the pro- portion we please, (fig. 1. plate 1.) Caroline. This figure renders it very clear : then two bodies cannot fall to the earth in parallel lines ? Mrs, B. Never. Caroline, The reason that a heavy body falls quicker than a light one, is, I suppose, because the earth attracts it more strongly T 3Irs. B, The earth, it is true, attracts a heavy body more than a light one ; but that would not make the one fall quicker than the other. Caroline. Yet since it is attraction that occasions the fall of bodies, surely the more a body is attracted, the more rapidly it will fall. Besides, experience proves it to be so. Do we not every day see heavy bodies fall quickly, and light bodies slowly ? Emily. It strikes me, as it does Caroline, that as at- traction is proportioned to the quantity of matter, the earth must necessarily attract a body which contains a great quantity more strongly, and therefore bring it to the ground sooner than one consisting of a smaller quantity. Mrs. B. You must consider, that if heavy bodies are attracted more strongly than light ones, they require more attraction to make them fall. Remember that bo- 77. Why would they not be ? 78. Why is not their con- Tergency perceptible I 79. What fij^ure illustra,tes the con- vergency of two lines suspended perpendicularly to the surface of the earth ? 80. Do heavy and light bodies fall to the ground with equal rapidity ? 3* 30 ON THE ATTRACTION OF GRAVITF. dies have no natural tendency to fall, any more than to rise, or to move laterally, and that they will not fall un- less impelled by some force ; now this force must be pro- portioned to the quantity of matter it has to move : a body consisting of 1000 particles of matter, for instance, requires ten times as much attraction to bring it to the ground in the same space of time as a body consisting of only 100 particles. Caroline. I do not understand that ; for it seems to me that the heavier a body is, the more easily and rea- dily it falls. Emily, I think I now comprehend it ; let me try if 1 can explain it to Caroline. Suppose that I draw towards me two weighty bodies, the one of lOOlbs., the other of lOOOlbs., must I not exert ten times as much strength to draw the larger one to me, in the same space of time as is required for the smaller one ? And if the earth draw a body of lOOOlbs., weight to it in the same space of time that it draws a body of lOOlbs., does it not follow that it attracts the body of lOOOlbs. weight with ten times the force that it does that of lOOlbs. 1 Caroline, I comprehend your reasoning perfectly ; but if it were so, the body of lOOOlbs. weight, and that of lOOlbs. would fall with the same rapidity ; and the consequence would be, that all bodies, whether light or heavy, being at an equal distance from the ground, would fall to it in the same space of time : now it is very evident that this con- elusion is absurd ; experience every instant contradicts it ; observe how much sooner this book reaches the floor than this sheet of paper, when I let them drop together. Emily, That is an objection I cannot answer. I must refer it to you, Mrs. B. Mrs. B. I trust that we shall not find it insurmount- able. It is true that, according to the laws of attraction, all bodies at an equal distance from the earth, should fall to it in the same space of time ; and this would actually take place if no obstacle intervened to impede their fall. But bodies fall through the air, and it is the resistance of the air which makes bodies of different density fall with different degrees of velocity. They must 81. To what must the force of gravity be proportional neces- sary in causing bodies of different weights to fall to the ground ? 82. What are the laws of attraction in regard to the falling of bodies at equal distances from the earth ? 83. But why then do heavy bodies fall quicker than light ones ? ON THE ATTRACTION OF GRAVITY. 31 all force their way through the air, but dense heavy bodies overcome this obstacle more easily than rarer and lighter ones. The resistance which the air opposes to the fall of bo- dies is proportioned to their surface, not to their weight ; the air being inert, cannot exert a greater force to support the weight of a cannon-ball, than it does to support the weight of a ball (of the same size) made of leather ; but the cannon-ball will overcome this resistance more easily, and fall to the ground, consequently, quicker than the leather ball. Caroline, This is very clear, and solves the difficulty perfectly. The air offers the same resistance to a bit of lead and a bit of feather of the same size ; yet the one seems to meet with no obstruction in its fall, whilst the other is evidently resisted and supported for some time by the air. Emily, The larger the surface of a body, then, the more air it covers, and the greater is the resistance it meets with from it. Mrs, B. Certainly ; observe the manner in which this sheet of paper falls ; it floats awhile in '&iQ air, and then gently descends to the ground. I will roll the same piece of paper up into a ball : it offers now but a small surface to the air, and encounters therefore but little re- sistance : see how much more rapidly it fcJls. The heaviest bodies may be made to fiodt awhile in the air, by making the extent of their surface counterbaiance their weight. Here is some gold, which is the most dense body we are acquainted with, but it has been beaten into a very thin leaf, and offers so great an extent of surface in propor- tion to its weight, that its fall, yoa see, is still more retarded by the resistance of the air than that of the sheet of paper. Caroline, That is very curious ; and it is, I suppose, upon the same principle that iron boats may be made to float on water ? But, Mrs. B., if the air is a real body, is it not also subjected to the laws of gravity ? Mrs, B, Undoubtedly. Caroline, Then why does it not, like all other bodies, fall to the ground ? 84. To what is the resistance, that the air opposes to falling bodies, proportioned ? 85. How can heavy bodies be made to float awhile in the air instead of falling immediately to the ground ^ S6. Does the air gravitate towards the earth ^ 32 eN THE ATTRACTION OP GRAVITY. Mrs. B, On account of its spring or elasticity. The air is an elastick Jiuid ; a species of bodies, the peculiar property of which is to resume, after compression, their ori- ginal dimensions ; and you must consider the air of which the atmosphere is composed as existing in a state of com- pression, for its particles bemg drawn towards the earth by gravity, are brought closer togetJier than they would otherwise be, but the spring or elasticity of the air by which it endeavours to resist compression gives it a coTistant ten- dency to expand itself, so as to resume the dimensions it would naturally have, if not under the iuPj.ience of gravity. The air may therefore be said r.onrtantly to struggle with the pov/er of gravity without being able to overcom^e it. Gravity thus confines the air to the regions of our globe, whilst its elasticity prevents it from fUlImg like other bo- dies to the ground. Emily, The air then is, I suppose, thicker, or I should rather say more dense, near the surface of the earth, than in the higher regions of the atmosphere ; for that part of the air which is nearer the surface of the earth must be most strongly attracted. Mrs. B. The diminution of the force of gravity, at so small a distance as that to which the atmosphere extends (compared with the size of the earth) is so inconsiderable as to be scarcely sensible ; but the pressure of the upper parts of the atmosphere on those beneath, renders the air near the surface of the earth much more dense than the upper regions. The pressure of the atmosphere has been compared to that of a pile of fleeces of w ool, in which the lower fleeces are pressed together by the w^eight of those above ; these lie light and loose, in proportion as they approach the up- permost fleece, which receives no external pressure, and is confined merely by the force of its own gravity. Caroliyic. It has just occurred to me that there are some bodies w^hich do not gravitate towards the earth. Smoke and steam, for instance, rise instead of falling. 87. Why then does it not fall like other bodies completely to the surface of the earth ? 88. What two forces continually operate against each other on the air ? 89. Is the air of the same density at the surface of the earth as at a distance from it ? 90. At which is the density the greatest ? 91. Why is the air more dense at the surface of the earth than at a distance from it ? 92. To what has the pressure of the atmosphere been compared f ON THE ATTRACTION OF GRAVITY. 33 Mrs. B, It is still gravity which produces their as- cent ; at least, were that power destroyed, these bodies would not rise. Caroline, I shall be out of conceit with gravity, if it is so inconsistent in its operations. 3Irs. B. There is no difficulty in reconciling this ap- parent inconsistency of effect. The air near the earth is heavier than smoke, steam, or other vapours ; it conse- quently not only supports these light bodies, but forces them to rise, till they reach a part of the atmosphere, the weight of which is not greater than their own, and then they remain stationary. Look at this basin of water : why does the piece of paper which I throw into it float on the surface T Emily. Because, being lighter than the water, it is supported by it. Mrs. B. And now that I pour more water into the basin, why does the paper rise ? Emily. The water being heavier than the paper, gets beneath it and obliges it to rise. Mrs. B. In a similar manner are smoke and vapour forced upwards by the air ; but these bodies do not, like the paper, ascend to the surface of the fluid, because, as we observed before, the air being thinner and lighter as it is more distant from the earth,vapours rise only till they attain a region of air of their own density. Smoke , indeed, ascends but a very little way ; it consists of minute particles of fuel carried up by a current of heated air from the fire below : heat, you recollect, expands all bodies ; it consequently ra- refies air, and renders it lighter than the colder air of the atmosphere ; the heated air from the fire carries up with it vapour and small particles of the combustible materials which are burning in the fire. When this current of hot air is cooled by mixing with that of the atmosphere, the minute particles of coal or other combustible fall, and it is this which produces the small black flakes which render the air and every thing in contact with it, in London, so dirty. Caroline. You must, however, allow me to make one more objection to the universal gravity of bodies ; which 93. How does gfavity operate in causing smoke and steam to rise instead of falling lo the earth ? 94. How high will they rise hefore they become stationary ? 95. What familiar illus- tration is given of the principle upon which smoke and vapour ascend ^ 96. Of what does smoke consist ^ 34 ON THE ATTRACTION OF GRAVITY. is the ascent of air balloons, the materials of which are undoubtedly heavier than air : how, therefore, can they be supported by it ? Mrs, B. I admit that the materials of which balloons are made are heavier tlian the air ; but the air with which •they are filled is an elastick fluid, of a different nature from the atmospherick air, and considerably lighter ; so that on the whole, the balloon is lighter than the air which it dis- places, and consequently will rise, on the same principle as smoke and vapour. Now, Emily, let me hear if you can explain how the gravity of bodies is modified by the effect of the air ? Emihj. The air forces bodies which are lighter than itself to ascend ; those that are of an equal weight will remain stationary in it ; and those that are heavier will descend through it ; but the air will have some effect on these last ; for if they are not much heavier, they will with difficulty overcome the resistance they meet with in pass- ing through it, they will be borne up by it, and their fall will be more or less retarded. Mrs, B. Very well. Observe how slowly this light feather falls to the ground, while a heavier body, like this marble, overcomes the resistance which the air makes to its descent much more easily, and its fall is proportionally more rapid. I now throw a pebble into this tub of water ; it does not reach the bottom near so soon as if there were no water in the tub» because it meets with resistance from the water. Suppose that we could empty the tub, not only of water, but of air also, the pebble would then fall quicker still, as it would in that case meet with no resistance at all to counteract its gravity. Thus you see that it is not the different degrees of gravity, but the resistance of the air, which prevents bo- dies of different weight from fallmg with equal velocities ; if the air did not bear up the feather, it would reach the ground as soon as the marble. Caroline, I make no doubt that it is so ; and yet I do not feel quite satisfied. I wish there were some place void of air, in which the experiment could be made. Mrs, B. If that proof will satisfy your doubts, I can give it you. Here is a machine called an air pump, (fig. 2. pi. I.) by means of which the air may be expelled from I.>7. On what principle does a balloon rise, since it is made of materials heavier than the air through which it rises ? 98 How is tliQ t^ravity of bodies modified by the effect of the air P MO What is the uac of the air pump ' ON THE ATTRACTION OF GRAVITY. 35 any close vessel which is placed over this opening, through which the air is pumped out. Glasses of various shapes, usually called receivers, are employed for this purpose. We Siiall naw exhaust the air from this tall receiver which is placed over the opening, and we shall find that bodies of whatever weight or size vvithin it, will fall from the top to the bottom in the same space of time. Caroline, Oh, I shall be delighted with this experi- ment ; what a curious machine ! how can you put the two bodies of diiferent weight within the glass, without admitting the air ? Mrs, B. A guinea and a feather are already placed there for the purpose of the experiment : here is, you see, a contrivance to fasten them in the upper part of the glass ; as soon as the air is pumped out, I shall turn this little screw, by which means the brass plates which support them will be inclined, and the two bodies will fall. — Now I believe I have pretty well exhausted the air. Caroline, Pray let me turn the screw. I declare, they both reached the bottom at the same instant ! Did you see, Emily, the feather appeared as heavy as the guinea ? Emily, Exactly ; and fell just as quickly. How w^on- derful this is ! what a number of entertaining experi- ments might be made v/ith this machine ! Mrs, B, No doubt there are a great many ; but we shall reserve them to elucidate the subjects to which they relate ; if I had not explained to you why the guinea and the feather fell with equal velocity, you would not have been so well pleased with the experiment. Emily, I should have been as much surprised, but not so much interested ; besides, experiments help to imprint on the memory the facts they are intended to illustrate ; it will be better therefore for us to restrain our curiosity, and wait for other experiments in their proper places. Caroline, 'Pray by what means is the air exhausted in this receiver ? Mi^s, B, You must learn something of mechanicks in order to understand the construction of a pump. At our next meeting, therefore, I shall endeavour to make you acquainted with the laws of motion, as an introduction to that subject. 100. Can a feather be placed in a situation to fall as quickly as a stone ^ 101. In what manner can it be done ? 36 ON THE LAWS OF MOTION. CONVERSATION III. ^ ON THE LAWS OF MOTION. On Motion ; Of the Inertia of Bodies ; Of Force to produce Motion ; Direction of Motion ; Velocity^ Ah^ solute and Relative ; Uniform Motion ; Retarded Mo^ tion; Accelerated Motion; Velocity of Falling Bo- dies; Momentum; Action and Re-action Equal; Elasticity of Bodies ; Porosity of Bodies ; Reflected Motion ; Angles of Incidence and Reflection, MRS. B. The science of mechanicks is founded on the laws of motion ; it will, therefore, be necessary to make you ac- quainted with these laws before we examine the mecha- nical powers. Tell me, Caroline, what do you understand by the word motion ? Caroline. I think I understand it perfectly, though I am at a loss to describe it. Motion is the act of moving about, going from one place to another ; it is the contrary of remaining at rest. Mrs, B, Very well. Motion then consists in a change of place ; a body is in motion whenever it is changing its situation with regard to a fixed point. Now since we have observed that one of the general properties of bodies is Inertia, that is, an entire passiveness either with regard to motion or rest, it follows that a body cannot move without being put into motion ; the power which puts a body into motion is called force ; thus, the stroke of the hammer is the force which drives the nail ; the pulling of the horse that which draws the carriage, &c. Force then is the cause which produces motion. Emily, And may we not say that gravity is the force which occasions the fall of bodies ? Mrs, B, Undoubtedly. I had given you the most fa- miliar illustrations in order to render the explanation clear ; but since you seek for more scientifick examples, you may say that cohesion is the force which binds the particles of bodies together, and heat that which drives them asunder. 102. On what is the science of mechanicks founded ? 103. What is to bo understood by the term motion ? 104. What is the power called that puts a body in motion ? ON THE LAWS OF MOTION. 37 The motion of a body a^ted upon by a single force is always in a straight line, in the direction in which it re- ceived the impulse. Caroline, That is very natural ; for as the body is in- ert, and can move only because it is impelled, it will move only in the direction in which it is impelled. The degree of quickness with wliich it moves, must, I suppose, also de- pend upon the degree of force with which it is impelled. Mrs* B, Yes ; the rate at which a body moves, or the shortness of the time which it takes to move from one place to another, is called its velocity ; and it is one of the laws of motion that the velocity of the moving body is proportional to the force by which it is put in motion. We must distinguish between absolute and relative ve- locity. The velocity of a body is called absolute, if we consider the motion of the body in space, without any reference to that of other bodies. When for instance a horse goes fifty miles in ten hours, his velocity is five miles an hour. The velocity of a body is termed relative, when com- pared with that of another body which is itself in motion. For instance, if one man walks at the rate of a mile an hour, and another at the rate of two miles an hour, the relative velocity of the latter is double that of the former, but the absolute velocity of the one is one mile, and that of the other two miles an hour. Emily. Let me see if I understand it. The relative velocity of a body is the degree of rapidity of its motion compared with that of another body ; thus, if one ship sail three times as far as another ship in the same space of time, the velocity of the former is equal to three times that of the latter. Mrs. B, The general rule may be expressed thus : the velocity of a body is measured by the space over which it moves, divided by the time which it employs in that motion : thus if you travel one hundred miles in twenty hours, what is your velocity in each hour 1 105. In what direction is the motion of a body acted on by. a single force ? 106. What is meant by the velocity of motion .'* 107. To what is the velocity of a moving body proportional ? 108. What is called absolute velocity ? 109. When is the velocity of a moving- body called relative ? 110. What would be instances of relative velocity ^ 111. What is the general rule for calculating the velocity of a moving body ? 4 38 ON THE LAWS OF MOTION. Emily, I must divide the space, which is one hundred miles, by the time, which is twenty hours, and the answer will be '^\e miles an hour. Then, Mrs. B., may we not reverse this rule and say, that the time is equal to the space divided by the velocity ; since the space one hun- dred miles, divided by the velocity five miles, gives twen- ty hours for the time ? Mrs. B, Certainly ; and we may say also that space is equal to the velocity multiplied by the time. Can you tell me, Caroline, how many miles you will have travelled, if your velocity is three miles an hour, and you travel six hours ? Caroline. Eighteen miles ; for the product of 3 mul- tiplied by 6, is 18. Mrs. B. I suppose that you understand what is meant by the terms uniform, accelerated, and retarded motion. Emily. I conceive uniform motion to be that of a body whose motion is regular, and at an equal rate throughout ; for instance, a horse that goes an equal number of miles every hour. But the hand of a watch is a much better example, as its motion is so regular as to indicate the time. Mrs. B. You have a right idea of uniform motion ; but it would be more correctly expressed by saying, that the motion of a body is uniform when it passes over equal spaces in equal times. Uniform motion is produced by a force having acted on a body once, and having ceased to act ; as for instance, the stroke of a bat on a cricket ball. Caroline. But the motion of a cricket ball is not uni- form ; its velocity gradually diminishes till it falls to the ground. Mrs. B. Recollect that the cricket ball is inert, and has no more power to stop than to put itself in motion ; if it falls, therefore, it must be stopped by some force supe- riour to that by which it was projected, and which destroys its motion. Caroline. And it is no doubt the force of gravity which counteracts and destroys that of projection ; but if there were no such power as gravity, would the cricket ball never stop ? Mrs. B. If neither gravity nor any other force, such as the resistance of the air, opposed its motion, the cricket X12. When is the motion of a body termed uniform ? 113. How is uniform motion produced ? ON THE LAWS OF MOTION. 39 ball, or even a stone thrown by the hand, would proceed onwards in a right line, and with a uniform velocity for ever. Caroline, You astonish me ! I thought that it was im- possible to produce perpetual motion ? Mrs. B, Perpetual motion cannot be produced by art, because gravity ultimately destroys all motion that hu- man powers can produce. Emily. But independently of the force of gravity, I cannot conceive that the little motion I am capable of giving to a stone would put it in motion for ever. 3Irs, B. The quantity of motion you communicate to the stone would not influence its duration : if you threw it with little force it would move slowly ; for its velocity, you must remember, will be proportional to the force with which it is projected ; but if there is nothing to obstruct its passage, it will continue to move with the same velocity, and in the same direction as when you first projected it. Caroline, This appears to me quite incomprehensible ; we do not meet with a single instance of it in nature. Mrs, B, I beg your pardon. When you come to study the motion of the celestial bodies, you will find that nature abounds with examples of perpetual motion ; and that it conduces as much to the harmony of the system of the universe as the prevalence of it would to the destruc- tion of all comfort on our globe. The wisdom of Provi- dence has therefore ordained insurmountable obstacles to perpetual motion here below ; and though these obstacles often compel us to contend with great difficulties, yet there results from it that order, regularity, and repose, so essential to the preservation of all the various beings of which this world is composed. Now can you tell me what is retarded motion ? Caroline. Retarded motion is that of a body which moves every moment slower and slower : thus when I am tired with walking fast, I slacken my pace ; or when a stone is thrown upwards, its velocity is gradually di- minished by the power of gravity. Mrs, B. Retarded motion is produced by some force acting upon the body in a direction opposite to that which first put it in motion : you who are an animated being, endowed with power and will, may slacken your pace, or 114. What is the reason that perpetual motion cannot be pro- duced ? -U5. What is retarded motion ? 116. How is re- tarded motion produced ? 40 ON THE LAWS OP MOTION* stop to rest when you are tired ; but inert matter is inca- pable of any feeling of fatigue, can never slacken its pace and never stop, unless retarded or arrested in its course . by some opposing force ; and as it is the Islws of inert bodies which mechanicks treat of, I prefer your illustra- tion of the stone retarded in its ascent. Now, Emily, it is your turn ; what is accelei' cited motion ? Emily, Accelerated motion, I suppose, takes place when the velocity of a body is increased ; if you had not objected to our giving such active bodies as ourselves as examples, I should say that my motion is accelerated if I ciiange my pace from walking to running. I cannot think of any instance of accelerated motion in inanimate bodies ; all motion of inert matter seems to be retarded by gravity. Mrs. B. Not in all cases ; for the power of gravitation sometimes produces accelerated motion ; for instance, a stone falling from a height moves with a regularly acce- lerated motion. Emily. True ; because the nearer it approaches the earth, the more it is attracted by it. Mrs. B. You have mistaken the cause of its accele- ration of motion ; for though it is true that the force of gravity increases as a body approaches the earth, the dif- ference is so trifling at any small distance from its surface as not to be perceptible. Accelerated motion is produced when the force which put a body in motion continues to act upon it during^ its motion, so that its motion is continuaJly increased. When a stone falls from a height, the impulse which it re- ceives from gravity during the first instant of its fall, would be sufficient to bring it to the ground with a uniform ve- locity : for, as we have observed, a body having been once acted upon by a force, will continue to move with a uni- form velocity ; but the stone is not acted upon by gravity merely at the first instant of its fall — this power continues to impel it during the whole of its descent, and it is this continued impulse which accelerates its motion. Emily. 1 do not quite undertand that. Mrs. B. Let us suppose that the instant after you have let fall a stone from a high tower, the force of gra- vity were annihilated, the body would nevertheless con- 117. What is accelerated motion? IJ8. What is an in- stance of accelerated motion ? 119. How does gravity accele- rate the motion of falling bodies ? ON THE LAWS OF MOTION. 41 tinue to move downwards, for it would have received a first impulse from gravity, and a body once put in motion will not stop unless it meets with some obstacle to impede its course ; in this case its velocity would be uniform, for though there would be no obstacle to obstruct its descent, there would be no force to accelerate it. Emily, That is very clear. Mrs. B. Then you have only to add the power of gravity constantly acting on the stone during its descent, and it will not be difficult to understand that its motion will become accelerated, since the gravity which acts on the stone during the first instant of its descent, will con- tinue in force every instant till it reaches the ground. Let us suppose that the impulse given by gravity to the stone during the first instant of its descent be equal to one, the next instant we shall find that an additional impulse gives the stone an additional velocity equal to one, so that the accumulated velocity is now equal to two ; the following instant another impulse increases the velocity to three, and so on till the stone reaches the ground. Caroline, Now I understand it ; the effects of preced ing impulses must be added to the subsequent velocities. Mrs. B. Yes ; it has been ascertained both by expe- riment and calculations, which it would be too difficult for us to enter into, that heavy bodies descending from a height by the force of gravity, fall sixteen feet the first second of time, three times that distance in the next, five times in the third second, seven times in the fourth, and so on, regu- larly increasing their velocities according to the number of seconds during which the body has been falling. Emily. If you throw a stone perpendicularly upwards, is it not the same length of time ascending that it is de- scending ? Mrs. B. Exactly ; in ascending, the velocity is di- minished by the force of gravity ; in descending, it is ac- celerated by it. Caroline. I should then have imagined that it would have fallen quicker than it rose 1 Mrs. B. You must recollect that the force with which it is projected must be taken into the account ; and that 120. What distance will a heavy body, suspended in the air, fall the first second of time ? What distance the second ? What the third ? 121. How does the time of an ascending body al- ways compare with the time of its descent ? 4* 42 ON THE LAW& OF MOTION. this force is overcome and destroyed by gravity before the body falls. Caroline. But the force of projection given to a stone in throwing it upwards, cannot always be equal to the force of gravity in bringing it down again, for the force of gravity is always the same, whilst the degree of im- pulse given to the stone is optional ; I may throw it up gently or w ith violence. Mrs, B. If you throw it gently, it will not rise high ; perhaps only sixteen feet, in which case it will fall in one second of time. Now it is proved by experiment, that an impulse requisite to project a body sixteen feet upwards, will make it ascend that height in one second ; here then the times of the ascent and descent are equal. ^ But sup- posing it be required to throw a stone twice that height, the force must be proportionally greater. You see then, that the impulse of projection in throw- ing a body upwards, is always equal to the action of the force of gravity during its descent ; and that it is the greater or less distance to which the body rises, that makes these two forces balance each other. I must now explain to you what is meant by the mo- mentiim of bodies. It is the force, or power, with which a body in motion, strikes against another body. The momentum of a body is composed of its quantity of matter^ multiplied by its quantity of motion ; in other words its weight and its velocity. Caroline, The quicker a body moves, the greater, no doubt, must be the force with which it would strike against another body. Kmihj. Therefore a small body may have a greater mo- mentum than a large one, provided its velocity be sufficient- ly greater ; for instance, the momentum of an arrow shot from a bow must be greater than a stone thrown by the hand. Caroline. We know also by experience, that the heavier a body is, the greater is its force ; it is not there- fore difficult to understand, that the whole power or mo- mentum of a ])ody must be composed of these two pro- perties ; but I do not understand, why they should 122. To what is the impulse of projection, in throwing a body upwards, equal? 123- What is the momentum of a body .^ 124. Of what is the momentum of a body composed ^ 125. In what way can a smaller body have a greater moraentunt than a larger body ? ON THE LAWS OP MOTION. 43 be multiplied, the one by the other ; I should have sup- posed that the quantity of matter should have been added to the quantity of motion 1 Mrs, B. It is found by experiment, that if the weight of a body is represented by the number 3, and its velocity also by 3, its momentum will be represented by 9 ; not 6, as would be the case, were these figures added, instead of being multiplied together. I recommend it to you to be careful to remember the definition of the momentum of bodies, as it is one of the most important points in mecha- nicks ; you will find, that it is from opposing motion to matter, that machines derive their powers.* The re-action of bodies is the next law of motion which I must explain to you. When a body in motion strikes against another body, it meets with resistance from it ; the resistance of the body at rest will be equal to the blow struck by the body in motion ; or to express myself in philosophical language, action and re-action will be equal, and in opposite directions. Caroline, Do you mean to say, that the action of the body which strikes, is returned with equal force by the body which receives the blow 1 Mrs. B. Exactly. Caroline, But if a man strikes another on the face with his fist, he surely does not receive as much pain by the re-action as he inflicts by the blow 1 Mrs, B, No ; but this is simply owing to the knuckles having much less feeling than the face. Here are two ivory balls suspended by threads, (plate 1. fig. 3.) draw one of them. A, a little on one side, — now let it go ; — it strikes you see against the other ball B, and drives it off, to a distance equal to that through which the * In comparing together the momenta of different bodies, we must be attentive to measure their weights and velocities, by tha same denomination of weights and of spaces, otherwise the results would not agree. Thus if we estimate the weight of one body in ounces, v/e must estimate the weight of the rest also in ounces, and not in pounds ; and in computing the velocities, in like man- ner, we should adhere to the same standard of measure, both of space and of time ; as for instance, the number of feet in one se- cond, or of miles in one hour. 126. If the weight of a body be respresented by 3, and its ve- locity by 3, what will be it- momentum ? 127. WJiat is meant by the term re-action, in mechanicks ? 128. To what is re-action equal ? 129. What does figure 3, Plate T. illustrate ? 44 ON THE LAWS OF MOTION. first ball fell ; but the motion of A is stopped, because when it struck B, it received in return a blow equal to that it gave, and its motion was consequently destroyed. Emily. I should have supposed that the motion of the ball A was destroyed, because it had communicated all its motion to B. Mrs, B. It is perfectly true, that when one body strikes against another, the quantity of motion communi- cated to the second body, is lost by the first ; but this loss proceeds from the action of the body which is struck. Here are six ivory balls hanging in a row, (fig. 4.) draw the first out of the perpendicular, and let it fall against the second. None of the balls appear to move, you see, except the last, which flies off as far as the first ball fell ; can you explain this 1 Caroline, I believe so. When the first ball struck the second, it received a blow in return, which destroyed its motion ; the second ball, though it did not appear to move, must have struck against the third; the re-action of which set it at rest ; the action of the third ball must have been destroyed by the re-action of the fourth, and so on till mo- tion was communicated to the last ball, which, not being re-acted upon, flies off. 3Irs, B, Very well explained. Observe, that it is only when bodies are elastick, as these ivory balls are, that the stroke returned is equal to the stroke given. I will show you the difference with these two balls of clay, (fig. 5.) which are not elastick ; when you raise one of these, D, out of the perpendicular, and let it fall against the other, E, the re-action of the latter, on account of its not being elastick, is not sufficient to destroy the motion of the for- mer ; only part of the motion of D will be communicated to E, and the two balls will move on together to d and e which is not so great a distance as that through which D fell. Observe how useful re-action is in nature. Birds in fly- ing strike the air with their wings, and it is the re- action of the air which enables them to rise, or advance forwards ; re-action being always in a contrary direction to action. 130. How would you explain the operation of action and re- action, as illustrated by the six ivory balls in Figure 4, Plate I. ? 131 . Is the re-action of all bodies equal to the action when a blow is given ? 132. In what ones is it equal .'' 133. What is the object of figure 5, Plate I. .'' 134. How does this figure show that the re-action of non-elastick bodies is not equal to the action ? 135. On what mechanical principle is it that birds arc able to %. ON THE LAWS OP MOTION. 45 Caroline. I thought that birds might be lighter than the air, when their wings were expanded, and by that means enabled to fly. Mrs, B. When their wings are spread, they are bet- ter supported by the air, as they cover a greater extent of surface ; but they are still much too heavy to remain in that situation, without continually flapping their wings, as you may have noticed, when birds hover over their nests : the force with which their wings strike against the air must equal the weight of their bodies, in order that the re-action of the air may be able to support that weight ; the bird will then remain stationary. If the stroke of the wings be greater than is required merely to support the bird, the re-action of the air will make it rise ; if it be less, it will gently descend ; and you may have observed the lark, sometimes remaining with its wings extended, but mo- tionless : in this state it drops rapidly into its nest. Caroline. What a beautiful effect this is of the law of re-action ! But if flying is merely a mechanical operation, Mrs. B., why should we not construct wings, adapted to the size of our bodies, fasten them to our shoulders, move them with our arms, and soar into the air. Mrs. B. Such an experiment has been repeatedly at- tempted, but never with success ; and it is now considered as totally impracticable. The muscular power of birds is greater in proportion to their weight than that of man ; were we therefore furnished with wings sufficiently large to enable us to fly, we should not have strength to put them in motion. In swimming, a similar action is produced on the water, as that on the air in flying ; and also in rowing ; you strike the water with the oars, in a direction opposite to that in which the boat is required to move : and it is the re-ac- tion of the water on the oars which drives the boat along. Emily. You said, that it was in elastick bodies only, that re-action was equal to action ; pray what bodies are elastick besides the air. Mrs. B. In speaking of the air, I think we defined elasticity to be a property, by means of which, bodies that are compressed returned to their former state. If I bend 136, How must a bird strike the air with its wings so as to re- main stationary ? — So as to rise ? — So as to descend ? 137. If flying is only the effect of re-action, why could not a man bo fur- nished with wings so as to fly ? 138. How is swimming effect- ed ? 139. On what principle is a boat moved upon the water f -140. What is to be understood by the elasticity of a body - 46 ON THE LAWS OF MOTION. this cane, as soon as I leave it at liberty it recovers its former position ; if I press my finger upon your arm, as soon as I remove it, the flesh, by virtue of its elasticity, rises and destroys the impression I made. Of all bodies, the air is the most eminent for this property, and it has thence obtained the name of elastick fluid. Hard bodies are in the next degree elastick : if two ivory, or metallic balls are struck together, the parts at which they touch will be flattened : but their elasticity will make them instanta- neously resume their former shape. Caroline. But when two ivory balls strike against each other, as they constantly do on a billiard table, no mark or impression is made by the stroke. Mrs, B, I beg your pardon ; but you cannot perceive any mark, because their elasticity instantly destroys all trace of it. Soft bodies, which easily retain impression, such as clay, wax, tallow, butter, &.c. have very little elasticity ; but of all descriptions of bodies liquids are the least elastick. Emily, If sealing-wax were elastick, instead of retain- ing the impression of a seal, it would resume a smooth surface as soon as the weight of the seal was removed. But pray what is it that produces the elasticity of bodies 1 Mrs. B. There is great diversity of opinion upon that point, and I cannot pretend to decide which ap- proaches nearest to the truth. Elasticity implies suscep- tibility of compression, and the susceptibility of compres- sion depends upon the porosity of bodies ; for were there no pores or spaces between the particles of matter of which a body is composed, it could not be compressed. Caroline. That is to say, that if the particles of bodies were as close together as possible, they could not b« squeezed closer. Emily. Bodies then, whose particles are most distant from each other, must be most susceptible of compression, and consequently most elastick ; and this you say is the case with air, which is perhaps the least dense of all bodies ? Mrs. B. You will not in general find this rule hold good, for liquids have scarcely any elasticity, whilst hard bodies are eminent for this property, though the latter are certainly of much greater density than the former ; elas- 141. What bodies are most distinguished for elasticity?—— 142. What bodies are not elastick.? 143. On what is elasti- city supposed to depend r ON THE LAWS OF MOTION. 47 ticity implies, therefore, not only a susceptibility of com- pression, but depends upon the power of resuming its for- mer state after compression. Caroline. But surely there can be no pores in ivory and metals, Mrs. B. ; how then can they be susceptible of compression ? Mrs. B, The pores of such bodies are invisible to the naked eye, but you must not thence conclude that they have none ; it is, on the contrary, well asceitained that gold, one of the most dense of all bodies, is extremely po- rous, and that these pores are sufficiently large to admit water when strongly compressed to pass through them. This was shown by a celebrated experiment made many years ago at Florence. Emily. If water can pass through gold, there must certainly be pores or interstices which afford it a passage ; and if gold is so porous, what must other bodies be which are so much less dense than gold ! 3Trs. B. The chief difference in this respect is, I be- lieve, that the pores in some bodies are larger than in others ; in cork, sponge, and bread, they form considerable cavities ; in wood and stone, when not polished, they are generally perceptible to the naked eye ; whilst in ivory, me- tals, and all varnished and polished bodies, they cannot be discerned. To give you an idea of the extreme porosity of bodies, Sir Isaac Newton conjectured that if the ear.th were so compressed as to be absolutely without pores, its dimen- sions might possibly not be more than a cubic inch. Caroline. What an idea \ Were we not indebted to Sir Isaac Newton for the theory of attraction, I should be tempted to laugh at him for such a supposition. What insignificant little creatures we should be ! Mrs. B. If our consequence arose from the size of our bodies, we should indeed be but pigmies ; but remem- ber that the mind of Newton was not circumscribed by the dimensions of its envelope. Emily. It is, however, fortunate that heat keeps the pores of matter open and distended, and prevents the at- traction of cohesion from squeezing us into a nut-shell. Mrs. B. Let us now return to the subject of re-action, on which we have some further observations to make. 144. Is it supposed that ivory balls, metals, and other hard sub- stances are porous ? 145. How has it been proved that gold is porous ? 14(5. What conjecture did Sir Isaac Newton form concerning the porosity of the earth .'* 48** ON THE LAWS OF MOTION. It is re-action, being contrary to action, which produces reflected motion. If* you throw a ball against the wall, it rebounds ; this return of the ball is owing to the re-action of the wall against which it struck, and is called reflected motion, Emily, And I now understand why balls filled with air rebound better than those stuffed with bran and wool, air being most susceptible of compression and most elas- tick, the re-action is more complete. Caroline. I have observed that when I throw a ball straight against the wall, it returns straight to my hand ; but if I throw it obliquely upwards, it rebounds still higher, and I catch when it falls. Mrs, B, You should not say straight, but perpendi- cularly against the wall ; for straight is a general term for lines in all directions which are neither curved nor bent, and is therefore equally applicable to oblique or perpendi- cular lines. Caroline, I thought that perpendicularly meant either directly upwards or downwards. Mrs, B, In those directions lines are perpendicular to the earth. A perpendicular line has always a reference to something towards which it is perpendicular ; that is to say, that it inclines neither to the one side nor the other, but makes an equal angle on every side. Do you understand what an angle is ? Caroline, Yes, I believe so : it is two lines meeting in a point. Mrs, B, Well then, let the line A B (plate II, fig. 1 ,) re- present the floor of the room, and the line C D that in which you throw a ball against it : the line C D, you v/ill observe, forms two angles with the line A B, and those two angles are equal. Emihj, How can the angles be equal, while the lines which compose them are of unequal length ? Mrs, B, An angle is not measured by the length of the lines, but by their opening. Emihj, Yet the longer the lines are, the greater is the opening between them. Mrs, B, Take a pair of compasses and draw a circle over these angles, making the angular point the centre. 147. What is reflected motion ? 148. What produces it .^ . 149. AVhat is meant by a perpendicular line ^ 150. What is an angle 1 151. What does Fig. I, plate II. illustrate .?-- — 15^. By what is an angle measured ? ON THE LAWS OF MOTION. 49 Emily. To what extent must I open the compasses 1 Mrs. B. You may draw the circle what size you please, provided that it cuts the lines of the angles we are to measure. All circles, of whatever dimensions, are supposed to be divided into 360 equal parts, called de- grees; the openmg of an angle, being therefore a portion of a circle, must contain a certain number of degrees ; the larger the angle, the greater the number of degrees, and the two angles are said to be equal when they con- tain an equal number of degrees. Emily. Now I understand it. As the dimensions of an angle depend upon the number of degrees contained between its lines, it is the opening and not the length of its lines, which determines the size of the angle. Mrs. B. Very well : now that you have a clear idea of the dimensions of angles, can you tell me how many degrees are contained in the two angles formed by one line falling perpendicular on another, as in the figure I have just drawn 1 Emily. You must allow me to put one foot of the compasses at the point of the angles, and draw a circle round them, and then I think I shall be able to answer your question : the two angles are together just equal to half a circle, they contain therefore 90 degrees each ; 90 degrees being a quarter of 360. Mrs. B. An angle of 90 degrees is called a right angle, and when one line is perpendicular to another, it forms, you see, (fig. 1.) a right angle on either side. Angles contaming more than 90 degrees are called obtuse angles (fig, 2;) and those containing less than 90 degrees are called acute angles, {fig. 3.) Caroline. The angles of this square table are right angles, but those of the octagon table are obtuse angles ; and the angles of sharp-pointed instruments are acute angles. Mrs. B. Very well. To return now to your obser- vation, that if a ball is thrown obliquely against the wall it will not rebound in the same direction ; tell me, have you ever played at billiards ? 153. Into hAv many degrees are all circles divided ? 154. When are two angles said to be equal ? 155. How many de- grees are contained in the two angles formed by the figure named ? 156. What is called a right angle ? — An obtuse angle ? — An acute angle r 50 ©N THE LAWS OF MOTION. Caroline, Yes, frequently ; and I have observed that when I push the ball perpendicularly against the cushion, it returns in the same direction ; but when I send it ob- liquely to the cushion, it rebounds obliquely, but on the opposite side ; the ball in this latter case describes an ang e, the point of which is at the cushion. I have ob- served too, that the more obliquely the ball is struck against the cushion, the more obliquely it rebounds on the opposite side, so that a billiard player can calculate with great accuracy in what direction it will return. Mrs. B. Very well. This figure (fig. 4. plate II.) represents a billiard table ; now if you draw a line A B from the point where the ball A strikes perpendicular to the cushion, you will find that it will divide the angle which the ball describes into two parts, or two angles ; the one will show the obliquity of the direction of the ball in its passage towards the cushion, the other its ob- liquity in its passage back from the cushion. The first is called the angle of incidence, the other the angle of re- flection, and these angles are always equal.* Caroline. This then is the reason why, when I throw a ball obliquely against the wall, it rebounds in an oppo- site oblique direction, forming equal angles of incidence and of reflection. Mrs. B. Certainly ; and you will find that the more obliquely you throw the ball, the more obliquely it will rebound. We must now conclude : but I shall have some further observations to make upon the laws of motion, at our next meeting. * The Angle of Incidence is that which is contained between the line described by the incident ray, and a line perpendicular to the surface on which the ray strikes, raised from the point of incidence. The Angle of Reflection is that which is contained between the line described by the reflected ray, and a line per- pendicular to the reflecting surface at the point in which the in- cident ray strikes that surface. 157. How does the angle of incidence compare, as to size, with the angle of reflection ? 158. How would* you illustrate the angle of incidence and reflection by Fig. 4, plJte II ^ 159. What is an angle of incidence ? 160. What is an angle of reflection ? ^ ON COMPOUND MOTION. 51 CONVERSATION IV. ON COMPOUND MOTION. Compound Motion^ the Result of two Opposite Forces ; Of Circular Motion, the Result of two Forces, one of which confines the Body to a Fixed Point ; centre of Mo- tion, 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 which confines a Body to a fixed Central Point ; Centrifugcd Force, that lohich impels a Body to fly from the Centre ; Fall of Bodies in a Parabola; Centre of Gravity, the Centre of Weight, or point about which the Parts balance each other. MRS. B. I MUST now explain to you the nature of compound mo- tion. Let us suppose a body to be struck by two equal forces in opposite directions, how will it move ? Emily. If the directions of the forces are in exact op- position to each other, I suppose the body would not move at all. Mrs, B. You are perfectly right ; but if the forces, instead of acting on the body in opposition, strike it in two directions inclined to each other, at an angle of nine- ty degrees, if the ball A (fig. 5, plate II.) be struck by equal forces at X and at Y, will it not move ? Emily. The force X would send it towards B, and the force Y towards C, and since these forces are equal, I do not know how the body can obey one impulse rather than the other, and yet I think the ball would move, be- cause as the two forces do not act in direct opposition, they cannot entirely destroy the effect of each other. Mrs. B. Very true ; the ball will therefore follow the direction of neither of the forces, but will move in a line between them, and will reach D in the same space of time that the force X would have sent it to B, and the 162. Of what does the fourth Conversation treat? 163. What would be the effect if two bodies were to strike each other, when moving in opposite directions and with equal forces ? 164. What would be the effect if they were to strike in directions inclined to each other, at an an;^le of ninety degrees .''—165 How would you explain Fig 5, plate II. .'' 5^ ON COMPOUND MOTTON^. force Y would have sent it to C. Now if you draw two lines from D, to join B and C, you will form a square, and the oblique line which the body describes is called the diagonal of the square. Caroline, That is very clear, but supposing the two forces to be unequal, that the force X, for instance, be twice as great as the force Y ? Mrs, B. Then the force X would drive the ball twice as far as the force Y, consequently you must draw the line A B (fig. 6.,) twice as long as the line A C, the body will in this case move to D ; and if you draw lines from that point to B and C, you will find that the ball has moved in the diagonal of a rectangle. Emily, Allow me to put another case ? Suppose the two forces are unequal, but do not act on the ball in the direction of a right angle, but in that of an acute angle, what will result ? Mrs. J5. Prolong the lines in the directions of the iwo forces, and you will soon discover which way the ball will be impelled ; it will move from A to D, in the diagonal of a parallelogram, (fig. 7.) Forces acting in the direction of lines forming an obtuse angle, will also produce motion in the diagonal of a parallelogram. For instance, if the body set out from B, instead of A, and was impelled by the forces X and Y, it would move in the dotted diagonal B C. We may now proceed to circular motion : this is the result of two forces on a body, by one of which it is pro- jected forward in a right line, whilst by the other it is confined to a fixed point. For instance, when I whirl this ball, which is fastened to my hand with a string, the ball moves in a circular direction ; because it is acted on by two forces, that which I give it which represents the force of projection, and that of the string which confines it to my hand. If during its motion you were suddenly to cut the string, the ball would fly off in a straight line : being released from confinement to the fixed point, it would be acted on but by one force, and motion produced by one force, you know, is always in a right line. 166. What is the oblique hne called, which is described by two equal forces moving in. right angular directions? 167. What does Fig. 6, of that plate illustrate ^ 163. What is illustrated by Fig. 7, plate IT. ^ 169. Of what is circular motion the re- suit .' 170. What simple instance of circular motion thus pro duced could you give - ON COMPOUND MOTION. 53 Caroline, This is a little more difficult to comprehend than compound motion in straight lines. Mrs, B. You have seen a mop trundled, and have observed that the threads which compose the head of the mop fly from the centre ; but being confined to it at one end, they cannot part from it ; whilst the water they contain, being unconfined, is thrown off in straight lines. Emily, In the same way, the flyers of a windmill, when put in motion by the wind, would be driven straight forwards in a right line, were they not confined to a fixed point round which they are compelled to move. Mrs. B, Very well. And observe, that the point to which the motion of a small body, such as the ball with the string, which may be considered as revolving in one plane, is confined, becomes the centre of its motion. But when the bodies are not of a size or shape to allow of oar considering every part of them as moving in the same plane, they in reality revolve round a line, which line is called the axis of motion. In a top, for instance, when spinning on its point, the axis is the line which passes through the middle of it, perpendicularly to the floor. Caroline, The axle of the flyers of the windmill is then the axis of its motion ; but is the centre of motion always in the middle of a body 1 Mrs, B, No, not always. The middle point of a body is called its centre of magnitude, or position, that is, the centre of its mass or bulk. Bodies have also another centre, called the centre of gravity, which I shall explain to you ; but at present we must confine ourselves to the axis of motion. This line you must observe re- mains at rest, whilst all the other parts of the body move around it ; when you spin a top the axis is stationary whilst every other part is in motion round it. Caroline. But a top generally has a motion forwards, besides its spinning motion ; and then no point within it can be at rest ? Mrs, B, What I say of the axis of motion relates only to circular motion ; that is to say, to motion round a line, and not to that which a body may have at the same time in any other direction. There is one circumstance 171. What is meant by the axis of motion ? 172. Is the centre of motion always in the middle of a body ? 173. What is the middle point of a body called ? 174 How is the ve- locity of motion at different distances from the axis of motion ? 5* 54 ON COMPOUND MOTION. in circular motion, which you must carefully attend to ; which is, that the; further any part of a body is from the axis of motion, the greater is its velocity ; as you approach that line, the velocity of the parts gradually diminish till you reach the axis of motion, which is perfectly at rest. Caroline, But, if every part of the same body did not move with the same velocity, that part which moved quickest, must be separated from the rest of the body, and leave it behind ? Mrs, B. You perplex yourself by confounding the idea of circular motion, with that of motion in a right line ; you must think only of the motion of a body round a fixed line, and you will fmd, that if the parts farthest from the centre had not the greatest velocity, those parts would not be able to keep up with the rest of the body, and would be left behind. Do not the extremities of the vanes of a windmill move over a much greater space than the parts nearest the axis of motion ] (pi. III. fig. 1.) The three dotted circles describe the patlis in which three different parts of the vanes move, and though the circles are of different dimensions, the vanes describe each of them in the same space of time. Caroline. Certainly they do ; and I now only wonder that we neither of us ever made the observation before ; and the same effect must take place in a solid body, like the top in spinning ; the most bulging part of the surface must move with the greatest rapidity. Mrs, B, The force which confines a body to a cen- tre, round which it moves, is called the centripetal force ; and that force which impels a body to fiy from the centre is called the centrifugal force ; in circular motion these two forces constantly balance each other ; otherwise the revolving body would either approach the centre, or re- cede from it, according as the one or the other prevailed. Caroline, When I see any body moving in a circle, I shall remember that it is acted on by two forces. Mrs, B. Motion, either in a circle, an ellipsis, or any other curve-line, must be the result of the action of two forces ; for you know, that the impulse of one single force always produces motion in a right line. 175. What fiorure illustrates this? 176. What are the forces called in circular motion, that balance or act in opposition to each other? 177. What is meant by centripetal motion r • 178. What is meant by centrifugal motion ? ON COMPOUND MOTION. 65 Emily. And if any cause should destroy the centripetal force, the centrifugal force would alone impel the body, and it would, I suppose, fly off in a straight line from the centre to which it had been confined. Mrs, B, It would not fly ofl* in a right line from the centre ; but in a right line in the direction in which it was moving, at the instant of its release ; if a stone, whirl- ed round in a sling, gets loose at the point A (plate III. fig. 2.) it flies ofl" in the direction A B ; this line is called a tangent, it touches the circumference of the circle, and forms a right angle with a line drawn from that point of the circumference, to the centre of the circle C. Emily, You say, that motion in a curve-line is owing to two forces acting upon a body ; but when I throw this ball in a horizontal direction, it describes a curve line in falling ; and yet it is only acted upon by the force of pro- jection ; there is no centripetal force to confine it, or pro- duce compound motion. Mrs, B, A ball thus thrown is acted upon by no less than three forces ; the force of projection, v/hicli you com- municated to it ; the resistance of the air through which it passes, which diminishes its velocity, without changing its direction ; and the force of gravity, which finally brings it to the ground. The power of gravity, and the resistance of the air, being always greater than any force of projection we can give a body, the latter is gradually overcome, and the body brought to the ground ; but the stronger the projectile force, the longer will these powers be in subduing it, and the further the body will go before it falls. Caroline, A shot fired from a cannon, for instance, will go much further, than a stone projected by the hand. 3Irs, B, Bodies thus projected, you observed, describ- ed a curve-line in their descent ; can you account for that? Caroline, No; I do not understand, why it should not fall in the diagonal of a square. Mrs, B, You must consider that the force of projec- tion is strongest when the ball is first thrown ; this force, 179. What would be the consequence, if, in circular motion, the centripetal should be destroyed ? 180. Which figure il- " lustrates tins ' 181. What is the line called in which a body would fiv ^^ 'ftho centripetal force were destroyed .'* 182. If a ball is thrown horizontally, how many forces operate upon it-? 163. What are they called f* 56 ON COMPOUND MOTION. as it proceeds, being weakened by the continued resist- ance of the air, the stone, therefore, begins by moving in a horizontal direction ; but as the stronger powers pre- vail, the direction of the ball will gradually change from a horizontal to a perpendicular line. Projection alone would drive the ball A to B, (fig. 3,) gravity would bring it to C ; therefore, when acted on in different directions, by these two forces, it moves between, gradually inclining more and more to the force of gravity, in proportion as this accumulates ; instead therefore of reaching the ground at D, as you supposed it would, it falls somewhere about E. Caroline, It is precisely so ; look, Emily, as I throw this ball directly upwards, how the resistance of the air and gravity conquer projection ! Now I will throw it upwards obliquely : see, the force of projection enables it, for an instant, to act in opposition to that of gravity ; but it is soon brought down again. Mrs. B, The curve-line which the ball has described, is called in geometry, di parabola ; but when the ball is thrown perpendicularly upwards, it will descend perpen- dicularly ; because the force of projection, and that of gravity, are in the same line of direction. We have noticed the centres of magnitude, and of mo- tion ; but I have not yet explained to you what is meant by the centre of gravity ; it is that point in a body, about which all the parts exactly balance each other ; if, there- fore, that point is supported, the body will not fall. Do you understand this 1 Emily, I think so ; if the parts round about this point have an equal tendency to fall, they will be in equilibrium, and as long as this point is supported, the body cannot fall. Mrs, B. Caroline, what would be the effect, were any other point of the body alone supported ? Caroline, The surrounding parts, no longer balancing each other, the body, I suppose, would fall on the side at which the parts are heaviest. Mrs, B, Infallibly : whenever the centre of gravity is unsupported, the body must fall. This sometimes hap- pens with an overloaded wagon winding up a steep hiD, 184. How would you explain Fig. 3. plate III.? 185. What is a parabola ? 186. Why will a stone thrown perpendicular- ly into the air descend perpendicularly .'' 187. vVhat is meant by the centre of gravity : 1S8. What part of a body must be supported to keep it from falhng ^ ON COMPOUND MOTION. 57 one side of the road being more elevated than the other ; let us suppose it to slope as is described in this figure, (plate III. fig 4,) we will say, that the centre of gravity of this loaded wagon is at the point A. Now your eye will tell you that a wagon, thus situated, will over- set ; and the reason is, that the centre of gravity, A, is not supported ; for if you draw a perpendicular line from it to the ground at C, it does not fall under the wagon within the wheels, and is therefore not supported by them. Caroline, I understand that perfectly ; but what is the meaning of the other point B ? Mrs, B. Let us, in imagination, take oif the upper part of the load ; the centre of gravity will then change its situation, and descend to B, as that will now be the point about which the parts of the less heavily laden wa- gon will balance each other. Will the wagon now be upset ? Caroline, No, because a perpendicular line from that point falls within the wheels at D, and is supported by them ; and when the centre of gravity is supported, the body will not fall. Emily. Yet I should not much like to pass a wagon in that situation ; for, as you see, the point D is but just within the left wheel ; if the right wheel was merely raised, by passing over a stone, the point D would be thrown on the outside of the left wheel, and the wa- gon would upset. Caroline, A wagon, or any carriage whatever, will then be most firmly supported, when the centre of gra- vity falls exactly between the wheels ; and that is the case in a level road. Pray, whereabouts is the centre of gravity of the hu- man body ? Mrs, B, Between the hips ; and as long as we stand upright, this point is supported by the feet ; if you lean on one side, you will find that you no longer stand firm. A rope-dancer performs all his feats of agility, by dexte- rously supporting his centre of gravity ; whenever he finds that he is in danger of losing his balance, he shifts the heavy pole, which he holds in his hands, in order to throw 18^. What explanation would you give of Fig. 4, plate III. ? 190. Why do persons in ascendin? a hill incline forward, and in descending it incline backward ? 191. How is it thnt rope- dancers are able to perform their feats of agility without falling ? 58 ON COMPOUND MOTION. the weight towards the side that is deficient ; and thus by changing the situation of the centre of gravity, he restores his equihbriuni. Caroline. When a stick is poised on the tip of the finger, is it not by supporting its centre of gravity ? 3Irs. B. Yes ; and it is because the centre of gravity is not supported, that spherical bodies roll down a slope. A sphere being perfectly round, can touch the slope but by a single point, and that point cannot be perpendicularly under the centre of gravity, and therefore cannot be sup- ported, as you will perceive by examining this figure, (fig. o. plate III.) Emily. So it appears ; yet I have seen a cylinder of wood roll up a slope ; how is that contrived ? Mm. B. It is done by plugging one side of the cylin- der with lead, as at B. (fig. 5. plate III.) the body being no longer of a uniform density, the centre of gravity is removed from the middle of the body to some point in the lead, as that substance is much heavier than wood ; now you may observe that in order that the cylinder may roll down the plane, as it is here situated, the centre of gra- vity must rise, which is impossible ; the centre of gravity must always descend in moving, and will descend by the nearest and readiest means, which will be by forcing the cylinder up the slope, until the centre of gravity is sup- ported, and then it stops. Caroline. The centre of gravity, therefore, is not al- ways in the middle of a body. Mrs. B. No, that point we have called the centre of magnitude ; when the body is of a uniform density the centre of gravity is in the same point ; but when one part of the body is composed of heavier materials than another part, the centre of gravity being the centre of the weight of the body can no longer correspond with the centre of magnitude. Thus you see the centre of gravity of this cylinder, plugged with lead, cannot be in the same spot as the centre of magnitude. Emily. Bodies, therefore, consisting but of one kind 192. Why do spherical bodies roll down a slope or inclined plane ? 193. By which figure is this illustrated ? 194. How can a cylinder of wood be made to roll up a slope .'* 195. Is the centre of gravity always the centre of magnitude? 190. When is the centre of gravity in the same point with the centre of magnitude? 197. When will they not be in the same point? ON COMPOUND MOTION. 59 of substance, as wood, stone, or lead, and whose densities are consequently uniform, must stand more firmly, and be more difficult to overset, than bodies composed of a variety of substances, of different densities, which may throw the centre of gravity on one side. Mrs, B. Yes ; but there is another circumstance which more materially affects the firmness of their position, and that is their form. Bodies that have a narrow base are easily upset, for if they are the least inclined, their centre is no longer supported, as you may perceive in fig. 6. Caroline, I have often observed with what difficulty a person carries a single pail of water ; it is owing, 1 suppose, to the centre of gravity being thrown on one side, and the op}X)site arm is stretched out to endeavour to bring it back to its original situation ; but a pail hanging on each arm is carried without difficulty, because they ba- lance each other, and the centre of gravity remains sup- ported by the feet. Mrs. B, Very well ; I have but one more remark to make on the centre of gravity, which is, that when two bodies are fastened together, by a line, string, chain, or any power whatever, they are to be considered as forming but one body ; if the two bodies be of equal weight, the centre of gravity will be in the middle of the line which unites them, (fig. 7,) but if one be heavier than the other, the centre of gravity will be proportionally nearer the heavy body than the light one. (fig. 8.) If you were to carry a rod or pole with an equal weight fastened at each end of it, you would hold it in the middle of the rod, in order that the weights should balance each other ; whilst if it had unequal weights at each end, you would hold it nearest the greater weight, to make them balance each other. Emily, And in both cases we should support the cen- tre of gravity ; and if one weight be very considerably larger than the other, the centre of gravity will be thrown out of the rod into the heaviest weight. (fig. 9.) Mrs, B, Undoubtedly. 198. What bodies stand most firmly, and what ones are most easily upset ? 199. What is the object of Fig. 6, plate III. t 200. Why can a person carry two pails of water, one in each hand, easier than a sinj^le pail ? 201. If two bodies are connect- ed togetlier, how are they to be considered as to their centre of gra- vity ^ 20*2. If they are of equal weight, where will the centre of gravity be ? 203. If they are of unequal weight, where will it be ? 204. What is the object of Fig. 7, 8, and 9, of plate III. ? 60 ON THE MECHANICAL POWERS. 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 be- tween 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 beticeen the Fulcrum and the Weight. MRS. B. We may now proceed to examine the mechanical pow- ers ; they are six in number, one or more of which enters into the composition of every machine. The lever, the pulley, the ivheel, and axle, the inclined plane, the wedge, and the screiv. In order to understand the power of a machine, there are four things to be considered. 1st. The power that acts : this consists in the effort of men or horses, of weights, springs, steam, &c. 2dly. The resistance which is to be overcome by the power ; this is generally a weight to be moved. The power must always be superiour to the resistance, other- wise the machine could not be put in motion. Caroline, If, for instance, the resistance of a carriage was greater than the strength of the horses employed to draw it, they would not be able to make it move. Mrs, B, 3dly. We are to consider the centre of mo- tion, or as it is termed in mechanicks, the fulcrum ; this, you may recollect, is the point about which all the parts of the body move ; and lastly, the respective velocities of the power, and of the resistance. Emily, That must depend upon their respective dis- tances from the axis of motion ; as we observed in the motion of the vanes of the windmill. Mrs, B, We shall now examine the power of the lever. The lever is an inflexible rod or beam of any kind, that is to say, one which will not bend in any direction, 205. How many of the mechanical powers are there ?■ 206. What are the names of them ? '207. In order to un- derstand the power of a machine, how many things are to be considered 208. What is the first ? — the second ? — the third ^ ^200. What is the lever - ON THE MECHANICAL POWERS. 61 For instance, the steel rod to which tliese scales are sus- pended is a lever, and the point in which it is supported the fulcrum, or centre of motion ; now, can you tell me why the two scales are in equilibrium ? Caroline, Being both empty, and of the same weight, they balance each other. Emily, Or, more correctly speaking, because the centre of gravity common to both is supported. Mrs, B, Very well ; and which is the centre of gra- vity of this pair of scales? (fig. 1. plate IV.) Emily, You have told us that when two bodies of equal weight were fastened together, the centre of gravity was in the middle of the line that connected them ; the centre of gravity of the scales must therefore be in the ful- crum F of the lever which unites the two scales ; and cor- responds with the centre of motion. Caroline, But if the scales contained different weights, the centre of gravity would no longer be in the fulcrum of the lever, but removed towards that scale which contained the heaviest weight ; and since that point would no longer be supported, the heavy scale would descend and out- weigh the other. Mrs, B, True ; but tell me, can you imagine any mode by which bodies of different weights can be made to balance each other, either in a pair of scales, or simply suspended to the extremities of the lever ? for the scales are not an essential part of the machine, they have no me- chanical power, and are used merely for the convenience of containing the substance to be weighed. Caroline, What ! make a light body balance a heavy one ? I cannot conceive that possible. 3Irs, B, The fulcrum of this pair of scales (fig. 2.) is moveable, you see ; I can take it off the prop, and fasten it on again in another part ; this part is now become the fulcrum, but it is no longer in the centre of the lever. Caroline, And the scales are no longer true ; for that which hangs on the longest side of the lever descends. Mrs, B, The two parts of the lever divided by the ful- crum are called its arms, you should therefore say the longest arm, not the longest side of the lever. These 210. Why are the scales as seen in Fig. 1, plate IV. in equi- lifbrium ? 211. What is the centre of gravity to two scales in e/iuilibrium as seen in that figure ? ^212. What are the arms of a lever ? 6 Q% ON THE MECHANICAL POWERS. arms are likewise frequently distinguished by the appella- tions of the acting and the resisting part of the lever. Your observation is true that the balance is now de- stroyed ; but it will answer the purpose of enabling you to comprehend the power of a lever when the fulcrum is not in the centre. Emily, This would be an excellent contrivance for those who cheat in the weight of their goods ; by making the fulcrum a little on one side, and placing the goods in the scale which is suspended to the longest arm of the lever, they would appear to weigh more than they do in reality. Mrs, B, You do not consider how easily the fraud would be detected ; for on the scales being emptied, they would not hang in equilibrium. Emily. True ; I did not think of that circumstance. But I do not understand why the longest arm of the lever should not be in equilibrium with the other. Caroline, It is because it is heavier than the shortest arm ; the centre of gravity, therefore, is no longer sup- ported. Mrs, B, You are right ; the fulcrum is no longer in the centre of gravity ; but if we can contrive to make the fulcrum in its present situation become the centre of gra- vity, the scales v/ill again balance each other ; for you recollect that the centre of gravity is that point about which every part of the body is in equilibrium. Emily, It has just occurred to me how this may be accomplished ; put a great weight into the scale suspended to the shortest arm of the lever, and a smaller one into that suspended to the longest arm. Yes, I have disco- vered it — look, Mrs. B., the scale on the shortest arm will carry 21bs., and that on the longest arm only one, to re- store the balance, (fig. 3.) MrSf B, You see, therefore, that it is not so imprac- ticable as you imagined to make a heavy body balance a light one ; and this is in fact the means by which you thought an imposition in the weight of goods might be effected, as a weight of ten or twelve ounces might thus be made to balance a pound of goods. Let us now take 213. What is the reason that the arms of the lever, as seen Fig. 2, plate IV. are not supported ^ 214. In what way can Jhey be made to support each other .'< 215. What is illustrated bj Fig. 3, plate IV. ^ ON THE MECHANICAL 1»0>VERS. 63 off the scales that we may consider the lever simply ; and in this state you see that the fulcrum is no longer the cen- tre of gravity ; but it is, and must ever be, the centre of motion, as it is the only point which remains at rest, while the other parts move about it. Caroline, It now resembles the two opposite vanes of a windmill, and the fulcrum the point round which they move. Mrs, B, In describing the motion of those vanes, you may recollect ouf observing that the further a body is from the axis of motion, the greater is its velocity. Caroline, That I remember and understood perfectly. Mrs, B, You comprehend then, that the extremity of the longest arm of a lever must move with greater velocity than that of the shortest arm ? Emily, No doubt, because it is furthest from the cen- tre of motion. And pray, Mrs. B., when my brothers play at see-saw, is not the plank on which they ride a kind of lever ? Mrs, B, Certainly ; the log of wood which supports it from the ground is the fulcrum, and those who ride represent the power and the resistance at each end of the lever. And have you not observed that when those who ride are of equal weight, the plank must be sup- ported in the middle to make the two arms equal ; whilst if the persons differ in weight, the plank must be drawn a little further over the prop, to 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 ; I 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 the velocity with which your little brother moves, renders his momentum equal to yours. Caroline, Yes ; I have the most gravity, he the great- est velocity ; so that upon the whole our momentums 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 ? SI 6. What is the velocity of the extremity of the longest arm of a lever compared with that of the shortest arm ? 64 ON THE MECHANICAL POWERS. Mrs. B, Because each person at his descent touches the ground with his feet ; the re-action of which gives him an impulse which increases his velocity ; this spring is requisite to destroy the equilibrium 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 m.ake a sketch of you and your brother riding on a plank, in order to convince you of your error, (fig. 4, pi. IV.) You may now observe that a lever can move only round the 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 ; you must in rising and he in descending describe arcs of your respective circles. This drawing shows you also how much superiour his velocity must be to yours ; for if you could swing quite round, you would each complete your respective 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 I 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 say- ing, that in mechanicks, motion was opposed to matter, for it is my brother's velocity which overcomes my w^eight. 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 comparison to the resisting part, the greater is the effect produced by it ; because the greater is the velocity of the power com- pared to that of the weight. There are three different kinds of levers ; in the first the fulcrum is between the power and the weight. 217. What does a levor in its motion describe ? 218. What is the design of Fig.^4, plate IV. .? 219, To what is the great- ness of effect produced by the lever proportional ? 220. How many kinds of levers aro there ? ON THE MECHANICAL POWERS. 65 Caroline, This kind then comprehends the several levers you have described. Mrs, B, Yes, when in levers of the first kind, the ful- crum 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 lever being equal, the velocity of their extremities must be so likewise. The balance is therefore of no assistance as a mechanical power, but it is extremely useful to estimate the respective weights of bodies. But when (fig. 5.) 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 superiour velocity ; as we observed in the see-smv, 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 re- quired ; 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 ap- plied 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 composed of two levers, united in one common fulcrum. Caroline. A pair of scissors ! Mrs. B. You are surprised, but if you examine their construction, you will discover that it is the power df the lever that assists us in cutting with scissors. 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 fingers is applied, 221. Where is the fulcrum in the first kind ? 222. How are we to use levers of the first kind in raisins^ large weights ? 223. What power of mechanicks do the common scissors involve .'' 224. How may the scissors be explained as formed by the lever =" € * 66 ©W THE MECtfANlCAL POWERS. are the extremities of the acting part of the leversy and the cutting part of the scissors, are the resisting parts of the levers : therefore, the longer the handles and the shorter the points of the scissors, the more easily you cut with them. Emily, That I have often observed, for when I cut pasteboard or any hard substance, I always make use of that part of the scissors nearest the screw or rivet, and I now understand why it increases the power of cutting ; but I confess I never should have discovered scissors 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 powef 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 1 Caroline, Oh yes ; and this was a lever of the second 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 kver ; 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 225. How is the second kind of lever designated ? 226* Wliich figures illustrate the use of levers of the second kind? -^ — 227. To what is the advantage gained in the use of the se- cond kind of lever proportional ? ON THE MECHANICAL POWERS. 67 into the sea, by means of slippery pieces of board whicli 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, our 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 consequently occupies the whole of the space between the power and the fulcrum. Nut-crackers are double levers 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 resistance 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 further 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 the 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 tinrd 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. 228. What are the most common examples of levers of the se- cond kind ? 229. How would you explain the opening of a common door, as involving the principle of the second kind of le- vers ? 230. What is the third kind of levers ? 231. What is an instance of its use ? 232. 'How does the raising of a weight by the hand represent this kind of levers .'' 68 OS THE MECHANICAL POWERS. 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 resulting from this structure of the arm : and it is no doubt that which is best adapted to enable it to perform its various functions. We have dwelt so long on the lever, that we must re- serve the examination of the other mechanical powers to our next interview. CONVERSATION V. CONTINUED. ON THE MECHANICAL POWERS. Of the Pulley ; Of the Wheel and Axle ; Of the Inclined 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, (pi. 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 employ- ed 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 mechanicks ? 233. What is the second mechanical power ? 234. What is a pulley ? 235. How does Fig. 1. plate V. illustrate the fixed pulley ^ 236. How must the power compare with the weight in order to move it, by the use of the fixed pulley ? ON THE MECHANICAL POWERS. W Mrs. B. The next figure represents a pulley which is not fixed, (fig» 2.) and thus situated you will perceive that it aflfords us mechanical assistance. In order to raise the weight (W) one inch, P, the power, 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 at- tached to it, can be raised only half an inch. Caroline. I am ashamed of my stupidity ; but I con- fess that I do not understand this ; it appears to me that the weight would be raised as much as the string is short- ened 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 advanced one yard. Mrs, B, This exemplifies the nature of a single fixed pulley only. Now unfawSten the string, and replace the chair where it stood before. In order to represent the moveable pulley, we must draw the chair forwards by put- ting the string round it ; one end of the string may be fas« tened 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 represents the weight to which the moveable pulley is attached ; and it is very clear that the weight can be drawn only half the length you draw the string. I believe the cir- cumstance that perplexed me was. that I did not observe the difference that results from the v/eight being attached to the pulley, instead of being fastened to the string, as is the case in the fixed pulley. Emily, But I do not yet understand the advantage of pulleys ; they seem to me to increase rather than diminish the difhculty of raising weights, since you must draw the string double the length that you raise the weight ; whilst 237. What kind of pulley does Fig. 2, plate V. represent, and hov/ would you explain it ? 70 ON THE MECHANICAL POWERS. with a single pulley, or without any pulley, the weight k raised as much as the string is shortened. Mrs, B. The advantage of a moveable pulley consists in dividing the difficulty ; we must draw, it is true, twice tlie length of the string, but then only half the strength is reqiiired that would be necessary to raise the weight without the assistance of a moveable 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 momentums equal. Caroline. Pulleys act then on the same principle as the lever, the deficiency of strength of the power being compensated by its superiour 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 1 Mrs. B. Tliat, my dear, is the fundamental law in mechanicks : 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 mecha- nical powers then, if what we gain by them one way is lost another. Mrs. B. Since we are not able to increase our natu- ral strength, is not that science of wonderful utility, by means of which we may reduce the resistance or weight of any body to the level of our strength ? This the mechanical powers enable us to accomplish, by dividing the resistance of a body into parts which we can succes- 238. In what does the advantage of a moveable pulley consist ? 239. How do the weight and power of a moveable pulley com- pare, that their momenta be equal ? 240. On what principle are all mechanical powers founded.' 241. Is there any loss of time in the use of the moveable pulley ? 242. And to what is this loss of time proportional ? 243. What then is the ad- vantage of this pulley, or of any of the mechanical powers, if there Lsas much loss in time as gain in power r ON THE MECHANICAL POWERS- 71 aively 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 unlimited command of time. You can now under- stand, that the greater the number of pulleys connected by a string, the more easily the weight is raised, as the difficulty is divided among 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 sys- tem, or tackle of pulleys, (fig. 3.) You may have seen them suspended from cranes to raise goods into ware- houses, and in ships to draw up the sails. Emily, But since a fixed pulley affords us no mecha- nical aid, why is it ever used ? Mrs, B. Though it does not increase our power, k is frequently useful for altering its direction. A single pulley enables us to draw up a curtain, by drawing down the string connected with it ; and we should be much at a loss to accomplish this simple operation without its as- sistance. Caroline, There would certainly be some difficulty 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 an- swer a very useful purpose, Mrs, B. In shipping, both the advantages of an in- crease 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 me- chanical power of a combination of pulleys. Emily, But the pulleys on ship-board do not appear to me to be united in the manner you have shown us. Mrs, B. They are, I believe, generally connected as described in figure 4, both for nautical, and a variety of other purposes ; but in whatever manner pulleys are con- nected by a single string, the mechanical power is the same. 244. What is a system or tackle of pulleys, and which fi^^ure exhibits it ? 245. If there is no mechanical aid from the fixed pulley, why is it used ? 7/J ON THE MECHANICAL POWERS. The third mechanical power is the wheel and axle. Let us suppose (plate V. fig. 5.) the 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 as- sistance 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 increased in the same pro- portion 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 be- lieve, instead of a wheel attached to the axle, only a crooked handle, which answers the purpose of winding the rope round the axle, and thus raising the bucket. Mrs. J5. In this manner (fig. 6.) ; now if you observe the dotted circle which the handle describes in winding up the rope, you will perceive that the branch of the han- dle 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 affords no mechanical aid, merely serving as a handle to turn the wheel. Wheels are a very essential part to most machines : 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. 246. What is the third mechanical power?- 247. What ^oes Fig. 5, plate V. illustrate .' 248. In what proportion is the power of the wheel increased ^ 249. How may a wheel he compared to the lever ? 250. How does Fig. 6, plate V. repre- fient a wheel ' ON THE MECHANICAL POWERS. 73 Mrs. B, Certainly. If you have ever seen any con- siderable 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 povverful and the most convenient mode of turning the wheel. Caroline, Do not the vanes of a windmill represent a wheel, Mrs. B. ? 3Irs* J5. Yes ; and in this instance we have the ad- vantage 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 ex- pansive 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 declivity, 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 perpendicularly. 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, m.ust move from B to C, and as the 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 con- fined to the short line A C, is spread over the long line BC. Mrs. B. The wedge, which is the next mechanical power, is composed of two inclined planes, (fig. 8.) : you 251. On what mechanical force is the wind-mill operated ? 252. What is f-^und to be the most powerful and convenient mode of turning the wheel ? 253. What is one of the great benefits resultins: from tho use of machinery ? 254. What is the fourth mechanical power.' 2.'5. What is an inclined plane ? 256. How would you explain Fig. 7, plate V. .' 257. How much is the resistance of the weight dimin^'shed by the use of the inclined plane ? 258. Of what is the wed^e com- posed ."* 7 T4 ON THE MECHANICAL POWERS. may have seen wood-cutters use it to cleave wood. The resistance consists in the cohesive attraction of the wood, .or any other body which the v/edge is employed to sepa- rate ; and the advantage gained by this power is in the proportion of half its width to its length ; for while the wedge forces asunder the coherent particles of the wood to A and B, it penetrates downwards as far as C. Emily. The wedge, then, is rather a compound than a distinct mechanical power, since it is composed of two inclined planes. Mrs, 13. 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, like the chisel, may be referred to the inclined plane ; whilst the axe, the hatchet, and the knife (when used to split asun- der) are used as wedges. Carolme. But a knife cuts best when it is drawn across the substance it is to divide. We use it thus in cutting meat, we do not chop it to pieces. 3Irs, 13. The reason of this is, that the edge of a knife is really a very fine saw, and therefore acts best when used like 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 tliread ; 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 which screws on the box as you have described ; but what is this handle which projects from the nut ? 3Irs. B. It is a lever, which is attached to the nut, without which the screw is never used as a mechanical 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 referrible to one of the most simple of the mechanical powers ; which of them do you think it is ? 259. In what does the resistance of the wedge consist .•' 260. On what mechanical principles are cutting instruments de- signed .? 261. Whicli is the last mechanical power ? 262. Of what is the screw composed ? 263. What is the construc- tion of the screw and nut ? 264. How would vou explain Fig. 9, plate V. ? ON THE MECHANICAL POWERS. 75 Carolhie, In appearance, it most resembles the wheel and axle. 3Irs. B, The lever, it is true, has the effect of a wlieel, as it is the means by which you wind the nut round; but the lever is not considered as composing a part of the screvv, though it is true, that it is necessarily attached to it. But observe, that tho lever, considered as a u'heel, 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 uay in which you turn it. Emihj, The spiral thrend of the screw resembles, I think, an inclined piaffe : it is a sort of slope, by means of v/hich 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 protu- berance of the screw, (fig. 10.) Emily. Very true ; the nut then ascends an inclined plane, but ascends it in a spiral, instead of a straight line ; the closer the thread of the screw, the more easy the as- cent ; it is like having shallow, instead 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 clo- ser the threads of the screw, the greater the number of revolutions the winch must make ; so that v^^e return to the old principle, — what is saved in power is lost in time. Emily, Cannot the power of a screw be increased 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, employed 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 presses, 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 265. To which of the other mechanical powers is the screw referrible r ^(5(), How can the power of the screw be in- creased ? 76 ON THE MECHANICAL POWERS. more remark to make to you relative to them, which is, that friction in a considerable degree diminishes their force, allowance must therefore always be made for it in the construction of machinery. Caroline. Ey friction, do you mean one part of the machine rubbing against another pari 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 evenness 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 w ill 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 J Mrs. JB. In proportion as the surfaces of bodies are well polished, the friction is doubtless diminished ; but it is always considerable, and it is usually computed to de- stroy one-third of the power of a machine. Oil or grease is used to lessen friction ; it acts as a polish by tilling up the cavities of the rubbing 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-not withstanding their being polished and oiled, a con- siderable degree of friction is produced. There are two kinds of friction ; the one occasioned 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 considerable, for great fcwce is required to enable the sliding body to overcome 266. What diminishes the force of all machinery ? 667. What are we to understand by friction in machinery ? 268. In what proportion is the friction of machinery destroyed ? ^269. How much of the power of a machine is reckoned ta be destroyed by friction ? 270. What is commonly used to lessen the friction of machinery ? 271 . Why will oil and grease lessen the friction of machinery ^ ^272. How many kinds of friction are there ? ^273. What are they .^ 274. Which is the most considerable .' ON tflfi MECHANICAL POWERS. ^^ 77 the resistance which the asperities of the surfaces in con- tact oppose to its motion, and it must be either lifted over or break through them ; wiiilst, in the other kind of fric- tion, the rough parts roll over each other with comparative facility ; hence it is, that wheels are often used for the sole purpose of diminishing the resistance of friction. Eniilji, This is one of the advantages of carriage- wheels ; is it not ? 3Irs, B. Yes ; and the larger the circumference of the wheel, the more readily it can overcome any consider- able 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 in- creasing the friction. Caroline, That is to say, by converting the rolling fric- tion 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 into tlie rolling friction. Mrs. B, There is another circumstance which we have already noticed, as diminishing the motion of bodies, and v/hich greatly affects the power of machines. This is the resistance of the medium in which a machine is worked. All fluids, whether of the nature of air, or of water, are called mediums ; and their resistance is pro- portioned 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 . Emih/. 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 me- chanical powers. At our next meeting I shall endeavour to give you an explanation of the motion of the heavenly bodies. 275. Which will most readily overcome obstacles, a large or a small wheel ? 276. Why is a wheel fastened on descending a hill ? 277. What besides friction diminishes the force of all machinery ? ^278. What is meant by mediums ? 279. To what is their resistance proportioned ? 280. In what state would the force of machinery be perfect ? •7* 78 CAUSES OF THE EARTH's ANNUALr MOTION. CONVERSATION VI. CAUSES OF THE EARTH's ANNUAL MOTION. Of the Planets, and their Motion ; Of the Diurnal Mo- tion 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 pow- erful objection to your theory of attraction, that I doubt whether even your conjuror Newton, with his magick 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 proportion 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, pre- tend to say that we are falling towards the sun ? Emily, However j)lausible your objection appears, Caroline, I think you place too much reliance upon it : when any one has given such convincing proofs of saga- city and wisdom as Sir Isaac Newton, when we find that his opinions are universally received and adopted, is it to be expected that any objection we can advance should overturn them 1 Caroline, Yet I confess that I am not inclined to yield implicit faith even to opinions of the great 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 theories 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 ques- tions ; you 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 281. If bvodies attract eachjother in proportion to the quantity of matter they contain, why does not the sun attract the earth completely to itself? CAUSES OF THE EARTH's ANNtJAL MOTION. 79 with so much confidence, in order that the discovery of iheir 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 consum- ed 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 caba- listical figures, which I must draw for him. 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 6., A represents the earth, and S the sun. We shall suppose the earth to be arrived at the point in which it is represented 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 forces of projection and attraction do not act in opposition, but perpendicu- larly, 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 act- ed upon by two forces perpendicular to each other w^ould move in the diagonal of a parallelogram ; if, therefore, I complete the parallelogram by drawing the lines C D, B D, the earth will move in the diagonal A D. Mrs. B. A ball struck by two forces acting perpen- dicularly 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 deviation from its course in a right line, which converts it into that of a curve line ; every point of which may be considered as constituting the diagonal of an infinitely small parallelogram. 282. If the earth at its creation had been put in motion by a single force without resistance, what would have been its course ? — - — 283. How would you illustrate this by the figure ? 284. What prevents the earth from proceeding on in a right line, as im- pelled by its projectile force ? 285. In what direction does the attractix)n of the sun operate on the projectile force of the earth ? 286 When two forces operate perpendicularly on each other, in what direction will be their compound motion ^ 287. Why then is the line A D in Figure 1, circular instead of being a right line diagonal to the parallelogram, A B D C ? 80 CAUSES OF THE EARTH's ANNUAL MOTION. 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 ten- dency to fly off in a straight line ; but a straight line would now carry it away to F, whilst the sun would at» tract it in the direction D S ; how then will it proceed ? Emily, It will go on in a cuive line, in a direction between that of the two forces. Mrs, JB, 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 pro- jection, 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 parallel- ogram, Mrs. B. Let me consider in what direction will the force of projection now impel the earth. 3Irs. B, First draw a line from the earth to the sun representing the force of attraction : then describe 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 H I 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 diagonals 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 continue to follow, as long as it remains in existence. Emily, What a grand and beautiful effect resulting from so simple a cause ! Caroline, It affords an example on a magnificent scale, of the circular motion which you taught us in mechanicks. The attraction of the sun is the centripetal force, which confines the earth to a centre ; and the im- 288. How would yon explain the continued motion of the earth about the sun by the. use of Fig. 1, plate VI ^ 289. What is the attraction of the sun called .' 290. And what is the projectile force of the earth called P CAUSES OF THE EARTh's ANNUAL MOTION. 81 pulse 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 illustrating 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 angular point re- presenting the earth, and to fasten the extremity of one of the legs of the angle to a fixed point, which we shall con- sider as the sun. Thus situated, the angle will represent both the centrifugal and centripetal forces ; and if you draw it round the fixed point, you will see how the di- rection of the centrifugal force varies, constantly forming a tangent to tlie circle in which the earth moves, as it is constantly at a right angle with the centripetal force. Emily, The earth, then, gravitates towards the sun without the slightest danger either of approaching nearer or receding further from it. How admirably this is con- trived ! If the two forces which produce this circular mo- tion had not been so accurately adjusted, one would ulti- mately 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 you that these two forces are not, in fact, so proportion- ed as to produce circular motion in the earth 1 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 gravity, so as to enable these powers conjointly to carry it round the sun in a circle ; the earth, instead of describing the line A C, as in the former figure, will 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 ad- vance towards it, and produces an accelerated velocity in the earth, which increases the danger. 291. What simple illustration is given in Fig. 2, plate VI. of the combined forces, which produced the revolution of the earth about the sun .'' 292. Does the earth revolve in an exact cir- cle about the sun ? 293. What is the design of Fig. 3, plate VI. .' 294. In Fig. 3, plate VI. why is the earth in the line at B instead of the line at C according to the principle of Fig. I. ^ 82 CAUSES OF THE EARTH's ANNUAL MOTION. Mrs, jB. And there is yet another danger, of which you are not aware. Observe, that as the earth approaches the sun, the direction of its projectile force is no longer per- pendicular to that of attraction, but inclines more nearly to it. When the earth reaches that part of its orbit at B, the force of projection 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 ether 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 continu^s^pproach- ing the sun with a uniformly increasing accelerated mo- tion, 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 situat- ed 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 centri- fugal force increases with the velocity of the body, or, in other words, the quicker it moves, the stronger is its ten- dency to fly off in a right line. When the earth, there- fore, arrives at E, its accelerated motion will have so far increased its velocity, and consequently its centrifugal force, that the latter will prevail over the force of at- traction, and drag the earth away fi"om 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 w^e recede from it, the force of its attraction, and, conse- quently, the velocity of the earth's motion are dimi- nished. 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 retarded motion, till it has completed its revolution. Thus you see, that the earth travels round the sun, not in a circle, but an 205. When the erirth arrives at E in the figure, why does it not revolve in a small circular orbit instead of recedin*^ off in tlie direction G ? 2*-0. What is the figure called that the earth t'e- .•icrites in its revolut.'on about the sun - CAUSES OF THE EARTH's ANNUAL MOTION. 83 ellipsis, of which the sun occjpies one of the foci; and that in its coarse the earth alternately approaches, and recedes from it, without any danger of being either swal- lowed up, or being eiitirely carried away from it. Caroline, And I 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. Mrc^. B. It is mathematically demonstrable, that, in moving round a point towards v/hich 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., di- vided into a number of areas, or spaces, 1, 2, 3, 4, 6lc, all of which are of equal dimensions, though of very different forms ; some of them, you see, are long and narrow, others broad an.l short : but they each of them contain an equal quantity of space. An imaginary line drawn from the cen- tre of tlie earth to that of the sun, and keeping pace with the earth in its revolution, passes over equal areas in equal 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 per- form in tlie 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 ap- pears in this figure ; for the earth's orbit is not so eccen- trick 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. 297. What is the name of the place occupied by the sun with- in the orbit of the earth ? 298. Is the earth's motion in moving round the sun uniform ? 299. What is mathematically demon- strable in relation to abodv moving round a point towards which it is attracted ? 300. What is the desis^n of Fiff. 4, plate VI. ? 301 . What is that part of the earth's orbit called which is most dis- tant from th3 sun.' 302. What is that part called which is nearest the sun .' 303. How much nearer is the earth to the sun in perihehon than at its aphelion .' 84 CAUSES OF THE EARTH'S ANNUAL MOTION. 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 sum- mer, the earth is in that part of its orbit which is moFt distant from the sun, and it is during the severity of win- ter, 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 ? 3Irs. B. The difference of the earth's distance from the sun in summer and winter,\vhen compared with its total distance from the sun, is but inconsiderable. 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 diffe- rence, would scarcely be sensible, w^ere it not completely overpowered by other causes which produce the variations of the seasons ; but these I shall defer explaining till we liave 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 ? 3Irs. B. It actually does when accurately measured ; but the apparent difference in size, is, I believe, not per- ceptible to the n?ked eye. Emily. Then, since the earth moves with the 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? 3frs. B. Yes, it is about seven days longer perform- ing the summer-half of its orbit, than the winter-holf. The revolution of all the planets round the sun is the re- sult of the same causes, and is performed in the same manner as that of the earth. Caroline. Fray what are the planets ? 3Irs. B. They are those celestial bodies, which re- volve like our earth about the sun ; they are supposed to resemble the earth also in many other respects ; and we 304. Is the earth nearest tlie sun in summer or^Yinte^ ? 305. How much Jono-PT is the earth performing the snmnier-half than the winter -hah of its orbit ? 306. What are the planets ? CAUSES OF THE EARTH'S ANNUAL MOTION. 85 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 a stretch of the imagination 1 Mrs, B, Some of the planets are proved to be larger than the earth ; it is only their immense distance from us, which renders their apparent dimensions so small. Now, if we consider them as enormous globes, instead of small twinkling spots, we shall be led to suppose, that the Al- mighty would not have created them merely for the pur- pose of giving us a little light in the night, as it was formerly imagined, 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, blessed by his providence. Both in a moral as well as a physical point of view, it appears to me more rational to consider the planets as worlds revolving round the sun ; and the fixed stars as other suns, each of them attended by their re- spective system of planets, to which they impart their in- fluence. We have brought our telescopes to such a de- gree of perfection, that from the appearances which the moon exhibits when seen through them, we have very good reason to con hide, 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 val- leys ; and some astronomers have gone so far as to ima- gine they discovered volcanoes. Emily, If the fixed stars are suns, with planets re- volving 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. Second- ly, 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 307. Why do we suppose the planets are inhabited ? 308. If the planets are worlds like our own, why do they appear so small ? 309. If the fixed stars are suns, with planets revolv- ing round them, why should we not see those planets as well as their suns ? 8 86 CAUSES OF THE EARTH'S ANNUAL MOTION. 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 day-light. 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 atmo- sphere, that it is entirely effaced 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 diffused 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 1 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 faintness 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 towards the sun ; and that this force combined with that of projection, will occasion their revolution round the sun, in orbits more or less elliptical, according to the proportion which these two forces bear to each other. But the planets have also another motion ; they re- volve upon their axes. The axis of a planet is an ima- ginary line which passes through its centre, and on which it turns ; and it is this motion which produces day and night. With that side of the planet facing the sun it is day ; and with the opposite side, which remains in dark- ness, it is night. Our earth, which we consider as a planet, is 24 hours in performing one revolution on its 310. Why do we not see the stars in the daytime^ oil. What motion have the planets besides that about the sun ? 311,* What is the axis of a planet ? CAUSES OF THE EARTH's ANNUAL MOTION. 87 axis ; in that period of time, therefore, we have a day and a night ; hence this revolution is called the earth's diur- nal 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 independ- ent of any planet, travelling in the skies, and looking up- on 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, we look upon them either as brilliant suns or habitable worlds, and we consider the whole together as forming one vast and magnificent system, worthy of the Divine hand by which it was created. Emily, I can scarcely conceive the idea of this im- mensity of creation ; it seems too sublime for our ima- gination : — and to think that the goodness of Providence extends over millions of worlds throughout a boundless universe — Ah ! Mrs. B., it is we only who become trifling and insignificant beings in so magnificent a creation. Mrs, B. This idea should teach uis humility, but with- c^ut producing despondency. The same Almighty hand which guides these countless worlds in their undeviating course, conducts with equal perfection the blood as it cir- culates 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 forgotten. 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 illuminated by the sun, the other in obscurity. But would you believe it, Ca- roline, 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 31o. What are we taught by science ? 314. If the planets are only seen by the reflected light of the sun, how is it that they can be seen in the night ? 88 CAtJSES OF THE EARTh's ANNUAL M<5tI0N. because it is night with them ; whilst, in reality, the sun never ceases to shine upon every planet. When, there- fore, these little ignorant beings look around them during their night, and behold all the stars shining, they cannot imagine why the planets, which are dark bodies, should shine, concluding, that since the sun does not illumine themselves, the whole universe must be in darkness. Caroline. I confess that I was one of these ignorant people ; but I am now very sensible of the absurdity of such an idea. To the inhabitants of the other planets, then, we must appear as a little star ? Mrs, JB. Yes, to those wliich revolve 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. Emihj, But they may see our sun as we do theirs, in 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 1 Mrs. B, I shall defer the explanation of the motion of the moon, till our next interview, as it would prolong our present lesson too much. 315. How must the earth appear to the inhabitants of other planets ^ 3! 6. How much larger does the earth appear viewed at the mooUj than the moon appenrK- viewed at the earth ? ON THE PLANETS. 89 CONVERSATION VII. ON THE PLANETS. Of the Satellites or Moons ; Gravity diminishes as the Square of the distance ; Of the Solar System ; Of Co- mets ; Constellations, Signs of the Zodiach ; Of Co^ pernicus, Neivton<, 6^c, MRS. B. The planets are distinguished into primary and secon- dary. Those which revolve immediately about the sun are called primary. Many of these are attended in their course by smaller planets, which revolve round 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 proportional 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 greatest quantity of matter in that system. You must recollect, that the force of attraction is not only proportional to the quantity of matter, but to the degree of proximity of the attractive body : this power is weakened by being diffused, and diminishes as the squares of the distances increase. The square is the product of 317. How are the planets distinguished ? 318. What are the primary planets .? 319. What are the secondary planets ^ 320. By what other names are the secondary planets called ? 321 . To what is the force of attraction proportional besides the quantity of matter in the attracting bodies ^ ■ 322. What is meant by the square of distance ^ 8* pO ON THE PLANETS* 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 itself is four. Caroline, Then the more distant planets move sJou er in their orbits ; for their projectile force must be propor- tioned to that of attraction ? But I do not see how this accounts for the motion of the secondary round the pri- mary planets, in preference to the sun. Emily. Is it not because the vicinity of the primary 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 at- tracted 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 attraction is pro- portionally 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 gravity 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, pro- vided the bodies were of equal weight ; and if they diflfered in weight, it would be nearer the larger body. If then the earth and moon had no projectile force which pre- vented their mutual attraction from bringing them to- gether, they would meet at their common centre of gravity. Caroline, The earth then has a great variety of mo- tions, it revolves round the sun, upon its axis, and round the point towards which the moon attracts it. Mrs. B. Just so ; and this is the case with every planet which is attended by satellites. The complicated effect of this variety of motions, produces certain irregu- larities, which, however, it is not necessary to notice at present. 323. How much less does a planet gravitate towards the sun than the earth, at twice the distance of the earth from the sun ? — 394. Why does not the sun attract the secondary planets from their primaries ? 325. What motion has the earth be- sides that about the sun and on its own axis ? 326. Where is the common centre of gravity to the sun and mx)ou ? ON THE PLANETS. 91 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 of the planets (even v^^hen taken collectively) 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, therefore, 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 1 Mrs, B, You were mistaken ; for besides that which I have just mentioned, which is indeed very inconsidera- ble, he revolves on his axis ; this motion is ascertained by observing certain spots which disappear, and re-appear regularly at stated times.* * The sun is a spherical body, situated near the centre of gravi- ty in the system of planets, of which our earth is one. Its dia- meter is 077,547 Enghsh miles ; or equal to 100 diameters of the earth ; and therefore its cubick magnitude must exceed that of the earth one million of times. It revolves round its axis in 25 days, and 10 hours, which has been determined by means of several dark spots seen with telescopes on that luminary. Dr. ITerschel sup- poses these spots in the sun to be the appearancb of the opaque body of the sun through the openings in his luminous atmosphere. Its similarity to the other globes of the solar system, in solidity, atmosphere, surface diversified with mountains and valleys, and rotation on its axis, lead us to suppose, that it is most probably in- habited like the rest of the planets, by beings whose organs are adapted to their peculiar circumstances. Though it may be objected, from the effects produced at the distance of 95,000,000 miles, that every thing must be scorched up at its surface, yet many facts show that heat is produced by the sun's rays only when they act on a suitable medium ; or when radiated and reflected by suitable surfaces. On the tops of moun- tains of sufficient height, we always find regions of ice and snow ; though if the solar rays themselves conveyed all the heat we find on this globe, it ought tol9e hottest where their course is the least interrupted. 327. Do the planets revolve round the centre of the sun ? 328. Around what do they revolve ? 329. Has the sun any motion ?- 330. How is it known that the sun turns on its axis ? 331. How much greater is the diameter of the sun than of the earth ? 332. How much does his cubick magnitude exceed that of the earth 9 333. What does Dr. Herschel suppose the dark spots on the sun's disk to be ? 334. What are we led to suppose from the similarity of the sun to the other globes of the solar system 9 92 ON THE PLANETS. Caroline. A planet has frequently been pointed out to me in the heavens ; but 1 could not perceive that its mo- tion ditlered from that of the fixed stars, which only appear to move. Mi's, B, The great distance of the planets renders their motion apparently so slow, that the eye is not sen- sible 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 I can give you of the situation and motion of the planets, will be by the examination of this diagram, (plate VII. tig. 1.) representing 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 appear 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. Mrs, IB, The orbits of the planets are so nearly cir- cular, and the common centre of gravity of the solar sys- tem so near the centre of the sun, that these deviations are scarcely worth observing. The dimensions of the planets, in their true proportions, you will find delineated in fig. 2. Mercury is the planet nearest the sun ; his orbit is con- sequently contained within ours ; but his vicinity to the sun occasions his being nearly lost in the brilliancy 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 consequently the length of his year. The time of his rotation 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 liquefied.* * The intenseness of the sun's heat, which is in the same pro- portion as his light, is seven times as great in Mercury as with us ; 335. Can the motion of the planets be seen by the naAed eye ? 336. What is the design of Fig. 1, plate VTl ?— 337. Which figure exhibits the dimensions of the planets m their true proportions ? 338. What planet is nearest the sun ? 339. In what time does Mercury revolve round the sun ? — —340. What is his distance from the sun ? 341. What is his diameter ? 342. How does the intenseness of the sun's heat at Mercury com- pare with it at our earth ? CTN THE PLANET«. 93 Caroline, Oh, what a dreadful climate. Mrs, B. Though we could not live there, it may be perfectly adapted to other beings destined to inhabit it. Venus, the next in the order of planets, is 68 millions 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 v/ithin ours ; during one half of her course in it, we see her before sun- rise, and she is called the morning star ; in the other part of her orbit, she rises later tha,n 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 approaching the horizon after sun-set : she is then called Hesperus, or the evening star. Do you recollect those beautiful lines of Milton ? Now came still evening on, and twilight gray Had in her sober livery all things clad : 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 glow'd the firmament With living sapphires, Hesperus, that led The starry host, rode brightest, till the moon Rising in clouded majesty, at length Apparent queen unveil'd her peerless light, And o'er the dark her silver mantle threw. so that water there would be carried off in the shape of steam, for by experiments with the thermometer, it appears that a heat seven times greater than that of the sun's beams in summer will serve to make water boil. * In most treatises on Astronomy, Mercury and Venus are call- ed inferiour, and those more distant from the sun than our earth, superiour planets ; but, it is considered a more proper distinction, to call the former interiour and the latter exteriour planets. 343. How much greater heat is required to make water hoil, tlian that of the sun in summer at the earth f 344. How far is Venus from the sun ? 345. In what time does it revolve round the sun ? 346. In what time does it revolve upon its axis ? 347. When is Venus called the morning and when the evening star ? 348. By lohat name have Mercury and Venus usually been distinguished from the other planets ? 349. How should the planets more distant, and those less distant from the sun than the earth, be distinguished from each other ? 94 ON THE PLANETS. 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 attended in our course by a single moon. Next follows Mars. He can never come between us and the sun, like Mercury and Venus ; his motion is, however, very perceptible, as he may be traced to differ- ent situations in the heavens ; his distance from the sun is 144 millions of miles ; he turns round his axis in 24 hours and 39 minutes ; and he performs his annual revo- lution in about 687 of our days : his diameter is 4120 miles. Then follow four very small planets, Juno, Ce- res, Pallas, and Vesta, which have been recently disco- vered, but whose dimensions 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 nearjy 12 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, therefore, you see, be conveniently delineated in a dia- gram. He is attended by four moons.t * These anomalous bodies, so unlike the other primary planets, Dr. Herschel has denominated Asteroids. Probably they are the fragments of some planet ; or perhaps other similar bodies abound in the solar system, though they have hitherto, from their small- ness or darkness, escaped observation. t Jupiter is surrounded by cloudy substances, subject to fre- quent changes in their situation and appearance, called Belts. These Belts are sometimes of a regular form ; sometimes inter- rupted and broken ; and sometimes not at all to be seen. 350. How far distant from the sun is the earth ? 351. In what time does it revolve round the sun r 352. Which planet is next to the earth in distance from the sun. 353. How far is Mars from the sun ? 354. How long time is occupied in his revolution about the sun ? 355. What four small planets are next to Mars in distance from the sun ? 356. What did Dr. Herschel call these planets? -357. What is the distance of Jupiter from the sun .•' 358. In what time does Jupiter com- plete his revolution ? 359. How much larg-er is Jupiter than our earth ? 360. How many satellites has this planet ?— ^ 3151. By ichat is Jupiter s^t^rounded 9 ON THE PLANETS. 95 The next planet is Saturn, whose distance from the sun is about 900 millions of miles ; his diurnal rotation is per- formed in 10 hours and a quarter : — his annual revolution in nearly 30 of our years. His diameter is 79,000 miles. This planet is surrounded by a luminous ring, the nature of which, astronomers are much at a loss to conjecture ; he has seven moons.* Lastly, we observe the Georgium 3idus, discovered 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 same time ; I think I should like to be an inhabitant of Jupiter 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. Can you tell me now how much more light we enjoy than Saturn 1 Caroline, The square of ten, is a hundred ; therefore Saturn has a hundred times less — or to answer your ques- tion exactly, we have a hundred times more light and heat than Saturn — this certainly does not increase my wish to become one of the poor wretches who inhabit that planet.t * This ring is set edgewise round it, and the distance of the ring- from the planet is equal to the breadth of the ring. The sun shines for almost fifteen of our years together on the northern side of the ring ; then goes off, and shines as long on the southern side of it, so there is but one day and one night on each side of the ring, in the time of Saturn's whole revolution about the sun, which takes up almost thirty of our years. t The sun's light at Saturn is 1000 times as great as the light of the full moon is to us. 362. What planet is next in order as to distance from the sun ^ -^ .363. What is its distance from the sun ? 364. In what time does it revolve round that luminary ? 365. What is its diameter } 366. How many moons has Saturn .? 367. By what is this planet surrounded? 368. What is said in the, note of Saturn's ring 9 369. How many moons has Herschel or the Georgium Sidus? 370. How much more light and heat do we enj)y thnn Saturn.' 371. How much greater is ths sun's light Hi Saturn than the moon's light at the earth ? 96 ON THE PLANETi5. 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 Almighty Power which created these planets, and placed them in their several orbits, has no donbt peopled them with beings whose bodies are adapted to the various temperatures 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-appearance of some of them, at stated times, they are known to revolve round the sun, but in orbits so extremely eccentrick, 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 oif 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 be- fore they make their re-appearance. The numbers that are known by their regular re-appearance is only three.* Emily. Pray, Mrs. B. what are the constellations ? ^ Above 500 comets have appeared since the commencement of the Christian era ; and accounts of many mor^ are extant. ,/ , _ — . — . _ -i 372. What are the comets supposed to be ? 373. From what fact is it concluded that the comets are planets ? 374. Whv must the inhabitant* of comets, if they are inhabited, expe- rience great vicissitudes of heat and cold/ 375. When in that part of their orbit nearest the sun, whptls their heat computed to be ? ^76. How many comets are known by their regular re- appearance ^ 377. Horn many different ones have been noticed ^ince the commencement of the Christian era f OS tHE PLANETS. 9*5^ 3Irs. IB. They are the fixed stars, which the ancients, in order to recognise them, formed into groupes, and gave the names of the figures, which you find delineated on tiie celestial globe. In order to show their proper situ- ations in the heavens, they should be painted on the in- ternal 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 con- stellations, called the signs of the zodiack, 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, Virgo, Libra, Scor- pio, Sagittarius, Capricornus, Aquarius, Pisces ; the whole occupying a complete circle, or broad belt, in the heavens, called the zodiack. (plate VIIL fig. 1.) Hence, a right line drawn from the earth, and passing through the sun, would reach 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 zodiack, is called the ecliptick. Caroline. But many of the stars in these constella- tions appear beyond the zodiack. Mrs. B. We have no means of ascertaining the dis- tance of the fixed stars. When, therefore, they are said to be in the zodiack, 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 zodiack.* * An easy distinction between a planet and a fixed star is this — 378. What are the constellations ? 379. In what manner can we have an idea of their proper situations ? 380. What are the names of the twelve constellations ? 381 . What is meant when the sun is said to be in a particular constellation ? 382- How would you illustrate this by the figure ^ 383. What is the circle called in which the sun appears to move through the zo- diack ^ 384. What is to be understood by the signs or cod* stellations being in the zodiack.' 385. How may a fixed siar be easily distinguished from a planet ? 9 98 ON THE PLANETS. Emihj, But are not those large bright stars, which are called stars of the first magnitude, nearer to us, than those small ones which we can scarcely discern ? Mrs. B. It may be so ; or the difference of size and brilliancy of the stars may proceed from their difference of dimensions ; this is a point which astronomers are not enabled to determine. Considering them as suns, I see no reason why different suns should not vary in dimen- sions as well as the planets belonging to them.* Etnily, What a wonderful and beautiful system this is, and how astonishing to think that every fixed star may probably be attended by a similar train of planets ! Caroline, You will accuse me of being very incredu- lous, 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 directly in opposition to the evidence of our senses. Mrs. B. 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 or- gans of sense. This faculty, which we call reason, has frequently proved to us, that our senses are liable to err. the former shines with a steady light, but the latter is constantly twinkling. What it is which occasions this twinkling or scintilla- tion of a star, yet remains undecided. * To the bare eye the stars appear of some sensible magnitude, owing to the glare of light arising from the numberless reflections of the rays in coming to the eye ; this leads us to imagine that the stars are much larger than they would appear, if we saw them only b}^ the few rays which come directly from them, so as to enter the eye, without being intermixed with others. 386. On what is the different size and brilliancy of the fixed stajrs depending ? 387. What caitses the fixed stars to appear to UB larger than they should appear f ON THE PLANETS. 99 If yoa have ever sailed on the water, with a very steady breeze, you must have seen the houses, trees, and every object move, while vou were sailing. Caroline. I remember thinking so, when I was very young ; but I now know that their motion is only appa- rent. It is true that my reason, in this case, corrects the errour of my sight. Mrs. B. ' It teaches you that the apparent motion ot the objects on shore, proceeds from your being yourself movinfif, and that you are not sensible of your own motion because you meet with no rp?istance. 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 would not perceive that you moved, for you could not ieei it, and you could see it only by observing the change oi place of the objects on shore. So it is with the motion of the earth ; every thing on it> surface, and the air that surrounds it, accomoanies it in its revolution ; it meets ^ilh no resistance : thereiore, like the crew ot a vessel sailing with a fair wind, in a calm sea, we are insensible of our motion. Caroline. But the principal reason why the crew of a vessel in a calm sea do not perceive their motion, is, be- cause they move exceedingly slowly : while the earth, you say, revolves with great velocity. Mrs. B. It is not because they move slowly, but be- ■cause they move steadily, and meet with no irregular re- sistances, that the crew of a vessel do not perceive their motion ; for they would be equally insensible to it, with the strongest wind, provided it were steady, that they mailed with it, and that it did not agitate the water ; but this last condition, you know, is not possible, for the wind will always produce waves which offer more or less resist- ance 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 in- habitants of the earth cannot have, — the apparent motion of the objects on shore. 388. What familiar illustration is given to show why we do not perceive the motion of the earth in its revolutions ? 389. Why do we not perceive its motion t 100 ON THE PLANETS. 3Irs, B. Have we not a similar proof of the earth's motion, in the apparent motion of the sun and stars ? Ima- gine the earth to be sailing round its axis, and succes- sively passing by every star, which, like the objects on land, we suppose to be moving instead of ourselves. I have heard it observed by an aerial traveller in a balloon, that the earth appears to sink beneath the balloon, in- stead 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 ac- complished by the most simple means ; and what reason have we to suppose this law infringed, in order 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 un- intelligible 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 considerable than our earth ; for our eyes vainly endeavour to persuade us, that they are little brilliants sparkling in the heavens, while science teaches us that they are immense spheres, whose apparent dimensions are diminished by distance. Why then should these enormous globes daily traverse such a prodigious space, merely to prevent the necessity of our earth's revolving on its axis ? Caroline. I think I must now be convinced. But you will, I hope, allow me a little time to familiarize my- self to an idea so different from that which I have been accustomed to entertain. And pray, at what rate do wc move ? 3Irs, B, The motion produced by the revolution of the earth on its axis, is about eleven miles a minute, to an inhabitant of London. Emily, But does not every part of the earth move with the same velocity ? 390. In case the earth revolves every 24 hours, do not the sun and stars appear to us as if they revolved about the earth ? 391. What law is mentioned that we discover throughout nature ? 392. Why does this law make it more probable that the earth re volves than that the sun and stars do ? 303. How fast doc:* z, person move in the latitude of London, in consequence of (he earth's motion upon its axis ? O^ THE PLANETS. 101 3Irs, J5. 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 furthest from the axis of motion. But in the earth's revolution round the sun, every part must move with equal velocity ? Mrs, IB, 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 motion. You would not tell me this sooner, Mrs. B., for fear of increasing my incredulity. Before the time of Newton, was not the earth supposed 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 Ptolem.y in ancient times ; but as long ago as the beginning of the sixteenth century it was discarded, and the solar system, such as I have shown you, was established by the celebrated as- tronomer 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 powerful genius of Newton, who lived at a much later period. Emily, It appears, indeed, far less difiicult to trace by observation the motion of the planets, than to divine by what power they are impelled and guided. I 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 cir- cumstance from which one should little have expected so grand a theory to have arisen. During the prevalence of the plague in the year 1665, Newton 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. 394. How fast does the earth move in its revolution about the sun ? 395. What was the system of Ptolemy concerning as- tronomy ? 396. What is the present system of astronomy called ? 397. When was the Copernican system of astronomy adopted ? 398. What important discovery did Newton make touching the Copernican system ? 399. What led Newton to make his discoveries ? 9* 102 ON THE EARTH. 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 superiour genius to find matter for wonder, observation, and research, in circum- stances which, to the ordinary mind, appear trivial, be- cause they are common, and with which they are satis- fied, because they arc natural, without reflecting that na- ture is our grand field of observation, that within it is con- tained our whole store of knowledge; 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 cir- cumstance of the fall of an apple, which led to the discovery of the laws upon which the Copernican system is found- ed ; 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 3ung by the poets. The apple of discord for which the goddesses contended ; the golden apples by which Ata- lanta won the race ; nay, even the apple which William Tell shot from the head of his son, cannot be compared to this ! CONVERSATION VIII. ON THE EARTH. Of the Terrestrial Glohe ; Of the Figttre 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^ and Equal or Mean Time. MRS. B. As the earth is the planet in which we are the most particularly interested, it is my intention this morning, to explain to yoa the effects resulting from its annual and 400. What does Mrs. Bryan consider a mark of superiour genius ? ON THE EARTH. lOS diurnal motions ; but for this purpose it will be necessa- ry to make you acquainted with the terrestrial globe : you have not either of you, I conclude, learnt the use of the globes ?* Caroline, No ; I once indeed learnt by heart the names of the lines marked on the globe, but as I was in- formed they were only imaginary divisions, they did not appear to me worthy of much attention, and were soon forgotten. Mrs, B, You suppose, then, that astronomers had been at the trouble of inventing a number of lines to little purpose. It will be impossible for me to explain to you the particular effects of the earth's motion without your having acquired a knowledge of these lines : in plate VIII. fig. 2. you will find them all delineated ; and you must learn them perfectly if you wish to make any profi- ciency 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. Mrs. B, The names of these lines would have con- veyed ideas of the figures they were designed to express, though the use of these figures might at that time have been too difficult for you to understand. Childhood is the sea- son when impressions on the memory 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- * The earth is of a globular form. For, 1. The shadow of the earth projected on the moon in an eclipse is "always circular;, which appearance could only be produced by a spherical body. 2. The convexity of the surface of the sea is evident ; the mast of an approaching ship being seen before its hull. 3. The north pole becomes more elevated by travelling northward, in proportion to the space passed over. 4. Navigators have sailed round the earth, and by sieering their course continually westward arrived, at length, at the place from whence they departed. 401. How is it proved that the earth is globular 9^"— -402. What is necessary to be learnt before one can understand the efi fects resulting from the earth's motions ' 104 ON THE EARTH. 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 philoso- phy ! 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 appropriate and scientifick terms would have conveyed more precise and accurate ideas ; but I was afraid of not being understood. Eniilij. You may depend upon our learning the names of these lines thoroughly, Mrs. B. ; but before we com- mit them to memory, will you have the goodness to ex- plain 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, dis- tinguished by the names of the north and south pole. The circle C D, which divides the globe into two equal parts between the poles, is called the equator, or equi- noctial 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 hemisphere. The small circle E F, which surrounds the north pole, is call- ed the arctick circle ; that G H, which surrounds the south pole, the antarctick circle. There are two inter- mediate circles between the polar circles and the equator ; that to the north, I K, called the tropick of Cancer ; that to the south, L M, called the tropick of Capricorn. Lastly, this circle, L K, which divides the globe into two equal parts, crossing the equator and extending northward as far as the tropick of Cancer, and southward as far as the tropick of Capricorn, is called the ecliptick. The delineation of the ecliptick on the terrestrial globe is not without danger of conveying false ideas ; for the ecliptick (as I have before said) is an imaginary circle in the heavens passing through the middle of the zodiack, and situated in the plane of the earth's orbit. 403. Wliat, in an artificial globe, represents the earth's axis? 404. What are the extremities of the axis called ? 405. What is the equator ? 406. What line in the figure represents the equator ? — What ones the Tropicks .■' — What ones the Polar Circles ? — What one the Ecliptick ? 407. By what name are the two tropicks distinrruished from each other ? 408 By what name are the polar circles distinjjuished from each other ? 409. Where is the ecliptick situated ? ON THE EARTH. 105 Caroline* I do not understand the meaning of the plane of the earth's orbit. Mrs, B, A plane, or plain, is an even level surface. Let us suppose a smooth thin solid plane cutting the sun through the centre, extending out as far as the fixed stars, and terminating in a circle which passes through the middle of the zodiack ; 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 zodiack is the eclip- tick. 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 ecliptick passing through the middle of the zodiack. Emily. If the ecliptick relates only to the heavens, why is it described upon the terrestrial globe 1 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 ecliptick shows the inclination of the earth's axis to the plane of its orbit. But to return to figr. 2. plate VIII. The spaces between the several parallel circles on the terrestrial globe are called zones ; that which is compre- hended between the tropicks is distinguished by the name of the torrid zone ; the spaces which extend from the tropicks to the polar circles, the north and south tempe- rate zones ; and the spaces contained within the polar circles, the frigid zones. The several lines which, you observe, are drawn from one pole to the 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 situated on the opposite meridian, it is consequently midnight. 410. What is to be understocd by the plane of the earth's orbit ? 41 1. By what figure is it represented ? 412. If the eclip- tick relate only to the heavens, why is it described on the ter- restrial globe ? 413. What are called the zones ^ 414. Where is the torrid zone ? 415. Where arc the temperate zones ? 41G. Where are the frigid zones ? 417. What are the meridian lines ? 418. When is it twelve o'clock at noon to all places under any particular meridian ? 419. To what places will it, at the same time, be midnight ? 106 ON THE EARTH. Emily, To places situated equally distant from these two meridians, it must then be six o'clock ? Mrs, B. Yes ; if they tire 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 proceeding towards that meridian. Those circles which divide the globe into two equal parts, such as the equator and the^ecliptick, are called greater circles ; to distinguish them from those which di- vide it into two unequal parts, as the tropicks and polar circles, wliich are called lesser circles. All circles are divided into 360 equal parts, called degrees, 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 diameter of that circle ; the di- ameter is equal to a little less than one-third of the cir- cuniA:-v<.«oo Can you tell me nearly how many decrees it contams ? 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 meridian ? 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 1 Caroline, The equator being equally distant from either pole, that distance must be half of a meridian, or a quarter of the circumference of a circle, and contain 90 degrees. Mrs, B, Besides the usual division of circles into de- grees, the ecliptick is divided into 12 equal parts, 420. To what places will it be six o'clock in the morning, and to what ones six in the evening ? 421. What circles are called greater circles ? 422. What ones are called lesser circles ^ 423. Into how many parts are all circles divided .'' 424. How are degrees divided : 425. What is the diameter of a cir- cle ? 426. How many degrees does the diameter of a circle contain ? 427. How" many degrees are there in a meridian reaching from one pole to the other .? 428. How many de- grees are there between the equator and the poles .'—429. How is the ecliptick divided ? ON THE EARTH- 107 called signs, which bear the names of the constellations throdgh 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 latitude ; those measured from east to west on the equator, the ecliptick, or any of the lesser circles, are called degrees of longi- tude ; hence these circles bear the name of longitudinal circles ; they are also called parallels of latitude. Eniihj. 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 cir- cles will be considerably smaller than those at the equa- tor ? 3Irs. B. Certainly ; since the degrees of circles of different dimensions do not vary in number, they must necessarily vary in length. The degrees of latitude, 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 lenojth is a degree of latitude ? Mrs, IB. Sixty geographical miles, which is equal to 69^ 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 flattened towards the poles. This form is supposed to proceed from the superi- our action of the centrifugal power at the equator. Caroline. I thought I had understood the centrifugal force perfectly, but I do not comprehend its effect in this instance. Mrs. B. You know that the revolution of the earth on its axis must give every particle a tendency to fly off 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 430. What is latitude P 431. What is longitude ? 432. Are the degrees of long-itude in different latitudes of the same length ? -433. What is the length of a degree of latitude .= 431. What is the reason that a degree of longitude on the equa- tor is not the same as a degree of latitude ? 435. What occa- sions the protuberance of the earth at the equator ^ 108 ON THE EARTH. 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 de- creases 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 originally in a fluid state, the particles in the torrid zone would re- cede much further 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 furthest from the centre of mo- tion must move with the greatest velocity : the axis of the earth is the centre of its diurnal motion, and the equa- torial 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 1 Mrs, 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 ve- ^locity. Emily, I have been reflecting that if the earth is not a perfect circle — ^- 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 equator than at the poles ? For the earth being thicker at the equator, 436. In what manner can you account for this protuberance from centrifugal motion ? 437. Why does the head of a per- son move faster than his feet in the revolution of the earth upon its axis ? 438. What is a sphere or globe ? t)N THE EARTH, 109 the attraction of gravity perpendicularly downwards must be stronger. 3Irs. B, Your reasoning has some plausibility, but I am sorry to be obliged to add that it is quite erroneous ; 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 quantity 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 ; I am referring only to any situation on the surface of the earth. Were you to pene- trate into the interiour, the attraction of the parts above you would counteract that of the parts beneath you, and consequently diminish the power of gravity in proportion as you approached the centre ; and if you reached that point, being equally attracted by the parts all around you, gravity would cease, and you would be without weight. Emihj. Bodies then should weigh less at the equator than at the poles, since they arp more distant from the centre of gravity in the former- than in the latter situation. Mrs. B. And this is r^^ally the case ; but the diffe- rence of weight would ^e scarcely sensible, were it not augmented by another circumstance. Caroline, An*^ what is this singular circumstance which seems io disturb the laws of nature ? Mrs. B. One that you are well acquainted with, as conducing more to the preservation than the destruction of order, — the centrifugal force. This we have just ob- served to be stronger at the equator ; and as it tends to drive bodies from the centre, it is necessarily opposed to, and must lessen the power of gravity, which attracts them towards the centre. We accordingly find that bo- 439. Will any body weigh the same at the equator as at the poles ? 440. Were one to penetrate deep into the earth, would the force of gravity increase ? 441. Why not .'' 442. Where will bodies weigh most, at the equator or poles ? 443. What besides the protuberance at the equator causes bodies tQ weigh less there than at the poles ? 10 110 ON THE EARTH. dies weigh lightest at the equator, where the centrifugal force is greatest ; and heaviest at the poles, where this power is least.* Caroline. Has the experiment been made in these different situations ? Mrs. B, Louis 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, have hitherto rendered every attempt to reach the pole abor- tive ; but the difference of gravity at the equator and in Lapland is very perceptible. Caroline. Yet I do not comprehend, how the diffe- rence of weight could be ascertained ; for if the body un- der trial decreased in weight, the weight which w^as op- posed to it in the opposite scale must have diminished in the same proportion. For instance, 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 as- certained by this means. Mrs. B. Your observation is perfectly just : the diffe- rence of gravity of bodies situated at the poles and at the equator cannot be ^»scertained by weighing them ; a pendulum was therefore us^d for that purpose. Caroline. What, the pendUum of a clock ? how could that answer the purpose ? Mrs. B. A pendulum consists <^i a line, or rod, to one end of which a weight is attached, -and it is suspend- ed by the other to a fixed point, about wl«ch it is made * If the diurnal motion of the earth round its axis vrere about 17 times faster than it is, the centrifugal force would, at the equa- tor, be equal to the power of gravity, and all bodies there would entirely lose weight. But if the earth revolved still quicker than this, they would all fly off. 444. How much faster must the earth move than it now does to have the centrifugal force balance that of gravity^ and thereby cav^e bodies entirely to lose their iceight ? 445. Has an at- tempt ever been made to ascertain whether bodies will weigh hea- vier at the poles than at the equator ? 446. By whom was it made ? 447. Could the experiment be made by the common scales ? 448. Why not ? 449. What instrument was used in the experiment ? 450. How would you describe a pendulum f ON THE EARTH. Ill to vibrate. Without being put in motion, a pendulum, like a plumb line, hangs perpendicular to the general sur- face of the earth, by which it is attracted ; but, if you raise a pendulum, gravity will bring it back to its perpen- dicular position. It will, however, not remain stationary there, for the velocity it has received durmg its descent will impel it onwards, 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 I thought you said that there was no per- petual 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 fric- tion of the part by which it is suspended ; were it possible to remove these obstacles, the motion of a pendulum would be perpetual, and its vibrations perfectly regular ; being of equal distances, and performed in equal times.* Einihj. That is the natural result of the uniformity of the power which produces these vibrations, for the force of gravity being always the same, the velocity of the pen- dulum 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 vibra- tions of the pendulum will be slower at the equator than at the poles. * The vibrations of pendulums are subject to many irregularities for which no effectual remedy has yet been devised. These are owing partly to the variable density and temperature of the air, partly to the ricridily and friction of the rod by which they are sus- pended, and principally to the dilatation and contraction of the ma- terials, of which ihey are formed. The metalline rods of pendu- lums are expanded by heat, and contracted by cold ; therefore clocks will go faster in winter, and slower in summer. The com- mon remedy for this inconvenience is the raising or lowering the bob of the pendulum, by means of a screw, as occasion may re- quire 451 . What causes the vibrations of a pendulum ? 452. Why are not its vibrations perpetual ? 453. To what is the irregu- laritij in the vibrations of pendulums oioing f 454. Why will clocks go faster in winter than in summer ? 455. Where do pendulums of the same length vibrate fastest ^ 118 ON THE EARTH. Mrs, B. You are perfectly right, Caroline ; it was by this means that the difference of gravity was discover- ed, and the true figure of the earth ascertained. Emily, But how do they contrive to regulate their tirne 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 from ours. Mrs, B, The only alteration required is to lengthen the pendulum in one case, and to shorten it in the other ; for the velocity of the vibrations of a pendulum depends on its length ; and when it is said, that a pendulum vi- brates quicker at the pole than at the equator, it is sup- posing it to be of the same length. A pendulum which vibrates a second in this latitude is 36^ inches long. In order to vibrate at the equator 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 va- riation of the seasons, and the difference of the length of the days and nights iri those seasons ; both effects result- ing from the same cause. ' In moving round the sun, the axis of the earth is not perpendicular to the plane of its orbit. Supposing this round table to represent the plane of the earth's orbit, and this little globe, which has a wire passing through it, re- presenting the axis and poles, we shall call the earth ; in: moving round the table, the wire is not perpendicular ta it, but oblique, * What is here stated concerning the length of pendulums as connected with the force of gravity i« at complete variance with fact. The force of gravitation is greater, it is well known, at the poles than at the equator ; and since the vibration of pendulums is occasioned by gravity, the lengths of pendulums vibrating in the same time must evidently be proportioned to the gravities at th& places where they vibrate. Accordingly, it is found, by observa- tion, in order to vibrate, at the equator, in the same space, the pendulum must not be lengthened, as above stated, but shortened ; and at the poles, it must not be shortened, but proportionally lengthened. 456. How do the pendulums used at the equator and at the polar regions compare in length in order to vibrate in the same time f ON THE EARTH. 113 Emily. Yes, I understand the earth does not go round the sun in an upright position, its axis is slanting or ob- lique. Mrs. B, All the lines, which you learnt in your last lesson, are delineated on this little globe ; you must con- sider the ecliptick as representing the plane of the earth s orbit ; and the equator which crosses the ecliptick in two places, shows the degree of obliquity of the axis of the earth in that orbit, which is exactly 23^ degrees. The points in which the ecliptick intersects the equator are call- ed nodes. But I believe I shall make this clear to you by revolv- ing the little globe round a candle, which shall represent the sun. (Plate IX. fig. 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 21st of June. Emily, You hold the wire awry, I suppose, in order to show that the axis of the earth is not upright ? Mrs. B. Yes ; in summer, the north pole is inclined towards the sun. In this season, therefore, the northern hemisphere enjoys much more of his rays than the south- ern. The sun, you see, now shines over the whole of the north frigid zone, and notwithstanding the earth's diur- nal revolution, which I imitate by 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 the same time completely in obscurity. Caroline. That is very strange : I never before heard that there was constant day or night in any part of the world ! How much happier the inhabitants of the north frigid zone n^ust be than those of the southern ; the first enjoy uninterrupted day, while the last are involved in perpetual darkness. Mrs. B. You judge with too much precipitation ; ex- amine a little further, and you will find, that the two frigid zones share an equal fate. 457. What causes the variation of the seasons and the diffe- rence of the length of the days and nights ? 458. How much is the axis of the earth inclined to the plane of its orbit ? 459. What are the points called where the ecliptick intersects the equator ? 460. When' does the summer solstice take place ? — - — 461. By which figure is the change of seasons illustrated ? 462. When is the north pole inclined towards the sun ? 463. What is the situation of the south pole when the north pole is inclined to the sun ? 10* 114 ON THE EARTH. We shall now make the earth set off from its position in the summer solstice, and carry it round the sun ; ob- serve that the pole is always inclined in the same direc- tion, and points to the same spot in the heavens. There 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 ecliptick cuts or crosses the equator, a.nd which is called 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 per- pendicular 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 of the year, therefore, the days and nights are equal in every part of the earth. But the next step she takes in her orbit, you see, involves the north pole in dark- ness, whilst it illumines that of the south ;. this change was gradually preparing as I moved the earth from sum- mer to autumn ; the arctick circle, which was at first en- tirely illumined, began to have short nights, which in- creased as the earth approached 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 advances, 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 day-light. Caroline, Then after all, the sun, which I thought so partial, confers his favours equally on all. Mrs, B, You mistake : the inhabitants of the torrid z;one have much more heat than we have, as the sun's rays fall perpendicularly on them, while they shine ob- 464 . To what part of the heavens does the north pole always point ? 4G5. What part of the figure represents the earth at the autumnal equinox ? 466. How does the sun shine upon the earth at this season of the year ? 4 67. When is the winter solstice ? 468. Why is the heat of the sun greater at tho equator than at a distance from it .'* ON THE EARTH. 115 liquely on the rest of the world, and almost 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 degrees at mid-day, than at mid-night. 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 tem- perate 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 equator ; but their days and' nights will vary in length, at different times of the year, according as their respective poles incline to- wards or from the sun, and the difference will be greater in proportion to their distance from the equator. Mrs. B. We shall now follow the earth through the other half of her orbit, and you will observe, that now ex- actly the same effect takes place in the southern hemi- sphere, 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 nights are longer than our days. When the earth arrives at the vernal equinox, D, where the ecliptick again cuts the equator, on the 25th of March, she is situated with respect to the sun, exactly in the same position, as in the autumnal equinox ; and the only diffe- rence 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 en- lightened, 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 equi- 469. In what direction do the rays of the sun fall upon the polar regions of the earth ? 470. When does day commence at the south pole ? 471, When does the earth arrive at the vernal equinox ? 472. What part of the figure exhibits the earth at the vernal equinox ? 116 ON THE EARTH. nox, which is derived from the Latin, meaning equal night. As the earth proceeds towards summer, the days length- en in the northern hemisphere, and shorten in the south- ern, till the earth reaches the summer solstice, 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 first accompanied her. Emily, This is, indeed, a most satisfactory explana- tion of the seasons ; and the more I learn, the more I ad- mire the simplicity of means by which such wonderful effects are produced. Mrs. B. I know not which is most worthy of our admiration, the cause or the effect of the earth's revolu- tion round the sun. The mind can find no object of contemplation, more sublime, than the course of this mag- nificent globe, impelled by the combined powers of pro- jection and attraction to roll in one invariable course around the source of light and heat : and what can be more delightful than the beneficent effects of this vivify- ing power on its attendant planet ! It is at once the grand principle which animates and fecundates nature. Einily, 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 reflect 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 reflect- ing 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 superiour heat of the equa- torial parts of the earth arises from the rays falling perpen- dicularly on those regions, whilst they fall obliquely on these more northern regions ; now I do not understand 472. Why are the points where the ecliptick cut3j6r crosses the equator called equinoxes ? ON THE EARTH. 117 why perpendicular rays should afford more heat than ob- lique rays. Caroline* You need only hold your hand perpendicu- larly 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. Mrs, B. You are quite right ; if Caroline had not been satisfied with ascertaining the fact, without under- standing it, she would not have brought forward the can- dle as an illustration ; the reason why you feel so much more heat if you hold your hand perpendicularly over the candle, than if you hold it sideways, is because a steam 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 perpendi- cularly, and this led you to suppose that the rays were hot- ter in the latter direction. Had you reflected, you would have discovered that rays issuing from the candle side- ways, are no less perpendicular to your hand when held opposite to them, than the rays which ascend when your hand is held over them. The reason why the sun*s rays afford less heat when m an oblique direction than when perpendicular, is be- cause fewer of them fall upon an equal portion 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 different 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 re- gions, where the sun shines perpendicularly ; 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 ; * It is well known, that the south side of a hill, in our hemisphere, is peculiarly warm ; and the north side, peculiarly cold. This is owing to the different degrees of obliquity, with which the rays 473. Why is the heat of perpendicular rays more intense than that of oblique ones ? 474. By which figure is this illustrated ? 475. How will you explain Fig. 1, plate X. as illustrating this subject ? 476. Why is the south side of a hill icarmer than the north side of it ? J 18 ON THE EARTH. as the sun shines less obliquely in summer than in winter. Mr:i. jB. This you will see exemplified in fig. 2, in which the earth is represented, as it is situated on the 21st 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 December, when the rays of the sun fall most obliquely upon her. But there is also another reason why oblique rays give less heat, than perpendicular rays ; which is, that they have a greater portion of the atmosphere to tra- verse ; and though it is true that the atmosphere is 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 atmo- sphere the sun's rays have to pass through in their way to the earth, the less heat they will retain when they reach it. This will be better understood by referring to figure 4. The dotted line round the earth, describes the extent of the atmosphere, and the lines which proceed from the sun to the earth, the passage of two equal por- tions 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 mid-day. Mrs. B, The diminution of heat, morning and even- ing, 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 difficul- ty 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. of the sun strike the different sides of a hill. And a south-western is warmer than a south exposure, because it receives the sun's rays in the warmest part of the day. 477. fVhy is a south-western exposure to the sun warmer than a soiith exposure 9 478. What is to be illustrated by Figures 2 &. 3 of plate X. .' 479. What is another reason why obhque rays give less heat than perpendicular ones P 480. By which figure is the effect that the atmosphere has on the heat of the sun's rays illustrated ? 481. Why does the sun give more heat at mid-dav, than in the morninir and evenini? - ON THE EARTH. 119 But the diminished obliquity of the sun's rays is not the sole cause of the heat of summer ; the length of the days greaily 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 perpen- dicular lays, are on the 21st of June ; and yet the great- est heat prevails in July and August. Mrs. B. Those parts of the earth which are once heat- ed, retain the heat for some length of time, and the addi- tional heat they receive, occasions an elevation of tem- perature, although the days begin to shorten, and the sun's rays fall more obliquely. For the same reason, we have generally more heat at three o'clock in the afternoon, than at twelve when the sun is on the meridian.* * There are also other causes which have an effect on tempera- ture. When the sun's rays strike upon the land, they are stop- ped and accumulated at the surface. They are then reflected into the air and to surrounding objects ; so that the reflected heat is often greater than the direct heat of the sun. Hence, the heat in valleys vv'here the rays are reflected by the hills and raoun- tainSj is sometimes very great. In an elevated valley in Switzer- land, the heat is so much increased by reflection, that in the cen- tre there is a spot of perpetual verdure, in the midst of perpetual snows and glaciers; and there are plains on the Himmaleh moun- tains 15,000 feet above the level of the sea, which produce fine pasturage ; and, at the height of 11,000 feet, which is above the region of perpetual snows on the Andes, in the same latitude, bar- ley and buckv/heat flourish. But, unless heat is thus increased, it is reckoned as continually diminishing as we ascend above the level of the sea, especially on lofiy mountains, where it is reflected into the dry, clear air around them, and is carried off by the winds which sweep over them, without any opportunity for accumula- tion. Thus an elevation of 500 yards produces the same effect as a distance of 5,000 miles from the equator. At the height of (3,000 or 8,000 feet under thetropicks, we find the same climate as in latitude 49^ in France. At 13,000 feet we find the frosts of the frigid zone ; and at 15,730 feet, the mountains, based upon the most scorching plains, are capped with perpetual snow. 482- What, besides the direction of the sun's rays, effects the temperature of the places where they fall ? 483* Why is it warmer in July and August than in June, when the days are longest ; and at 2 and 3P.M. than at noon ? 484. Why is the dcfrrce of heat increased in valleijs ? 485. What fact is stated relating to this suhject concerning a valley in Sicitzcrland ? 480, What facts are stated concerning the plains of H-mmalehf 487. How is temperature effected in ascending above the level of the sea ? 488. In what ratio, compared v/uh the degrees of latitude^ does heat diminish in rising above the level of the sea ? 120 ON THE EARTH. Emily » And pray, have the other planets the same vi- cissitudes of seasons as the earth ? Mrs, B, Some of ahem more, some less, according as their axes deviate more or less from the perpendicular to the plane of their orbits. The axis of Jupiter is near- ly perpendicular to the plane of his orbit ; the axis 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 seasons must therefore be conside- rably greater than ours. For further particulars respect- ing the planets, I shall refer you to Bonnycastle's Intro- duction to Astronomy. When the rays of the sun strike upon the water, they will pene- trate GOO or 700 feet, if there is that depth ; and the heat will be diffused through the mass, remainin6. How would you explain the production of the tides by Figure 3, plate XII ? 557. Is the opinion of Mrs. Bryan conr cernincr the tides, universally adopted 9 558. What is thought a more probable cause of the tide upon the part of the earth furthest from the moon than the centrifugal motion of the earth ? 12 184 ON THE MOON. Caroline, And when it is high water at A and D, it is low water at B and C : now I think I comprehend the nature of the tides again, though I confess it is not quite so easy as I at first thought. But, Mrs. B., why does not the sun produce tides as well as the moon ; for its attraction is greater than that of the moon ? Mrs, B. It would be, at an equal distance, but our vicinity to the moon makes her influence more powerful. The sun has, however, a considerable effect on the tides, and increases or diminishes them as it acts in conjunction with, or in opposition to the moon. Emily, I do not quite understand that. Mrs, B, The moon is a month in going round the earth ; twice during that time, therefore, at full and at change, she is in the same direction as the sun, both then act in conjunction on the earth, and produce very great tides, called spring tides, as described in fig. 4. at A and B ; but when the moon is at the intermediate parts of her orbit, the sun, instead of affording assistance, weakens her power by acting in opposition to it ; and smaller tides are produced, called neap tides, as represented in i\g, 5.* but as tV^re is not a sufficient degree of cohesive attraction in the watery parts of it to preserve perfectly its form, the waters upon Ihat part ot\t nearest the moon are drawn away from the land, while the lan^K which is supposed to constitute the central regions of the globe, is ie sun and moon, yet their effects are not immediate ; the highest tides happen not on the days of the full and chatige, neither do tht lowest tides happen on the days 658. How could you account for this tide, if produced by the moon's attraction f 559. As the sun is larger than the moon, why does not the sun produce the chief influence in the production of the tides.'' 560. But does the sun exercise no influence in the production of the tides ? 561. When does it increase, and when diminish the tides .^ 562. AVhat is meant by the sun ahd moon acting in conjunction on the tides ? 563. What are the spring tides ^ -564. What are the tides called when the sun and moon are in opposition ? -565. How would you explain the spring and neap tides by the Figures ^ ON TliE MOON. 135 Emily, 1 have often observed the difference of these tides when I have been at the sea side. But since attraction is mutual between the moon and the earth, we must produce tides in the moon ; and these must be more considerable in proportion as our planet is larger. And yet the moon does not appear of an oval form. Mrs. B, You must recollect, that in order to render the explanation of the tides clearer, we suppose the whole surface of the earth to be covered with the ocean ; but that is not really the case, either with the earth or the moon, and the land which intersects the water destroy?? the regularity of the effect. Caroline, True ; we may, however, be certain, that whenever it is high water the moon is immediately over our heads. Mrs. B, Not so either ; for as a similar effect is pro- duced on that part of the globe immediately beneath the moon, and on that part most distant from it, it cannot be over the heads of the inhabitants of both those situations at the same time. Besides, as the orbit of the moon is very nearly parallel to that of the earth, she is never ver- tical but to the inhabitants of the torrid zone ; in that climate, therefore, the tides are greatest, and they dimi- nish as you recede from it and approach the poles. Caroline. In the torrid zone, then, I hope you will grant that the moon is immediately over, or opposite the spots where it is high water ? Mrs. B. I cannot even admit that ; for the ocean na- turally partaking of the earth's motion, in its rotation from west to east, the moon, in forming a tide, has to contend of quadratures. But on account of the continuation of motion, it is, some time after ^ the exercise of the sun and moon's attraction, in the manner supposed, that the effect of their forces is most to be seen. So that the greatest spring tides commonly happen three days after the new and full moons ', and the least iie.ap tid/?s three days after the first and third quarters. 566. How much after the conjunction and opposition of the sun and moon do the spring and neap tides take place 9 567. In w-hat parts of the earth are the tides highest ? 568. Why are they highest in the equatorial regions ^ 136 ON THE MOON. against the eastern motion of the waves. All matter, you know, by its inertia, makes some resistance to a change of state ; the waters, therefore, do not readily yield to the attraction of the moon, and the effect of her influence is not complete till three hours after she has passed the me- ridian, where it is full tide. Emily, Pray what is the reason that the tide is three quarters of an hour later every day ] Mrs, B, Because it is twenty-four hours and three- quarters before the same meridian on our globe returns beneath the moon. The earth revolves on its axis in about twenty-four hours ; if the moon were stationary, therefore, the same part of our globe would, every twen- ty-four hours, return beneath the moon ; but as during our daily revolution the moon advances in her orbit, the earth must make more than a complete rotation in order to bring the same meridian opposite the moon : we are three quarters of an hour in overtaking her. The tides, there- fore, are retarded for the same reason that the moon rises later by three quarters^ of an hour every day.* We have now, I think, concluded the observations I had to make to you on the subject of astronomy ; at our next interview, I shall attempt to explain to you the ele- ments of hydrostaticks. ^ There are no tides in lakes, because they are generally so small that when the moon is vertical she attracts every part alike ; and by rendering all the waters equally light, no part can be rais- ed higher than another. The Mediterranean and Baltick seas have very small elevations, because the inlets by which they com- municate with the ocean are so narrow, that they cannot in so short a time either receive or discharge enough, sensibly to raise or sink their surfaces ? 569. Why is it not high water at a place, when the moon is di- rectly over the meridian of it .'* 570. How long after the moon passes the meridian of a place before the effect of her influence becomes complete ? 571. Why are the tides three quarters of an hour later every day ? -572. Why are there no tides on the lakes ? 573. Why are the tides small in the Mediterranean. and Boiltick seas ? ' ON THE MECHANICAL PROPERTIES OP FLUIDS. VA7 CONVERSATION X. ON THE MECHANICAL PROPERTIES OF FLUIDS. Definition of a Fluid ; Distinction between Fluids and Liquids; Of Non-Elasiich Fluids ; Scarcely suscepti- ble of Compression ; Of the Cohesion of Fluids ; Of their Gravitation ; Of their Equilibrium ; Of their Pressure; Of Specific^ Gravity ; Of the SpecificJc Gravity of Bodies heavier than Water ; Of those of the same Weight as Water ; Of those lighter than Wa- ter ; Of the Specifich Gravity of Fluids, We have hitherto confined our attention to the me- chanical properties of solid bodies, which have been illus- trated, and, I hope, thoroughly impressed upon your me- mory, by the conversations we have subsequently had on astronomy. It v/ill now be necessary for me to give you some account of the mechanical properties of fluids — a science which is called hydrostaticks. A fluid is a sub- stance which yields to the slightest pressure. If you dip your hand into a basin of water, you are scarcely sensible of meeting with any resistance. Emily, The attraction of cohesion is, then, I suppose, less powerful in fluids than in solids ? Mrs. B. Yes; fluids, generally speaking, are bodies of less density than solids. From the slight cohesion of the particles of fluids, and the facility with which they slide over each other, it is inferred, that they must he small, smooth, and globular ; smooth, because there ap- pears to be little or no friction among them ; and globu- lar, because touching each other but by a point would ac- count for the slightness of their cohesion.* * If the particles of fluids ^e round, there must be vacant spaces between them, in the same manner as there are vacuities between cannon balls that are piled together ; between these balls smaller 574. What is the science called that treats of the mechanical properties of fluids ? 575. What is meant by a fluid ? 576. In which is the attraction of cohesion the most powerful, solids or fluids ? 577. What is inferred from the slight cohesion of the particles of fluids, and the facility with which they slide over each other ? 12* I3§ ON THE MECHANICAL PROPERTIES OF FLUIDS* Caroline. Pray what is the distinction between a fluid and a liquid ? Mrs. B. Liquids comprehend only one class of fluids. There is another class distinguished by the name of elas- tick fluids, or gases, which comprehends the air of the atmosphere, and all the various kinds of air with which you will become acquainted when you study chemistry. Their mechanical properties we shall examine at our next meeting, and confine our attention this morning to those of liquids, or non-elastick fluids. Water and liquids in general, are scarcely susceptible of being compressed, or squeezed into a smaller space than that which they naturally occupy. This is supposed to be owing to the extreme minuteness of their particles, which, rather than submit to compression, force their way through the pores of the substance which confines them. This was shown by a celebrated experiment made at Florence many years ago. A hollow globe of gold was filled with water, and on its being submitted to great pressure, the water was seen to exude through the pores of the gold, which it covered with a fine dew. Fluids gravitate in a more perfect manner than solid bodies ; for the strong cohesive attraction of the particles of the latter in some measure counteracts the eflects of gravity. In this table, for instance, the cohesion of the particles of wood enables four slender legs to support a considerable weight. Were the cohesion destroyed, or, in other words, the wood converted into a fluid, no sup- port could he afforded by the legs, for the particles no shot may be plac€d,and between these, other still smaller, or gravel, or sand, may be diffused. In a similar manner, a certain quantity of particles of sugar can betaken up in water without increasing its bulk, and when the water has dissolved the sugar, salt may be dissolved in it, and yet tiie bulk remain the same : and admitting that the particles of water are round, this is easily accounted for. 578. What reason is given in the note for supposing that the particles of fluids are round ? 579. What is the distinction between a liquid and a fluid .'' 580. Are water and other liquids susceptible of compression .'' 581. What is the reason for sup- posing they are not ? 582. What experiment has been made to show that liquids are not compressible ^ 583. How do flu- ids gravitate compared with solids ? 584. What example is given to show that solids gravitate in a less perfect manner than- liquids - ON THE MECHANICAL PROPERTIES OF FLUIDS. 139 loDger cohering together, each would press separately and independently, and would be brought to a level with the surface of the earth. Emily. This want of cohesion is then the reason why fluids can never be formed into figures, or maintained in heaps ; for though it is true the wind raises water into waves, they are immediately afterwards destroyed by gra- vity, and water always finds its level. Mrs, B, Do you understand what is meant by the level, or equilibrium of fluids ? Emily, I believe I do, though I feel rather at a loss to explain it. Is not a fluid level when its surface is smooth and flat, as is the case with all fluids when in a state of rest. Mrs. B. Smooth, if you please, but not flat ; for the definition of the equilibrium of a fluid is, that every part of the surface is equally distant from the point to which gravity tends, that is to say, from the centre of the earth ; hence the surface of all fluids must be bulging, not flat, since they will partake of the spherical form of the globe. This is very evident in large bodies of water, such as the ocean, but the sphericity of small bodies of water is so trifling, that their surfaces appear flat. This level, or equilibrium of fluids is the natural re- sult of their particles gravitating independently of each other ; for when any particle of a fluid accidentally finds itself elevated above the rest, it is attracted down to the level of the surface of the fluid, and the readiness with which fluids yield to the slightest impression will enable the particle by its weight to penetrate the surface of the fluid and mix with it. Caroline. But I have seen a drop of oil float on the surface of water without mixing with it. Mrs, B. That is because oil is a lighter liquid than water. If youjwere to pour water over it, the oil would rise to the surface, being forced up by the superiour gravi- ty of the water. Here is an instrument called a water- level, (fig. 1, plate XIII.) which is constructed upon the principle of the equilibrium of fluids. It consists of a 5S5. Why cannot liquids be moulded into figures like solids ? 586. What is meant by the level or equilibrium of fluids ? 587. Of what is the level or equilibrium of fluids the result ? — —* 588. Why will oil remain upon the top of water ? 589. How is a water-level constructed ^ 140 ON THE MECHANICAL PROPERTIES OF FLUIDS. short tube, A B, closed at both ends, and containing a little water ; when the tube is not perfectly horizontal the water runs to the lower end, and it is by this means that the level of any situation to which we apply the instru- ment, is ascertained. Solid bodies you may, therefore, consider as gravitat- ing in masses, for the strong cohesion of their particles makes them weigh altogether, while every particle of a fluid may be considered as composing a separate mass, gravitating independently of each other. Hence the re- sistance of a fluid is considerably less than that of a solid body ; for the resistance of the particles acting separate- ly, they are more easily overcome. Emily, A body of water, in falling, does certainly less injury than a solid body of the same weight. Mrs. B. The particles of fluids acting thus indepen- dently, press against each other in every direction, not only downwards but upwards, and laterally or sideways; and in consequence of this equality of pressure, every particle remains at rest in the fluid. If you agitate the fluid you disturb this equality of pressure, and the fluid will not rest till its equilibrum is restored. Caroline, The pressure downwards is very natural ; it is the effect of gravity, one particle weighing upon another presses on it ; but the pressure sideways, and particularly the pressure upwards, I cannot understand. 3Irs, B. If there were no lateral pressure, water would not run out of an opening on the side of a vessel. If you fill a vessel with sand, it will not run out of such an opening, because there is scarcely any lateral pressure among its particles. Emily, When water runs out of the side of a vessel, is it not owing to the weight of the water above the opening 1 Mrs, B, If the particles of fluids were arranged in regular columns thus, (fig. 2.) there would be no lateral pressure, for when one particle is perpendicularly above the other, it can only press it downwards ; but as it must continually happen, that a particle presses between two particles beneath, {{\g, 3.) these last must suffer a lateral pressure. 590. Why do solid bodies gravitate in masses ? 591 . Why is the resistance of fluids less than that of solids ? 592. Why are fluids inclined to a state of rest or Qquihbrium ? 593. Why will liquids run out of an opening in the vessel containing them.-^ ON THE MECHANICAL PROPERTIES OP FLUIDS. 141 Emily » The same as when a wedge is driven 'into a piece of wood, and separates the parts laterally. Mrs, B, Yes. The lateral pressure proceeds, there- fore, entirely from the pressure downwards, or the weight of the liquid above ; and consequently the lower the ori- fice is made in the vessel, the greater will be the velocity of the water rushing out of it. Here is a vessel of water (fig. 5.) with three stop cocks at different heights ; we shall open them, and you will see with what different de- grees of velocity the water issues from them. Do you un- derstand this, Caroline ?* Caroline. Oh yes. The water from the upper spout receiving but a slight pressure, on account of its vicinity to the surface, flows but gently ; the second cock having a greater weight above it, the water is forced out with greater velocity, whilst the lowest cock, being near the bottom of the vessel, receives the pressure of almost the whole body of water, and rushes out with the greatest impetuosity. Mrs. B. Very well ; and you must .observe, that as the lateral pressure is entirely owing to the pressure down- wards, it is not effected by the horizontal dimensions of the vessel, which contains the water, but merely by its depth ; for as every particle acts independently of the rest, it is only the column of particles, immediately above the orifice, that can weigh upon and press out the water. Emily. The breadth and width of the vessel then can be of no consequence in this respect. The lateral pres- sure on one side, in a cubical vessel, is, I suppose, not so great as the pressure downwards. * An empty bottle being corked, and, by means of a weight, let down a certain depth into the sea, it will be broken, or the cork will be driven into it by the perpendicular pressure. But a bottle filled with water, or any other liquid, may be let down to any depth, without damage, because in this case the internal pressure is equal to the external ? 694. From what does the lateral pressure of liquids proceed ? 595. How would you illustrate the lateral and downward pressure of fluids by the figures ? 596. What fact is mentioned in the note concerning the pressure of liquids ? 597. To what is the velocity of liquids, issuing from an orifice in the side of a vessel, proportional ? 142 ON THE MECHANICAL PROPERTIES OF FLUIDS* Mrs, B, No, in a cubical vessel the pressure down- wards will be double the lateral pressure on one side ; for every particle at the bottom of the vessel is pressed upon by a column of the whole depth of the fluid, whilst the lateral pressure diminishes from the bottom upwards to the surface, where the particles have no pressure. Caroline, And from whence proceeds the pressure of fluids upwards ? that seems to me the most unaccounta- ble, as it is in direct opposition to gravity. Mrs, B, And yet it is a consequence of their pres- sure downwards. When, for example, you pour water into a tea-pot, the water rises in the spout to a level with the water in the pot. The particles of water at the bottom of the pot are pressed upon by the particles above them ; to this pressure they will yield, if there is any mode of making way for the superiour particles, and as they can- not descend, they will change their direction and rise in the spout. Suppose the tea-pot to be filled with columns of parti- cles of water similar to that described in fig. 4. the par- ticle 1 at the bottom will be pressed laterally by the par- ticle 2, and by this pressure be forced into the spout where, meeting with the particle 3, it presses it upwards, and this pressure will be continued, from 3 to 4, from 4 to 5, and so on till the w ater in the spout has risea to a level with that in the pot. Emily, If it were not for this pressure upwards, forc- ing the water to rise in the spout, the equilibrium of tha fluid would be destroyed. Caroline, True ; but then a tea-pot is wide and laag^^ and the weight of so great a body of water as the pot will contain, may easily force up and support so small a quan- tity as will fill the spout. But would the same effect be produced if the spout and the pot were of equal dimen- sions ? Mrs. B, Undoubtedly it would. You may even re- verse the experiment by pouring water into the spout, and you will find that water will rise in the pot to a level with that in the spout ; for the pressure of the small 598. How does the pressure downwards, in a cubical vessel, oompare with the lateral pressure ? 599. Whence proceeds the pressure of liquids upwards ? 600. How would you illus- trate, from the figure, the upward pressure of liquids occasioned by the downward pressure ? 601. What will be the effect, in relation to this sutjectj if water is poured into the spout '^ ON THE MECHANICAL PROPERTIES OF FLUIDS. 143 quantity of water in the spout will force up and support the larger quantity in the pot. In the pressure upwards, as well as that laterally, you see that the force of pressure depends entirely on the height, and is quite independent of the horizontal dimensions of the fluid. As a tea-pot is not transparent, let us try the experi- ment by filling this large glass goblet by means of this nar row tube. (fig. 6.) Caroline. Look, Emily, as Mrs. B. fills it, how the water rises in the goblet, to maintain an equilibrium with that in the tube. Now, Mrs. B., will you let me fill the tube by pouring water into the goblet. Mrs. B. That is impossible. However, you may try the experiment, and I doubt not but that you will be able to account for its failure. Caroline. It is very singular, that if so small a co- lumn of water as is contained in the tube can force up and support the whole contents of the gDblet ; that the weight of all the water in the goblet should not be able to force up the small quantity required to fill the tube : — oh, I see now the reason, the water in the goblet cannot force that in the tube above its level ; and as the end of the tube is considerably higher than the goblet, it can never be filled by pouring water into the goblet. Mrs. B. And if you continue to pour water into the goblet when it is full, the water will run over instead of rising above the level in the tube. I shall now explain to you the meaning of the specifick gravity of bodies. Caroline. What ! is there another species of gravity with which we are not yet acquainted ? Mrs. B. No ; the specifick gravity of a body, means simply its weight compared with that of another body of the same size. When we say, that substances, such as lead and stones are heavy, and that others, such as paper and feathers, are light, we speak comparatively ; that is to say, that the first are heavy, and the latter light, in comparison with the generality of substances in nature. Would you call wood and chalk light or heavy bodies 1 602. What is the object of figure 6» plate XIII.? 003. Wiial is meant by the specifick gravity of bodies .'' 604. When we say that such bodies as lead and stones are heavy, and that such as paper and feathers are light, how do v/e speak ' 144 ON THE MECHANICAL PROPERTIES OF FLUIDS. Caroline, Some kinds of wood are heavy, certainly, as oak and mahogany ; others are hght, as deal and box. Emily, I think 1 should call wood in general a heavy body, for deal and box are light only in comparison to wood of a heavier description. I am at a loss to deter- mine whether chalk should be ranked as a heavy or a light body ; I should be inclined to say the former, if it were not that it is lighter than most other minerals. I perceive that we have but vague notions of light and heavy. I wish there was some standard of comparison, to which we could refer the weight of all other bodies. Mrs. B, The necessity of such a standard has been so much felt, that a body has been fixed upon for this purpose. What substance do you think would be best calculated to answer this end ? Caroline. It must be one generally known and easily obtained, lead or iron for instance. Mrs. B. All the metals expand by heat, and condense by cold. A piece of lead, let us say a cubick inch for in- stance, would have less specifick gravity in summer than in winter ; for it would be more dense in the latter season. Caroline. But, Mrs. B., if you compare the weight of equal quantities of different bodies, they will all be alike. You know the old saying that a pound of feathers is as heavy as a pound of lead. Mrs. B. When therefore we compare the weight of different kinds of bodies, it would be absurd to take quan- tities of equal loeight^ we must take quantities of equal hulk ; pints or quarts, not ounces or pounds. Caroline. Very true ; I perplexed myself by thinking that quantity referred to weight, rather than to measure. It is true, it would be as absurd to compare bodies of the same size in order to ascertain which was largest, as to compare bodies of the same weight in order to discover which was heaviest. Mrs. B. In estimating the specifick gravity of bodies, therefore, we must compare equal bulks, and we shall find that their specifick gravity will be proportional to their 605. Why would not metals, as lead, or iron, answer for the standard to determine the specifick gravities of bodies ? 606. ON THE MECHANICAL PROPERTIES OF FLUIDS. 145 weights. The body which has been adopted as a stand* ard of reference is distilled water.* Emily, I am surprised that a fluid should have been chosen for this purpose, as it must necessarily be contain- ed in some vessel, and the weight of the vessel will re- quire to be deducted. Mrs, B, In order to learn the specifick gravity i)r a solid body, it is not necessary to put a certain measure of it in one scale, and an equal measure of water into the other scale ; but simply to weigh the body under trial in water. If you weigh a piece of gold in a glass of water, will not the gold displace just as much water, as is equal to its own bulk ? Caroline. Certainly, where one body is, another can- not be at the same time ; so that a sufficient quantity of water must be removed, in order to make way for the gold. Mrs. B, Yes, a cubick inch of water to make room for a cubick inch of gold ; remember that the bulk alone is to be considered, the weight has nothing to do with the quantity of water displaced, for an inch of gold does not ^ The method of ascertaining the specifick gravities of bodies waa discovered accidentally by Archimedes. He had been employed by the king of Syracuse to investigate the metals of a golden crown which he suspected had been adulterated by the workmen. The philosopher laboured at the problem in vain, till going one day into the bath, he perceived that the water rose in the bath in proportion to tlie bulk of his bod}'^ ; he instantly perceived that any other sub- stance of equal size would have raised the water just as much, though one of equal weight and less bulk could not have produced the same effect. He then got two masses, one of gold and one of silver, each equal in weight to the crown, and having filled a ves- sel very accurately with water, he first plunged the silver mass into it, and observed the quantity of water that flowed over ; he then did the same with the gold, and found that a less quantity had pass- ed over than before. Hence he inferred that, though of equal weight, the bulk of the silver was greater than that of the gold, and that the quantity of water displaced was, in each experiment, equal to the bulk of the metal. He next made trial with the crown, and found it displaced more water than the gold, and less than the sil- ver, which led him to conclude, that it was neither pure gold nor pure silver. 607. Who discovered the method of ascertaining the specifick gravities of bodies f 608. What led him to make the discovery f 146 ON THE MECHANICAL PROPERTIES OF iFLUIDS. occupy more space, and therefore will not displace more water than an inch of ivory, or any other substance that will sink in water. Well, you will perhaps be surprised to hear that the gold will weigh less in water, than it did out of it. Emilrj. And for what reason ? Mrs, B, On account of the upward pressure of the particles of water, which in some measure supports the gold, and by so doing diminishes its weight. If the body immersed in water was of the same weight as that fluid, it would be wholly supported by it, just as the water which it displaces was supported previous to its making way for the solid body. If the body is heavier than the water, it cannot be wholly supported by it ; but the water will offer some resistance to its descent. Caroline, And the resistance which water offers to the descent of heavy bodies immersed in it, (since it proceeds from the upward pressure of the particles of the fluid,) must, in ail cases, I suppose, be the same. Mrs, B, Yes ; the resistance of the fluid is propor- tioned to the bulk, and not to the weight of the body im- mersed in it ; all bodies of the same size, therefore, lose the same quantity of their weight in water. Can you form any idea* what this loss will be ? Emily, I should think it would be equal to the weight of the water displaced ; for, since that portion of the wa- ter was supported before the immersion of the solid body, an equal weight of the solid body will be supported. Mrs, B, You are perfectly right : a body weighed in water loses just as much of its weight, as is equal to that of the water it displaces : so that if you were to put the water displaced into the scale to which the body is sus- pended, it would restore the balance. You must observe, that when you weigh a body in water, in order to ascertain its specifick gravity, you must not sink the basin of the balance in the water ; but either suspend the body to a hook at the bottom of the basin, or else take off the basin, and suspend it to the arm of the balance, (fig. 7.) Now suppose that a cubick inch 609. Why does a body weigh less in the water than out of it ? . 610. To what is the resistance of water to a body immersed in it proportioned ? 611. How much does a body weighed in the water lose of its weight ? 612. Which figure shows the ;3:wjmer of weighing a body in water ^ ON THE MECHANICAL PROPERTIES OF FLUIDS. 147 of gold weighed 19 ounces out of water, and lost one ounce of its weight by being weighed in water, what would be its specifick gravity ? Caroline, The cubick inch of water it displaced must weigh that one ounce ; and as a cubick inch of gold weighs 19 ounces, gold is 19 times as heavy as water. Eituly, I recollect having seen a table of the com- parative weights of bodies, in which gold appeared to me to be estimated at 19 thousand times the weight of water. Mrs. B. You misunderstood the meaning of the table. In the estimation you allude to, the weight of water was reckoned at 1000. You must observe, that the weight of a substance, when not compared to that of any other, is perfectly arbitrary ; and when water is adopted as a standard, we may denominate its weight by any number we please ; but then the weight of all bodies tried by this standard must be signified by proportional numbers. Caroline. We may call the weight of water for exam- ple, one, and then that of gold would be nineteen ; or if we choose to call the weight of water 1000, that of gold would be 19,000. In short, the specifick gravity means how much more a body weighs than an equal bulk of water. Mrs. B. It is rather the weight of a body compared with that of water ; for the specifick gravity of many substances is less than that of water.* * Specifick Gravities of Various Bodies. Fine gold - - 19,640 Lead - - - 11,325 Fine Silver - 11,091 Copper - - 9,000 Iron - . 7,645 Marble - - 2,705 Glass - - . 3,000 Chalk - - - 1,793 Coal - - . 1,250 Mahogany 1,063 Milk 1,034 Rain water 1,000 Oil - ^ ,920 Ice ,908 Brandy - ,920 Living men - ,891 Cork ,240 Common air - - :ii2 Experiments have been made to ascertain the specifick gravity of living men, in order to know what weight of cork fastened to a per- son in the water will keep him from sinkin*;, on the supposition that most men were specifically heavier than river water ; but, con- trary to expectation, it was found from trials made upon ten diffe- 613. What is the specifick gravity of livino- men ^ 148 ON THE MECHANICAL PROPERTIES OF FLUIDS. Caraline. Then you cannot ascertain the specifick gravity of such substances in the same manner as that of gold ; for a body that is lighter than water will float on its surface without displacing any water. Mrs, B. If a body were absolutely light, it is true that it would not displace a drop of water ; but the bodies we are treating of have all some weight, however small ; and will, therefore, displace some quantity of water. If the body be lighter than water, it will not sink to a level with the surface of the water, and therefore it will not displace so much water as is equal to its bulk ; but it will displace as much as is equal to its weight. A ship, you mu:5t have observed, sinks to some depth in water, and the heavier it is laden the deeper it sinks, as it always displaces a quantity of water equal to its weight. Caroline, But you said just now, that in the immer- sion of gold, the bulk, and not the weight of body, was to be considered. Mi's, B, That is the case with all substances which are heavier than water ; but since those which are light- er do not displace so much as their own bulk, the quan- tity they displace is not a test of their specifick gravity. In order to obtain the specifick gravity of a body which is lighter than water, you must attach to it a heavy one^ whose specifick gravity is known, and immerse them to- gether ; the specifick gravity of the lighter body may then be easily calculated. Emily, But are there not some bodies which have ex- actly the same specifick gravity as water ? Mrs, B, Undoubtedly ; and such bodies will remain at rest in whatever situation they are placed in water. rent persons, that their mean specifick gravity was about l-9th less than common water. So long, therefore, as the lungs can be kept &ee from water, a person, although unacquainted with the art of swimming, will not completely sink. 614, How long will a person unacquainted with swimming remain in the water without sinking 9 615. How can the spe- cifick gravity of bodies lighter than water be obtained ? 616. How will bodies of the same specifick gravity of water remain when immersed in it - ON THE MECHANICAL PROPERTIES OF FLUIDS. 149 Here is a piece of wood, which, by being impregnated with a little sand, is rendered precisely of the weight of an equal bulk of water ; in whatever part of this vessel of water you place it, you will find that it will remain sta- tionary. Caroline, I shall first put it at the bottom ; from thence, of course, it cannot rise, because it is not lighter than water. Now I shall place it in the middle of the vessel ; it neither rises nor sinks, because it is neither lighter nor heavier than the water. Now I will lay it on the surface of the water ; but there it sinks a little — what is the reason of that, Mrs. B. ? Mrs. B, Since it is not lighter than the water, it cannot float upon its surface ; since it is not heavier than water it cannot sink below its surface ; it will sink, there- fore, only till the upper surface of both bodies are on a level, so that the piece of wood is just covered with water. If you poured a few drops of water into the vessel, (so gently as not to increase their momentum by giving them velocity) they would mix with the water at the surface, and not sink lower. Caroline, This must, no doubt, be the reason why in drawing up a bucket of water out of a well, the bucket feels so much heavier when it rises above the surface of the water in the well ; for whilst you raise it in the wa- ter, the water within the bucket being of the same spe- cifick gravity as the water on the outside, will be wholly supported by the upward pressure of the water beneath the bucket, and consequently very little force will be re- quired to raise it ; but as soon as the bucket rises to the surface of the well you immediately perceive the increase of weight. Emily. And how do you ascertain the specifick gravity of fluids ? Mrs, B, By means of an instrument called an hy- drometer, which I will show you. It consists of a thin glass ball A, (fig. 8, plate XIII.) with a graduated tube B, and the specifick gravity of the liquid is estimated by the depth to which the instrument sinks in it. There is 617. What solid body is of the same specifick gravity of water ? 618. How is the specifick gravities of fluids ascertained ? 619. How is a hydrometer constructed ? 620. Which figure represents an hydrometer ? 13* 150 -OF SPRINGS, FOUNTAINS, SlC* a smaller ball, C, attached to the instrument below, which contains a little mercury ; but this is merely for the pur- pose of equipoising the instrument, that it may remain upright in the liquid under trial. I must now take leave of you ; but there remain yet many observations to be made on fluids ; we shall, there- fore, resume this subject at our next interview. CONVERSATION XL OF SPRINGS, FOUNTAINS, &/C. Of the Ascent of Vapour and the Formation of Clouds; Of the Formation and Fall of Rain, S^c, ; Of the Formation of Springs ; Of Rivers and Lakes ; Of Fountains^ CAROLINE. There is a question I am very desirous of asking you respecting fluids, Mrs. B., which has often perplexed me. What is the reason that the great quantity of rain which falls upon the earth and sinks into it, does not, in the course of time, injure its solidity ? The sun and the wind I know, dry the surface, but they have no effect on the interiour parts, where there must be a prodigious accumu- lation of moisture. Mrs, B, Do you not know that, in the course of time, all the water which sinlis into the ground rises out of it again ? It is the same water which successively forms seas, rivers, springs, clouds, rain, and sometimes hail, snow, and ice. If you will take the trouble of following it through these various changes, you will understand why the earth is not yet drowned by the quantity of water which has fallen upon it since its creation ; and you will even be convinced, that it does not contain a single drop- more water now, than it did at that period. Let us consider how the clouds were originally formed. When the first rays of the sun warmed the surface of the 621. What is the reason that the great quantity of rain which falls upon the earth and sinks into it, does not, in the course of time, injure its solidity ' OP SPRINGS, FOUNTAINS, &C. 151 earth, the heat, by separating the particles of water, ren- dered them lighter than the air. This, you know, is the case with steam or vapour. What then ensues ? Caroline. When lighter than the air it will naturally rise ; and now I recollect your telling us in a preceding lesson, that the heat of the sun transformed the particles of water into vapour, in consequence of which it ascended into the atmosphere, where it formed clouds. Mrs. B. We have then already followed water through two of its transformations ; from water it becomes vapour, and from vapour clouds. Emily. But since this watery vapour is lighter than the air, why does it not continue to rise ? and why does it unite again to form clouds ? Mrs. B. Because the atmosphere diminishes in den- sity, as it is more distant from the earth. The vapour therefore which the sun causes to exhale, not only from seas, rivers, and lakes, but likewise from the moisture on the land, rises till it reaches a region of air of its own spe- cifick gravity ; and there, you know, it will remain sta- tionary. By the frequent accession of fresh vapour it gra- dually accumulates, so as to form those large bodies of va- pour, which we call clouds ; and these at length becoming too heavy for the air to support, they fall to the ground. Caroline. They do fall to the ground, certainly, when it rains ; but according to your theory, I should have ima- gined, that when the clouds became too heavy for the region of air in which they were situated to support them, they would descend till they reached a stratum of air of their own weight, and not fall to the earth ; for as clouds are formed of vapour, they cannot be so heavy as the low- est regions of the atmosphere, otherwise the vapour would not have risen. Mrs. B. If you examine the manner in which the clouds descend, it will obviate this objection. In falling, several of the watery particles come within the sphere of 602. What is the cause of the ascent of vapour or steam ? 623. How are the clouds formed ? 624. But since vapour is lio;hter than the air, why does it not continue to rise ? and why does it unite again to form clouds .'' 625. What prevents the clouds remaining in the atmosphere where they are formed ? 626. Why do the clouds descend to the earth in drops of water instead of vapour, as they ascended ? 152 OF SPRINGS, FOUNTAINS, &C. each other's attraction, and unite in the form of a drop of water. The vapour, thus transformed into a shower, is heavier than any part of the atmosphere, and consequent- ly descends to the earth. Caroline. How wonderfully curious ! Mrs, B, It is impossible to consider any part of na- ture attentively without being struck with admiration at the wisdom it displays ; and I hope you will never con- template these wonders without feeling your heart glow with admiration and gratitude towards their bounteous Author. Observe, that if the waters were never drawn out of the earth, all vegetation would be destroyed by the excess of moisture ; if, on the other hand, the plants were not nourished and refreshed by occasional showers, the drought would be equally fatal to them. If the clouds constantly remain in a state of vapour, they might, as you remarked, descend into a heavier stratum of the atmosphere, but could never fall to the ground ; or were the power of attraction more than sufficient to convert the vapour into drops, it would transform the cloud into a mass of water, which, instead of nourishing, would destroy the produce of the earth. Water then ascends in the form of vapour, and descends in that of rain, snow, or hail, all of which ultimately be- come water. Some of this falls into the various bodies of water on the surface of the globe, the remainder upon the land. Of the latter, part re-ascends in the form of vapour, part is absorbed by the roots of vegetables and part descends into the bowels of the earth, where it for^ springs. Emily, Is rain and spring-water then the same ? Mrs, B. Yes, originally. The only difference be- tween rain and spring water, consists in the foreign par- ticles which the latter meets with and dissolves in its pas- sage through the various soils it traverses. Caroline. Yet spring water is more pleasant to the taste, appears more transparent, and, I should have sup- posed, would have been more pure than rain water. My^s. B. No ; excepting distilled water, rain water is the most pure we can obtain ; and it is its purity which renders it insipid, whilst the various salts and different 627. What are the several changres which water undergoes in its ascent and descent ? 628. What is the difference between rain and spring water ^ 629, Which is the most pure ? OP SPRINGS, FOUNTAINS, &C. 153 ingredients, dissolved in spring water, give it a species of flavour, without in any degree affecting its transparency ; and the fihration it undergoes through gravel and sand in the bowels of the earth, cleanses it from all foreign matter which it has not the power of dissolving. When rain falls on the surface of the earth, it continues making its way downwards through the pores and cre- vices in the ground. When several drops meet in their subterraneous passage, they unite and form a little rivulet ; this, in its progress, meets with other rivulets of a similar description, and they pursue their course together in the bowels of the earth, till they are stopped by some sub- stance which they cannot penetrate. Caroline* But you said that water could penetrate even the pores of gold, and they cannot meet with a substance more dense ? ^ Mrs, B. But water penetrates the pores of gold only when under a strong compressive force, as in the Floren- tine experiment ; now in its passage towards the centre of the earth, it is acted upon by no other power than gra- vity, which is not sufficient to make it force its way even through a stratum of clay. This species of earth, thougb not remarkably dense, being of great tenacity, will not admit the particles of water to pass. When water en- counters any substance of this nature, therefore, its pro- gress is stopped, and the pressure of the accumulating waters forms a bed, or reservoir. This will be more clear- ly explained by fig. 9, plate XIII. which represents a sec- tion, or the interiour of a hill or mountain. A is a body of water such as I have described, which when filled up as high as B (by the continual accession of water it re- ceives from the ducts or rivulets a, «, «, a,) finds a pas- sage out of the cavity, and, impelled by gravity, it runs on, till it makes its way out of the ground at the side of the hill, and there forms a spring, C. Caroline. Gravity impels downward towards the cen- tre of the earth ; and the spring in this figure runs in a horizontal direction. 630. What renders spring water more pleasant to the taste, if it is less pure than rain water ? 631. How are springs and ri-* vulets at first formed ? 632. Through what species of earth will not water pass ? 633. Which figure represents the manner in which springs are formed ? ^634. How would you explain this figure ' 154 OF SPRINGS, FOUNTAINS, &C. Mrs, B. Not entirely. There is some declivity from the reservoir to the spot where the water isues out of the ground ; and gravity, you know, will bring bodies down an inclined plane, as well as in a perpendicular di- rection. Caroline, But though the spring may descend on first issuing, it must afterward rise to reach the surface of the earth ; and that is in direct opposition to gravity. 3Irs, B, A spring can never rise above the level of the reservoir whence it issues ; it must, therefore, find a pas- sage to some part of the surface of the earth that is lower or nearer the centre than the reservoir. It is true that, in this figure, the spring rises in its passage from B to C occasionally ; but this, I think, with a little reflection, you will be able to account for. Ernlly, Oh yes ; it is owing to the pressure of fluids up- wards, and the water rises in the duct upon the same prin- ciple as it rises in the spout of a tea-pot ; that is to say, in order to preserve an equilibrium with the water in the reservoir. Now I think I understand the nature of springs ; the water will flow through a duct, whether as- cending or descending, provided it never rises higher than the reservoir. Mrs, B, Water may thus be conveyed to every part of a town, and to the upper part of the houses, if it is ori- ginally brought from a height superiour to any to which it is conveyed. Have you never observed, when the pave- ment of the streets have been mending, the pipes which serve as ducts for the conveyance of the water through the town 1 Emily. Yes, frequently ; and I have remarked that when any of these pipes have been opened, the water rushes upwards from them with great velocity, which I suppose proceeds from the pressure of the water in the re- servoir, which forces it out. Caroline. I recollect having once seen a very curious glass, called Tantalus's cup ; it consists of a goblet, con- taining a small figure of a man, and whatever quantity of water you pour into the goblet, it never rises higher than 635. How high may a springr rise ? 636. On what princi- ple does water ascend as well as descend in its course, as is often the case in being carried in ducts ? 637. What is called 1 an« talus's cup ? OF sphings, fountains, &c. 155 the breast of the figure. Do you know how that is con- trived 1 Mrs, B, It is by means of a syphon, or bent tube, which is concealed in the body of the figure. It rises through one of the legs, as high as the breast, and there turning, descends through the other leg, and from thence through the foot of the goblet, w here the water runs out. (fig. I, plate XIV.) When you pour water into the glass A, it must rise in the syphon B, in proportion as it rises in the glass ; and when the glass is filled to a level with the upper part of the syphon, the water will run out through the other leg of the figure, and will continue run- ning out, as fast as you pour it in ; therefore the glass can never fill any higher. Emily, I think the new well that has been made at our country-house, must be of that nature. We had a great scarcity of water, and my father has been at con- siderable expense to dig a well ; after penetrating to a great depth before water could be found, a spring was at length discovered, but the water rose only a few feet above the bottom of the well ; and sometimes it is quite dry. Mrs, B, This has however, no analogy to Tantalus's cup, but is owing to the very elevated situation of your country house. Emily, I believe I guess the reason. There cannot be a reservoir of water near the summit of a hill ; as in such a situation there will not be a sufficient number of rivulets formed to supply one ; and without a reservoir, there can be no spring. In such situations, therefore, it is necessary to dig very deep, in order to meet with a spring ; and when we give it vent, it can rise only as high as the reservoir from whence it flows, which will be but little, as the reservoir must be situated at some con- siderable depth below the summit of the hill. Caroline, Your explanation appears very clear and satisfactory. But I can contradict it from experience. At the very top of a hill, near our country-house, there is a large pond, and, according to your theory, it would be impossible there should be springs in such a situation to supply it with water. Then you know that I have crossed 638. By what means is the water prevented from rising to the head of the figure ? 639. Why must weJIs on high land be dug deep in order to be supplied with water .'' 156 OF Springs, fountains, &.c. the Alps, and I can assure you, that there is a fine lake on the summit of Mount Cenis, the highest mountain we passed over. Mrs. B. Were there a lake on the summit of Mount Blanc, which is the highest of the Alps, it would indeed be wonderful. But that on Mount Cenis is not at all contradictory to our theory of springs ; for this mountain is surrounded by others much more elevated, and the springs which feed the lake must descend from reservoirs of water formed in those mountains. This must also be the case with the pond on the top of the hill ; there is doubtless some more considerable hill in the neighbour- hood which supplies it with water. Emily, 1 comprehend perfectly, why the water in our well never rises high : but I do not understand why it should occasionally be dry. Mrs, B, Because the reservoir from which it flows being in an elevated situation, is but scantily supplied with water ; after a long drought, therefore, it may be drained, and the spring dry, till the reservoir be reple- nished by fresh rains. It is not uncommon to see springs flow with great violence in wet weather, and at other times be perfectly dry. Caroline. But there is a spring in our grounds which more frequently flows in dry than in wet weather : how is that to be accounted for ? Mrs. B. The spring probably comes from a reservoir at a great distance, and situated very deep in the ground : it is, therefore, some length of time before the rain reaches the reservoir, and another considerable portion must elapse, whilst the water is making its way from the reservoir to the surface of the earth ; so that the dry wea- ther may probably have succeeded the rains before the spring begins to flow, and the reservoir may be exhausted by the time the wet weather sets in again. Caroline. I doubt not but this is the case, as the spring is in a very low situation, therefore the reservoir may be at a great distance from it. Mrs, B. Springs, which do not constantly flow are called intermitting, and are occasioned by the reservoir 640. How can the lake on Mount Cenis, one of the Alps, be reconciled to the theory of springs which has been ^iven ? 641. Why are wells frequently dry ? 642. Why do some springs flow more in dry than wet weather .'' 643. What springs are called intermitting P OP SPRINGS, FOUNTAINS, &/C. 157 being imperfectly supplied. Independently of the situ- ation, this is always the case when the duct or ducts which convey the water into the reservoir are smaller than those which carry it off. Caroline, If it run out faster than it run in, it will of course sometimes be empty. And do not rivers also derive their source from springs 1 Mrs, B, Yes, they generally take their source in mountainous countries, where springs are most abundant. Caroline, I understood you that springs were more rare in elevated situations. Mrs. B, You do not consider that mountainous coun- tries abound equally with high and low situations. Re- servoirs of water, which are formed in the bosom of moun- tains, generally find a vent either on their declivity, or in the valley beneath ; while subterraneous reservoirs formed in a plain, can seldom find a passage to the surface of the earth, but remain concealed, unless discovered by digging a well. When a spring once issues at the surface of the earth it continues its course externally, seeking always a lower ground, for it can no longer rise. Emily, Then what is the consequence, if the spring, or I should now rather call it a rivulet, runs into a situa- tion which is surrounded by higher ground ? Mrs, B, Its course is stopped, the water accumulates, and it forms a pool, pond, or lake, according to the di- mensions of the body of water. The lake of Geneva, in all probability, owes it origin to the Rhone, which passes through it ; if, when this river first entered the valley, which now forms the bed of the Lake, it found itself sur- rounded by higher grounds, its waters would there accu- mulate, till they rose to a level with that part of the valley where the Rhone now continues its course beyond the Lake, and from whence it flows through valleys, occasion- ally forming other small lakes till it reaches the sea. Emily, And are not fountains of the nature of springs ? Mrs, B, Exactly. A fountain is conducted perpen- dicularly upwards, by the spout or adjutage A, through 644. Why do rivers usually have their source in mountainous regions ? 645. When a spring once issues from the surface of the earth what is its course ? 646. What is the consequence if a spring runs into a situation which is surrounded by higher ground ?; 647. How was lake Geneva probably formed •'— »- €48. Are artificial fountains of the nature of springs ^ 14 158 ON THE MECHANICAL PROPERTIES OF AIR. which it flows ; and it will rise nearly as high as the reser- voir B, from whence it proceeds. (Plate XIV. figure 2.) Caroline, Why not quite as high ? Mrs, B, Because it meets with resistance from the air in its ascent ; and its motion is impeded by friction against the spout, where it rushes out. Emilif, But if the tube through which the water rises be smooth, can there be any friction ? especially with a fluid whose particles yield to the slightest impression. Mrs, B, Friction (as we observed in a former les- son,) may be diminished by polishing, but can never be entirely destroyed; and though fluids are less susceptible of friction than solid bodies, they are still affected by it. Another reason why a fountain will not rise so high as its reservoir, is, that as all the particles of water spout from the tube with an equal velocity, and as the pressure of the air upon the exteriour particles must diminish their velo- city, they will, in some degree, strike against the under parts, and force them sidevvays, spreading the column into a head, and rendering it both wider and shorter than it otherwise would be. At our next meeting, we shall examine the mechanical properties of the air, which, being an elastick fluid, differs in many respects from liquids. 649. Which figure represents an artificial fountain ? 650. Why in that representation does not the water rise as high as the reservoir ? CONVERSATION XII. ON THE MECHANICAL PROPERTIES OF AIR. Ofihe Spring or Elasticity of the Air ; Of the weight of the Air ; Experiments with the Air Pump ; Of the Barometer; Mode of weighing Air ; Specijick Gravity of Air ; Of Pumps ; Description of the Sucking Pump; Description of the Forcing Pump. MRS. B. At our last meeting we examined the properties of fluids in general, and more particularly of such fluids as are called liquids. ON THE MECHANrCAL PROPERTIES OF AIR. 159 There is another class of fluids, distinguished by the name of aeriform or elastick fluids, the principal of which is the air we breathe, which surrounds the earth, and is called the atmosphere. Emihj. There are then other kinds of air, besides the atmosphere. 3Irs, B. Yes ; a great variety ; but they differ only in their chemical, and not in their mechanical properties; and as it is the latter we are to examine, we shall not at present inquire into their composition, but confine our attention to the mechanical properties of elastick fluids in general. Caroline, And from whence arises this difference 1 Mrs, B, There is no attraction of cohesion between the particles of elastick fluids ; so that the expansive pow- er of heat has no adversary to contend with but gravity ; any increase of temperature, therefore, expands elastick fluids prodigiously, and a diminution proportionally con- denses them. The most essential point in which air differs from other fluids, is by its spring or elasticity ; that is to say, its power of increasing or diminishing in bulk, according as it is more or less compressed ; a power of which I have informed you liquids are almost wholly deprived. Emily. I think I understand the elasticity of the air very well from what you formerly said of it ; (see p. 32.) but what perplexes me is, its having gravity ; if it is heavy and we are surrounded by it, why do we not feel its weight ? Caroline, It must be impossible to be sensible of the weight of such infinitely small particles, as those of which the air is composed : particles which are too small to be seen, must be too light to be felt. Mrs. B. You are mistaken, my dear ; the air is much heavier than you imagine ; it is true, that the particles which compose it are small ; but then, reflect on their quantity : the atmosphere extends to alaout the distance 651 . How are the fluids called air distinguished from hquids ? G52. How do the other kinds of air diff'er from atmospherick air ? 653. Has the attraction of cohesion any influence upon the particles of elastick fluids ? 654. What'effect does heat have on them ? 655. What is to be understood by the elasti- city of the atmosphere ? 656. To what distance from the earth doDs the atmosphere extend ? 160 ON THE MECHANICAL PROPERTIES OP AIR. of 45 miles from the earth ; and its gravity is such, that a man of middling stature is computed (when the air is heaviest) to sustain the weight of about 14 tons.* Caroline. Is it possible ! I should have thought such a weight would have crushed any one to atoms. Mrs, B, That would, indeed, be the case, if it were not for the equality of the pressure on every part of the body ; but when thus diffused we can bear even a much greater weight, without any considerable inconvenience. In bathing we support the weight and pressure of the wa- ter, in addition to that of the atmosphere ; but because this pressure is equally distributed over the body, we are scarcely sensible of it ; whilst if your shoulders, your head, or any particular part of your frame were loaded with the additional weight of a hundred pounds, you would soon sink under the fatigue. Besides this, our bodies contain air, the spring ofw^hich counterbalances the weight of ex- ternal air, and renders us less sensible of its pressure. Caroline, But if it were possible to relieve me from the weight of the atmosphere, should I not feel more light and agile ? Mrs, B. On the contrary, the air within you, meeting with no external pressure to restrain its elasticity, would distend your body, and at length, bursting the parts which confined it, put a period to your existence. Caroline, This weight of the atmosphere, then, which I was so apprehensive would crush me, is, in reality, es- sential to my preservation. Emily, I once saw a person cupped, and was told that the swelling of the part under the cup was produced by taking away from that part the pressure of the atmo- sphere ; but I could not understand how this pressure pro- duced such an effect. Mrs, B, The air pump affords us the means of mak- ing a great variety of interesting experiments on the weight and pressure of the air : some <5f them you have ^' The height to which the atmosphere extends has never been accurately ascertained ; but at a greater distance than 45 miles it ceases to reflect the sun's rays. 657. What weight of air is a common sized man supposed to sustain ? 658. Why does not such a weight crush him to atoms ? 659. What would be the consequence, if the weight of external air were removed from us ? ON THE MECHANICAL PROPERTIES OP AIR. 161 already seen. Do you not recollect, that in a vacuum pro- duced within the air pump, substances of various weights fell to the bottom in the same time ? why does not this happen in the atmosphere ? Caroline, I remember you told us it was owing to the resistance which light bodies meet with from the air dur- ing their fall. Mrs* B. Or, in other words, to the support which they received from the air, and which prolonged the time of their fall. Now, if the air were destitute of weight, how could it support other bodies or retard their fall 1 I shall now snow you some other experiments, which illustrate, in a striking manner, both the weight and elas- ticity of air. I shall tie a piece of bladder over this glass receiver, which, you will observe, is open both at the top as well as below. Caroline, Why do you wet the bladder first 1 Mrs. B, It expands by wetting, and contracts in drying ; it is also more soft and pliable when wet, so that I can make it fit better, and when dry it will be tighter. We must hold it to the fire in order to dry ; but not too near, lest it should burst by sudden contrac- tion. Let us now fix it on the air-pump and exhaust the air from underneath it — you will not be alarmed if you hear a noise. Emily, It was as loud as the report of a gun, and the bladder is burst ! Pray explain how the air is concerned in this experiment. Mrs, B, It is the effect of the weight of the atmo- sphere on the upper surface of the bladder, when I had ta- ken away the air from the under surface ; so that there was no longer any re-action to counterbalance the pres- sure of the atmosphere on the receiver. You observed how the bladder was pressed inwards by the weight of the external air, in proportion as I exhausted the receiver : and before a complete vacuum was formed, the bladder, 660. Why do not bodies of various weights in the atmosphere fall in the same time ? 661. What does the fact prove, that Hght bodies are retarded by the air in falling to the earth .^ 662, How may it be shown that the air has weight .'' 14 * 1(52 ON THE MECHANICAL PROPERTIES OF AIR- unable to sustain the violence of the pressure, burst with the explosion you have just heard.* I shall now show you an experiment, which proves the expansion of the air, contained within a body when it is relieved from the pressure of the external air. You would not imagine that there was any air contained with- in this shrivelled apple, by its appearance ; but take no- tice of it wlien placed within a receiver, from which I shall exhaust the air. Caroline, How •strange! it grows quite plump, and looks like a fresh-gathered apple. Mrs, B, But as soon as I let the air again into the receiver, the apple you see returns to its shrivelled state. When I took away the pressure of the atmosphere, the air within the apple expanded and swelled it out ; but the instant the atmospherical air was restored, the expansion of the internal air was checked and repressed, and the apple shrunk to its former dimensions. You may make a similar experiment with this little bladder, which you see is perfectly flaccid and appears to contain no air : in this state I shall tie up the neck of the bladder, so that whatever air remains within it may not escape, and then place it under the receiver. Now observe, as I exhaust the receiver, how the bladder dis- tends ; this proceeds from the great dilatation of the small quantity of air which was enclosed within the blad- der when I tied it up : but as soon as I let the air into the receiver, that which the bladder contains, condenses * The weight of the atmosphere can also be ascertained from the following experiments. — The air being exhausted, by an air- pump, from a glass receiver, the receiver will be held fast by the pressure of the external air. If a small receiver be placed under a larger one, and the air be exhaiirted from both, the larger one v/ill be held fast by the pressure of external air, while the smaller one will be easily moved. Or, if the hand be placed upon a small open vessel in such a manner as to close its upper orifice, it will be held down with great force. 663. What experiments named in the note prove that air has iveight f 664. How may the elasticity or expansive power of the air be shown ? lue? ON THE MECHANICAL PROPERTIES OP AIR. 16S and shrinks into its small compass within the folds of the bladder.* Emily, These experiments are extremely amusing, and they afford clear proofs both of the weight and elas- ticity of the air ; but I should like to know exactly how much the air weighs. Mrs. B, A column of air reaching to the top of the atmosphere, and whose base is a square inch, weighs 151bs. when the air is heaviest ; therefore every square inch of our bodies sustains a weight of lolbs. : and if you wish to know the weight of the whole of the atmosphere, you must reckon how many square inches there are on the surface of the globe, and multiply them by 15.t Emily, But are there no means of ascertaining the weight of a small quantity of air ? Mrs, B, Nothing more easy. I shall exhaust the air from this little bottle by means of the air pump : and hav- ing emptied the bottle of air, or, in other words, pro- duced a vacuum within it, I secure it by turning this screw adapted to its neck : we may now find the exact weight of this bottle, by putting it into one of the scales of a ba- lance. It weighs you see just two ounces ; but when I turn the screw, so as to admit the air into the bottle, the scale which contains it preponderates. Caroline, No doubt, the bottle filled with air, is hea- vier than the bottle void of air ; and the additional weight required to bring the scales again to a balance, must be exactly that of the air which the bottle now contains. * If a tube, closed at one end, be inserted at its open end, in a vessel of water, the fluid in the tube will not rise to the level of the water in the vessel, being resisted by the elastick force of the air within the tube. It is on this principle that the diving bell is formed. ^^^ t It has been computed that the pressure of the atmosphere on the whole surface of the earth is equivalent to that of a globe of lead sixty miles in diameter. 665. How much does a column of air, reaching to the top of the atmosphere, of an inch in diameter, weigh } 666. How great has been estimated the whole 'pressure of the atmosphere upon the earth f 667. How can the weight of a small quantity of air be ascertained ^ 164 ON THE MECHANICAL PROPERTIES OF AIR. Mrs, B. That weight, you see, is almost two grains. The dimensions of this bottle are six cubick inches. Six cubick inches of air, therefore, at the temperature of this room, weigh nearly two grains. Caroline, Why do you observe the temperature of the room in estimating the weight of the air 1 Mrs, B, Because heat rarefies air, and renders it lighter ; therefore the warmer the air is which you weigh, the lighter it will be. If you should now be desirous of knowing the spe- cifick gravity of this air, we need only fill the same bottle with water, and thus obtain the weight of an equal quan- tity of water — which you see is 1515 grains; now by comparing the weight of water to that of air we find it to be in the proportion of about 800 to 1. I will show you another instance of the weight of the atmosphere, which I think will please you : you know what a barometer is ? Caroline, It is an instrument which indicates the state of the weather, by means of a tube of quicksilver ; but how, I cannot exactly say. Mrs, B. It is by showing the weight of the atmo- sphere. The barometer is an instrument extremely simple in its construction : in order that you may understand it, I will show you how it is made. I first fill a glass tube A B, (fig .3, plate XIV.) about three feet in length, and open only at one end, with mercury ; then stopping the open end with my finger, I immerse it in a cup C, containing a little mercury. Emily, Part of the mercury which was in the tube, I observe, runs down into the cup ; but why does not the whole of it subside in the cup, for it is contrary to the law of the equilibrium of fluids, that the mercury in the tube should not descend to a level with that in the cup. Mrs, B. The mercury that has fallen from the tube into the cup, has left a vacant space in the upper part of the tube, to which the air cannot gain access ; this space is therefore a perfect vacuum ; and consequently the 668. Why is it necessary in this experiment to observe the temperature of the room in which it is made ? 669. How much heavier is water than air ? 670. How is the specifick gravity of air determined? 671. What is a barometer .^ 672. Which figure represents a barometer ? 673. How is the weight of the atmosphere determined by a barometer r ON THE MECHANICAL PROPERTIES OP AIR. 165 mercury in the tube is relieved from the pressure of the atmosphere, whilst that in the cup remains exposed to it. Caroline, Oh, now I understand it ; the pressure of the air on the mercury in the cup forces it to rise in the tube, where it sustains no pressure. Emily, Or rather supports the mercury in the tube, and prevents it from falling. Mrs, B, That comes to the same thing ; for the pow- er that can support mercury in a vacuum, would also make it ascend when it met with a v acuum. Thus you see, that the equilibrium of the mercury is destroyed only to preserve the general equilibrium of fluids. Caroline, But this simple apparatus is, in appearance, very unlike a barometer. Mrs, B, It is all that is essential to a barometer. The tube and the cup or vase are fixed on a board, for the convenience of suspending it ; the board is graduated for the purpose of ascertaining the height at which the mercury stands in the tube ; and the small moveable me- tal plate serves to show that height with greater accuracy. Emily, And at what height will the weight of the at- mosphere sustain the mercury ? Mrs, B, About 28 inches, as you will see by this barometer ; but it depends upon the weight of the atmo- sphere, which varies much according to the state of the weather. The greater the pressure of the air on the mer- cury in the cup, the higher it will ascend in the tube. Now can you tell me whether the air is hesfVier in wet or dry weather 1 Caroline. Without a moment's reflection, the air must be heaviest in wet vveather. It is so depressing, and makes one feel so heavy ; while in fine weather, I feel as light as a feather, and as brisk as a bee. Mrs, B, Would it not have been better to have an- swered with a moment's reflection, Caroline ? It would have convinced you, that the air must be heaviest in dry weather, for it is then, that the mercury is found to rise in the tube, and consequently the mercury in the cup 674. At what height will the weight of the atmospliere sustain the mercury ? 675, According to what does the weight of the atmosphere vary ? 676. When is the air the heaviest, in v/et or dry weather ? 166 ON THE MECHANICAL PROPERTIES OF AIR. must be most pressed by the air : and you know, that we estimate the dryness and fairness of the weather, by the height of the mercury in the barometer, Caroline, Why then does the air feel so heavy in bad weather ? Mrs. IB, Because it is less salubrious when impreg- nated with damp. The langs under these circumstances do not play so freely, nor does the blood circulate so well : thus obstructions are frequently occasioned in the smaller vessels, from which arise colds, asthmas, agues, fevers, &.C. Emily, Since the atmosphere diminishes in density in the upper regions, is not the air more rare upon a hill than in a plain ; and does the barometer indicate this difference ? Mrs, B, Certainly. The hills in this country are not sufficiently elevated to produce any very considerable ef- fect on the barometer ; but this instrument is so exact in its indications, that it is used for the purpose of measuring the height of mountains, and of estimating the elevation of balloons. Emily. And is no inconvenience experienced from the thinness of the air in such elevated situations ? Mrs. B. Oh, yes ; frequently. It is sometimes op- pressive, from being insufficient for respiration ; and the expansion which takes place in the more dense air con- tained within the body is often painful : it occasions dis- tension, and sometimes causes the bursting of the smaller blood-vessels in the nose and ears. Besides, in such situ- ations, you are more exposed both to heat and cold ; for though the atmosphere is itself transparent, its lower re- gions abound with vapours and exhalations from the earth, which float in it, and act in some degree as a covering, vvhich preserves us equally from the intensity of the sun's ^ays, and from the severity of the cold. Caroline. Pray, Mrs. B., is not the thermometer con- structed on the same principles as the barometer 1 Mrs. B. Not at all. The rise and fall of the fluid in the thermometer is occasioned by the expansive power 677. Why then do our feelings indicate that the air is heaviest in wet weather, if that is not the fact r G78. Is the atmo- sphere of the same density on a hill or mountain as in a valley ? -■ 679. Does a person in elevated situations feel any inconveni- ence from the tliinness of the atmosphere ? 680. What causes the rise and fall of the fluid in the thermometer ? ON THE MECHANICAL PROPERTIES OF AIR. 167 of heat, and the condensation produced by cold ; the air has no access to it. An explanation of it would, therefore, be irrelevant to our present subject. Emily. I have been reflecting, that since it is the weight of the atmosphere which supports the mercury in the tube of a barometer, it would support a column of any other fluid in the same manner. Mrs, B. Certainly ; but as mercury is heavier than all other fluids, it will support a higher column of any other fluid ; for two fluids are in equilibrium, when their height varies inversely as their densities. We find the weight of the atmosphere is equal to sustaining a column of water, for instance, of no less than 32 feet above its level. Caroline, The weight of the atmosphere is, then, as great as that of a body of water the depth of 32 feet ? 3Irs, B, Precisely ; for a column of air of the height of the atmosphere, is equal to a column of water of o2 feet, or one of mercury of 28 inches. The common pump is constructed on this principle. By the act of pumping, the pressure of the atmosphere is ta- ken off* the water, which, in consequence, rises. The body of a pump consists of a large tube or pipe, whose lower end is immersed in the water which it is de- signed to raise. A kind of stopper, called a piston, is fit- ted to this tube, and is made to slide up and down it by means of a metallick rod fastened to the centre of the pis- ton. Emily, Is it not similar to the syringe, or squirt, with which you first draw in, and then force out water ? Mrs, B, It is ; but you know that we do not wish to force the water out of the pump at the same end of the pipe at which we draw it in. The intention of a pump is to raise water from a spring or well ; the pipe is there- fore placed perpendicularly over the water which enters it at the lower extremity, and it issues at a horizontal spout towards the upper part of the pump. The pump 681. Will the weight of the atmosphere support other fluids than mercury ? 082. What fluid is heaviest ? 683. When are two fluids of different density in equilibrium ? 684. How high a column of water will the weight of the atmosphere sustain .'' 685. What instrument in common use is constructed on this principle ? Q^Q. What causes the water to rise in a pump ? — — 687. How is a common pump constructed .'' 168 ON THE MECHANICAL PROPERTIES OF AIR. therefore, is rather a more comphcated piece of machine- ry than the syringe. Its various parts are delineated in this figure : (^^, 4. plate XIV.) A B is the pipe or body of the pump, P the piston, V a valve, or little door in the piston, which open- ing upwards, admits the water to rise through it, but pre- vents its returning, and Y a similar valve in the body of the pump. When the pump is in a state of inaction, the two valves are closed by their own weight ; but when, by drawing down the handle of the pump, the piston ascends, it raises a column of air which rested upon it, and produces a va- cuum betw^een the piston and the lower valve Y, the air beneath this valve, which is immediately over the surface of the water, consequently expands, and forces its way through it ; the water, then, relieved from the pressure of the air, ascends into the pump. A few strokes of the handle totally excludes the air from the body of the pump, and fills it with water, which, having passed through both the valves, runs out at the spout. Caroline, I understand this perfectly. When the piston is elevated, the air and the water successively rise in the pump ; for the same reason as the mercury rises in the barometer. Emily, I thought that water was drawn up into a pump, by suction, in the same manner as water may be sucked through a straw. Mrs, B, It is so, into the body of the pump ; for the power of suction is no other than that of producing a va- cuum over one part of the liquid, into which vacuum the liquid is forced, by the pressure of the atmosphere on another part. The action of sucking through a straw, consists in drawing in and confining the breath, so as to produce a vacuum in the mouth ; in consequence of which the air within the straw rushes into the mouth, and is fol- lowed by the liquid, into which the lower end of the straw is immersed. The principle, you see, is the same, and the only difference consists in the mode of producing 688. How would you explain the pump, by reference to fig. 4, plate XIV. ? 689. Is the power of suction, and that which causes water to rise in a pump, the same ? 690. What is the power of suction t 691. In what consists the action of sucking liquid through a straw or any small tube ? ON THE MECHANICAL PROPERTIES OF AIR. 169 a vacuum. In suction, the muscular powers answer the purpose of the piston and valves. Emily, Water cannot, then, be raised by a pump above 32 feet ; for the pressure of the atmosphere will not sustain a column of water above that height. Mrs. B, I beg your pardon. It is true that there must never be so great a distance as 32 feet from the level of the water in the well, to the valve in the piston, otherwise the water would not rise through that valve ; but when once the water has passed that opening, it is no longer the pressure of air on the rcvservoir which makes it ascend ; it is raised by lifting it up, as you would raise it in a bucket, of which the piston formed the bottom. This common pump is, therefore, called the sucking, or lifting-pump, as it is constructed on both these principles. There is another sort of pump, called the forcing-pump : it consists of a forcing power added to the sucking part of the pump. This additional power is exactly on the prin- ciple of the syringe : by raising the piston you draw the water into the pump, and by descending it you force the water out. Caroline. But the water must be forced out at the upper part of the pump ; and I cannot conceive how that can be done by descending the piston. Mrs, B, Figure 5, plate XIV. will explain the diffi- culty. The large pipe A B represents the sucking part of the pump, which differs from the lifting-pump, only in its piston P being unfurnished with a valve, in consequence of which the water cannot rise above it. When, there- fore, the piston descends, it shuts the valve Y, and forces the water (which has no other vent) into the pipe D : this is likewise furnished with a valve V, which, opening out- wards, admits the water, but prevents its return. The water is thus first raised in the pump, and then forced into the pipe, by the alternate ascending and de- scending motion of the piston, after a few strokes of the 692. What in auction answer the purpose of the piston and valves of the pump ? 693 Can water be raised in a pump more tiian 32 feet ? 6i)4. How can it, if the weight of the at- mosphere is only equal to a column of water of that height? 695 Of what does the forcing pump consist <' 696. Which , figure represents the forcing pump ? 697. How would you ex- plain the forcing pump by the figure ? 15 170 ON WIND AND SOUND. handle to fill the pipe, from whence the water issues at the spout. It is now time to conclude our lesson. When next we meet, I shall give you some account of wind, and of sound, which will terminate our observations on elastick fluids. Caroline. And I shall run into the garden, to have the pleasure of pumping, now that I understand the con- struction of a pump. Mrs. B. And, to-morrow I hope you will be able to tell me, whether it is a forcing or a common lifting pump. CONVERSATION XIII. ON WIND AND SOUND. Of Wind in General; Of the Trade Wind; Of the Periodical Trade Winds ; Of the Aerial Tides ; Of Sounds in General ; Of Sonorous Bodies ; Of Musicat Sounds; Of Concord or Harmony, and Melody. MRS. B. Well, Caroline, have you ascertained what kind of pump you have in your garden ? Caroline. I think it must be merely a lifting-pump, because no more force is required to raise the handle than is necessary to lift its weight ; and in a forcing pump, by raising the handle, you force the water into the smaller pipe, and the resistance the water offers must require an exertion of strength to overcome it. Mrs. B. I make no doubt you are right; for lifting pumps, being simple in their construction, are by far the most common. I have promised to-day to give you some account of the nature of wind. Wind is nothing more than the mo- tion of a stream or current of air, generally produced by a partial change of temperature in the atmosphere ; for when any one part is more heated than the rest, that part is rarefied ; the equilibrium is destroyed, and the air in consequence rises. When this happens, there neces- 698. What is wind ? 699, How is the air put in motion so as to produce wind ^ ON WIND AND SOUND. 171 sariiy follows a motion of the surrounding air towards that part, in order to restore it ; this spot, therefore, receives winds from every quarter. Those who live to the north of it experience 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 these winds meet and interfere ? Mrs, B. They have turbulent and boisterous wea- ther, whirlwinds, hurricanes, rain, lightning, thunder, &c. This stormy v/eather occurs most frequently in the torrid zone, where the heat is greatest : the air, being more ra- refied there than in any other part of the globe, is light- er, and consequently ascends ; whilst the air about the polar regions is continually flowing from the poles to re- store the equilibrium. ^ Caroline, This motion of the air would produce a re- gular 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 equa- tor, 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 den- ser 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 * Fill a large dish with cold water ; into the middle of this put a waiter, filled with warm water. The first will represent the ocean and the other an island, rarefying- the air above it. Blow out a wax candle, and if the air be still, on applying it successively to every side of the dish, the smoke will be seen to move towards the plate. — -Again, if the ambient water be warmed and the plate be filled with cold water, let the wick of smoking candles be held over the plate, and the contrary will happen. 700. What illustration of wind produced by change of tempera- ture is given in the note? 701. What is the consequence when winds from different quarters meet or interfere ? 702. Where does this mostly happen ? 703. Why does this mostly happen in the torrid zone ? 704. What regular wind prevaifs about the equator ? 705. Why is there a regular east wind at and near the equator ^ 172 ON WIND AND SOUND. his beams have produced in the equilibrium of the atmo- sphere. But I wonder how you will reconcile these va- rious winds, Mrs. B. ; you first led me to suppose there was a constant struggle between opposite winds at the equator producing storm and tempest ; but now I hear of one regular invariable wind, which must naturally be at- tended by calm weather. Emily, I think I comprehend it : do not these winds from the north and south combine with the 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 north and east, produces a constant north-cast 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 fur- ther distant from it experiencing only their respective north and south winds.* Caroline, But, Mrs. B., if the air is constantly flow- ing from the poles to the torrid zone, there must be a de- ficiency 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 atmosphere, ultimately flows from thence back to the poles, to restore the equilibrium : if it were not for this resource, the po- lar atmospherick 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. Caroline, 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 flow- ing back from the equator towards the poles. *^ On the coast of America, the trade winds are felt as far as forty degrees from the equator. By the aid of these winds, vessels sailing from Mexico to the Philippine islands, often finish a voyage, nearly equal to half the circumference of the globe, in 60 days, without altering their course, or chnnginff a sail. But in returning, they are obliged to go north, beyond the limits of the trade winds. 704. How are the trade winds occasioned ?^ 705. How far on each side of the equator do these winds extend r 706. IVhat is said of the trade winds on the coast of America ? 707. What fact is mentioned of vessels sailing from Mexico to the Philippine islands 9 .-708. Why do not the polar regions become exhausted of air, if it is continually blowing from them to the equator ? ON WIND AND SOUND. ITS 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 inclina- tion of the flame, that there is also a current of air setting into the room. 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 water ; 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 oc- casioned 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 varia- tion is produced by the earth's annual course round the sun, when the north pole is inclined towards that lumina- ry one half of the year, the south pole the other half. Du- ring the summer of the northern hemisphere, the countries of Arabia, Persia, India, and China, are much heated, 709. What familiar illustration can you give of the circulation of the air, first from the poles to the equator, and then rising and returning to the poles ? 710. Why are the periodical winds more regular at sea than on land ? 711. What winds are call- ed monsoons ^ 712. How is the variation of the monsoone produced ? 15* 174 ON WIND AND SOUND. and reflect great quantities of the sun's rays into the at- mosphere, by which it becomes extremely rarefied, and the equilibrium consequently destroyed. In order to re- store 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 produces 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 hemi- sphere, the ocean and countries towards the southern tropick are most heated, and the air over those parts most rarefied : then the air about the equator alters its course, and flows exactly in an opposite direction.* Caroline, This explanation of the monsoons is very curious ; but what does their breaking up mean ] Mr$, 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 he- misphere to the other : this change is usually attended by storms and hurricanes, very dangerous for shipping ; so that those seas are seldom navigated at the season of the equinox. Emily. I think I understand the winds in the torrid zone perfectly well ; but what is it that occasions the great variety of winds which occur in the temperate zones 1 for according to your theory, there should be only north and south winds in those climates. Mrs. B. Since so large a portion of the atmosphere as is over the torrid zone is in continued agitation, these agi- tations in an elastick fluid, which yields to the slightest impression, must extend every way to a great distance ; the air, therefore, in all climates, will suffer more or less perturbation, according to the situation of the country, the position of mountains, valleys, and a variety of other causes : hence it is easy to conceive, that almost every climate must be liable to variable winds. * The south-west monsoon, which blows from April to October, brings with it floods of rain, and dreadful tempests. During the rest of the year, the north-east monsoon produces a dry and agree- able state of the air. 713. What effect do the monsoons have on the weather ? 714. What does the breaking up of the monsoons mean ? 715. What is it that occasions the great variety of winds which occur in the temperate zones ' •^ ON WIND AND SOUND. 175 on the sea-shore, there is almost always a gentle sea-breeze setting in on the land on a summer's evening, to restore the equilibrium which had been disturbed by reflections from the heated surface of the shore during the day ; and when night has cooled the land, and condensed the air, we ge- nerally find it, towards morning, flowing back towards the sea. Caroline. I have observed that the wind, whichever way it blows, almost always falls about sun-set. Mrs, B. Because the rarefaction of air in the particu- lar spot which produces the wind, diminishes as the sun declines, and consequently the velocity of the wind abates. Emily, Since the air is a gravitating fluid, is it not affected by the attraction of the moon and the sun, in 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 recollect, we found to be about 800 to 1. Caroline, What a prodigious protuberance that must occasion ; how much the weight of such a column 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 pres- sure, I should suppose, would be rather diminished than increased ? Mrs, B, The weight of the atmosphere is neither in- creased nor diminished by the aerial tides. The moon's attraction augments the bulk as much as it diminishes the weight of the column of air ; these effects, 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 attract- tion affords the air, diminishes its weight or pressure, so as to occasion the mercury to fall one inch ; under these 716. What are the sea-breezes as they are termed ? 717. Why does the wind generally subside at the going down of the sun ? 71 8. Does the moon have any effect on the wind ? 719. How much greater are the aerial tides than those of water ? — — 720. Why do not the aerial tides aifect the baromete ? 176 ON WIN'b AND SOUND. circumstances the mercury must remain stationary. Thus you see, that we can never be sensible 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, hypo- thetical ; it is proved by the effect they produce on the apparent position of the heavenly bodies ; but this I can- not explain to you, till you understand the properties of light.* Emily. And when shall we learn them 1 Mrs, B, I shall first explain to you the nature of sound, which is intimately connected with that of air ; and I think at our next meeting we may enter upon the subject of opticks. We have now considered the effects produced by the wide and extended agitation of the air ; but there is ano- ther kind of agitation of which the air is susceptible — a sort of vibratory, trembling motion, which, striking on the drum of the ear, produces sound.i Caroline. Is not sound produced by solid bodies? The voice of animals, the ringing of bells, musical in- struments, 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 tremu- lous motion of the air ; and the sonorous bodies you enu- merate, are merely the instruments by which that peculiar species of motion is communicated to the air. * The quality of winds is affected by the countries over which they pass ; and they are sometimes rendered pestilential by the heat of deserts, or the putrid exhalations of marshes and lakes. Thus, from the deserts of Africa, Arabia, and the neighbouring countries, a hot wind blows, called Samiel or Simoom^ which some- times produces instant death. A similar wind blows from the Sa- hara, upon the western coast of Africa, called the Harmattan^ pro- ducing a dryness and heat which is almost insupportable, and scorching like the blasts of a furnace. t The science which treats of the nature, phenomena, and laws of sound, is called Acousticks. This science is particularly inte- resting and valuable from its extending to the theory of musical con- cord and harmony. 721. By what is the quality of winds affected ? 722. What facts are stated in the notes illustrating the effects thus produced on the wind ? 723. How is sound produced ^ ON WIND AND SOUND. 177 « 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, without this sense, there would be no sound. Emihj, I can with difficulty conceive that. A person born deaf, it is true, has no idea of sound, because he hears none ; yet that does not prevent the real 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 sonorous bodies, but that air or some other vehicle is necessary to its production, endeavour to ring the little 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 agi- tate it so violently, it does not produce the least sound. Mrs. B. By exhausting the receiver, I have cut off the communication between the air and the bell ; the lat- ter, 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 1 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 production of sound. Mrs. 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 sono- 724. What is sound, strictly speaking ? 725. How can it be shown that air is necessary in the production of sound ? 726. Why cannot a bell be heard in an exhausted receiver ? 727. Is the atmosphere the only conductor of sound ? 178 ON WIND AND SOUND. reus 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 tlie 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 key, and you will find that the sound is conveyed to the ear by means of the strings, in a much more perfect manner than if it had no other v^ehicle than the air. Caroline, That it is, certainly, for I am almost stun- ned 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 pro- duce clear, distinct, regular, and durable sounds, such as a bell, a drum, musical strings, wind instruments, 6lc, They owe this property to their elasticity ; for an elastick body, after having been struck, not only returns to its former situation, but having acquired momentum by its ve- locity, like the pendulum, it springs out on the opposite side. If I draw the siring A B, which is made fast at both ends, to C, it will not only return to its original po- sition, but proceed onwards to D. This is its first vibration, at the end of which it will re- tain sufficient velocity to bring it to E, and back again to F, which constitutes its second vibration ; the third vibra- tion will carry it only to G and H, and so on till the re- sistance of the air destroys its motion. The vibration of a sonorous body gives a tremulous mo- tion to the air around it, very similar to the motion com- municated to smooth water when a stone is thrown into it. This first produces a small circular wave around the spot in which the stone falls ; the 'wave spreads, and gradually communicates its motion to the adjacent wa- ters, producing similar waves to a considerable extent. The same kind of waves is produced in the air by the 7:28. What besides air convey the vibratory motion of sonorous bodies ?- 729. What bodies are called sonorous ? 730. To what do they owe their sonorous property ? 731. How would you explain Fig. 6, plate XIV. as illustrating the production of sound .•' 732. To what is the tremulous motion, given to the air by a sonorous body, compared ? i ON WIND AND SOUND. 179 motion of a sonorous body, but with this difference, that as air is an elastick fluid, the motion does not consist of regularly extending waves, but of vibrations, and are com- posed of amotion 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 directions. The aerial undulations being spherical. Emily. But if the air moves backwards as well as for- wards, how can its motion extend so as to convey sound to a distance. 3Irs. 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, driving them back again. The second set of undulations 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 waves in the air, corresponding with the succession of 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. 3Irs, 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. Emihj, 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 velocity of sound is computed to be at the rate of 1142 feet in a second. Caroline. With what astonishing rapidity the vibra- tions 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 than if it set the other way. 7:33 If the air reverberate, how can its motion extend so as to convey sound to a distance ? 734. Why is motion more easily communicated to air than to water ? 735. Why do we see the flash of a cannon, at a distance, before we hear the report ? » 736. What is the computed velocity of sound .'' 180 ON WIND AND SOUND. Mrs. B, The direction of the wind makes less diffe- rence 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 from which it proceeds ; as that of a vessel at sea firing a cannon, or that of a thunder cloud. If we do not hear tlie 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 produced ? Mrs. B. When the aerial vibrations meet with an ob- stacle, having a hard and regular surface, such as a 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 oppo- site ends of the gravel walk. My voice, or rather, I should say, the vibrations of air it occasions, 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 w^hen 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 prin- ciple of the reflection of sound. The voice, instead of being diffused in the open air, is confined within the trumpet: and the vibrations which spread and fall against the sides of the instrument, are reflected according to the angle of inci- dence, and fall into the direction 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 that spot, the sound is prodigiously incrr^as^^d. ■^37. What effect has the direction of the wind on the \ el city of sound ? 738. To what practical pur|30se can we ap?)ly the uniform velocity of sound ? 739. How is the sound of an echo . produced ? 740. On what principle are speaking-trumpets constructed ? ON WIND AND SOUND. 181 Figure 7, plate XIV. will give you a clearer idea of the speaking-trumpet : the reflected rays are distin^uibhed from those of incidence, by being dotted ; and they are brought to a focus at F. The trumpet used by deaf per- sons acts on the same principle ; but as the voice enters the trumpet at the large instead of the small end of the instrument, it is not so much confined, nor the sound so much increased. Emily, Are the trumpets used as musical instruments also constructed on this principle 1 Mrs, B, So far as their form tends to increase the sound, they are ; but, as a musical instrument, the trum- pet 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 notion x)f the nature of musical sounds, which as you are fond of musick 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 vibra^ tions 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 irregular, there will necessarily follow a confusion of aerial vibra- tions ; for a second vibration may commence before the first is finished, meet it half way on its return, interrupt it in its course, and produce harsh jarring sounds which are called discords, Kmily, But each set of these irregular vibrations, if repeated at equal intervals, v/ould, I suppose, produce a musical tone. It is only their irregular succession which makes them interfere, and occasions discord. 741. What does Figure 7, Plate XIV. represent ? 743. Where must the ear be situated in regard to the speaking-trumpet so as to receive an increased sound ? 743. How do the speak- ing-trumpets used by deaf persons differ from that in the figure ? 744. How far is a trumpet used for a musical instrument con- structed on the above principle .'' 745. How must a sonorous body be struck so that its vibrations produce in the mind the same uniform idea, or one musical tone ? 746. How are harsh jar- ring sounds or discords produced .'* 16 182 ON WIND AND SOUND. Mrs. JB. Certainly. The quicker a sonorous body vi- brates, 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 always gives the same tone. Mrs. B. Because the vibrations of the same string, at the same degree of tension, are always of a similar dura- tion. The quickness or slowness of the vibrations relate to the single tones, not to the various sounds which they may compose by succeeding each other. Striking the note in quick succession, produces a more frequent repe- tition of the tone, but does not increase the velocity of the vibrations of the string. The duration of the vibrations of strings or chords de- pends 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, serve to vary the duration of the vibrations, and consequently, the acuteness of gra- vity of the notes 1 Mrs. B. Yes. Among the variety of tones, there are some which, sounded together, please the ear, producing \vhat 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. Mrs. B. But concord, you know, is not confined to unison ; for two different tones harmonize in a variety of cases. If the vibrations of one string (or sonorous body whatever) vibrate in double the time of another, the se- eond vibration of the latter will strike upon the ear at the 747. On what does the acuteness or sharpness of a musical sound depend ? 748. On what does the duration of vibrations of strings or chords in musical instruments depend .'* 749. How is harmony or concord in sounds produced .'' 750. Howie an octave concord produced ^ ON OPTICKS. 1S3 same instant as the first vibration 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 vi- bration 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 ? Mrs, B. Yes; and the key-note struck with the fourth is likewise a concord, because the vibrations are av^ three to four. The vibrations of a major third with* the key-note, are as four to five ; 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 suc- cessively, give us the pleasure which is called melody. Upon these general principles the science of musick i? founded ; but I am not sufficiently 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 op- ticks, in which we shall consider the nature of vision, light, and colours. 751. How is that species of harmony, called a fifth, produced f CONVERSATION XIV. ON OPTICKS. Of Luminous, Transparent, and Opaque Bodies; Of the Radiation of Light ; Of Shadows ; Of the Reflect Hon of Light ; Opaque Bodies seen only by Refected Light ; Vision explained ; Camera Ohscura ; Image of Objects on the Retina, CAROLINE. I LONG to begin our lesson to-day, Mrs. B., for I ex- pect that it will be very entertaining. * When musick is made by the use of strings, the air is struck by the body, and the sound is excited by the vibrations : when it is made by pipes, the body is struck by the air ; but as action and re- action are equal, the effect is liie same in both cases. 184 Of^ OPTICKS. Mrs, B, Opticks is certainly one of the most interesi- ing 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 mean- ing of a luminous hodi/, an opaque hody, and a transparent body, Caroline, A kiminous 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 bodies 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 w ould be dark if it did not receive light from a luminous body ; it belongs, therefore, to the class of opaque or dark bodies, which comprehend all such as are neither luminous nor will admit the light to pass through them. Emily, And transparent bodies, are those which ad- mit 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 * The direct light of the sun is calculated to be equal to that of 6560 candles, placed at the distance of one foot from the object ; and that of the moon to the light of one candle at TJ feet distance \ of Jupiter at 1620 feet, and of Venus at 421 feet. Sir Isaac New- ton supposed rays of light to consist of exceedingly small particles, infinitely smaller than sand, moving from luminous bodies ; but later writers suppose them to consist of the undulations of an elas- tick medium, which fills all space, and which produces the sensa- tion of light to the eye, just as the vibrations of tlie air prodiice the sensation of sound to the ear. ' 752. What is the science called that treats of vision r 753^ What is a luminous body ? 754. To ichat is the direct light of the sun calculated to be equal .?— — 755. To ichat is the light of the moon — of Jupiter — ajid of Venus, respectively calculated to he %qual ? 756. What was Sir Isaac Kewton's opinion concerning the nature of li^rht ? 757. What is a modern opinion ? 758. What' are^ opaque bodies .=• 750. What are transparent bodies ? 760 AVhat are transparent bodies frequently called : O^ OPTICKS. 185 light which pass through them, are said to be transmitted by them. Light, when emanated from the sun, or any other lumi- nous 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 considered as a centre which ra- diates light in every direction. (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 ex- tremely minute, that they are never known to interfere 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 par- ticles like other bodies 1 Mrs. B. This is a disputed point upon which I can- not pretend to decide. In some respects, light is obedi- ent 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 in- fluenced by those of gravity. It has never been disco- vered to have weight, though a variety of interesting ex- periments have been made with a view of ascertaining that point ; but we are so ignorant of the intimate nature of light, that an attempt to investigate it would lead us into a labyrinth of perplexity, if not of errour ; we shall therefore confine 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 761. In what manner is light produced from luminous bodies ? 762. What is the reason th.it the progress of rays of light is not impeded by crossing each other ? 763. What is a ray of light ^ 764. What is a pencil of rays ? 765. Is light a sub- stance composed of particles of matter, like other bodies ■' 766. In what respect is it subject to the laws of matter ? 767. In what respect is it not subject to the laws of matter '* 766. What is the consequence when rays of light fall upon an opaque body ' 16* 186 ON OPTICKS. with an opaque body through which they are unable to pass, they are stopped short in their course ; for they can- not move iii a curve line round the body. Caroline, No, certainly ; for it would require some other force besides that of projection, to produce motion in a curve line. Mrs. B, The interruption of the rays of light, by the opaque body, produces, therefore, darkness on the oppo- site side of it ; and if this darkness fall upon a wall, a sheet of paper, or any object \; hatever, 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 degrees of darkness : for I should have supposed, from your defi- nition of a shadow, that it would have been perfectly black ? Mrs, B, It frequently happens that a shadow is pro- duced by an opaque body interrupting the course of the rays from one luminous body, while light from another reaches the space v/here 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 ex- tinguish 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 surround- ing objects. You must observe, also, that when a shadow is pro- duced by the interruption of rays from a single luminous body, the darkness is proportional to the intensity of the light. Emily, I should have supposed the contrary ; for as ihe light reflected from surrounding objects on the sha- dow, must be in proportion to the intensity of the light, the stronger the light, the more the shadow will be illumined. 769. What does this interruption produce in regard to the body ? 770. What is a shadow ? 771. Why are shadows of diffe- rent degrees of darkness ? 772. When a shadow is produced by the interruption of rays of light from a single opaque body, tc what is the darkness of the shadow proportional ? ON OPTICKS. 187 3frs, B, Your remark is perfectly just ; but as we have no means of estimating the degrees of light and of dark- ness but by comparison, the strongest light will appear to produce the deepest shadow. Hence a total eclipse of the sun occasions a more sensible darkness than midnight, as it is immediately contrasted with the strong light of noon-day. 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 shadows. If the luminous body A (fig. 3.) is larger than tlie opaque body B, the shadow will gradually diminish 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 vvliy is it not the case with the shadows of terrestrial objects, which are equally illumined by the sun ? but their shadows, far from diminishing, are always larger than the object, and in- crease with the distance from it. Mrs. B. In estimating the effect of shadows, we must consider the apparent not the real dimensions of the lu- minous body ; and in this point of view, the sun is a small object compared with the generality of the terrestrial bo- dies 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 magnified shadow. This will be best exemplified, by observing the shadow of an 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 candle that shines on me being much smaller than myself ? Mrs. B. Yes. The shadow of a figure A, (fig. 4.) varies in size, according to the distance of the several sur- faces B C D E, on which it is described. 773. Why does a total eclipse of the sun occasion a more sen- sible darkness than midnight ? 774. What will be the form of the shadow when a luminous body is larger than the opaque body upon which it shines ? 775. And why is it not the case with shadows of terrestrial objects, which are illumined by the sun ? 776. When the luminous body is less than the opaque body, how does th^ shadow increase ? 777. Which figure illustrates this ^ 188 ON OPTICKS. Caroline, I have observed, that two candles produce two shadows from the same object ; whilst it would ap- pear 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 (indifferent directions) while it decreases the intensity of the shadow, increases their number, which always corresponds with that of the lights ; for each light makes the opaque body cast a diffe- rent shadow, as illustrated by fig. 5. It represents a ball A, lighted by three candles B, C, D, and you observe the light B produces the shadow b, 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 of 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 pro- perty of light. Reflection, When rays of light encounter an opaque body, which they cannot traverse, part of them are absorbed by it, and part are reflected, and rebound just as an elastick ball which is struck against a wall. Emily, And is light in its reflection governed by the same laws as soli«l elastick bodies ? Mrs, B, Exactly. If a ray of light fall perpendicu- larly on an opaque body, it is reflected back in the same line, towards the point whence it proceeded. If it fall ob- liquely, it is reflected obliquely, but in the opposite direc- tion ; the angle of incidence being equal to the angle of reflection. You recollect that law in mechanicks ? Emily, Oh yes, perfectly. Mrs, B, If you will close the shutters, we shall ad- mit 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 perpendicularly upon it. 778. How may more shadows than one be produced by a single opaque body ? 779. By which figure is this illustrated ? 780. What is meant by the reflection of light ? 781. Is all the light that fails upon an opaque body reflected ? 782. By what laws is the reflection of light governed ? ^783. If a ray of light fall upon an opaque body perpendicularly, how will it be reflected ? 784. How will it be reflected if it fall upon an opaque body obliquely ? ^785. How does the angle of incidence compare with the angle of reflection ? ON OPTICKS. 181^ Caroline, I see the ray which falls upon the mirror, but not that which is reflected by it. Mrs, B. Because its reflection is directly retrograde^ The ray of incidence and that of reflection both being in the same line, though in opposite directions, are confound- ed together. Emily. The ray then which appears to us single, is really double, and is composed of the incident ray pro- ceeding to the mirror, and of the reflected ray returning 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 direc- tion. 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 reflection, and you will see that they are equal. Emily. Exactly ; and now that you hold the mirror 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 im- mediately 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 sun to the mirror, and its reflection ?* yet in neither case were those rays in a direction to enter our eyes. Mrs. B. No. What you saw was the light reflected 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 see a single ray which passes from the sun to the house ; you see no rays but 786. Which figure illustrates the manner in which li^ht is re- flected ? 787. By what rays do we see opaque bodies ? 788. How are we able to see light that falls upon an opaque body and is reflected; but not in a direction to meet the eye r 100 ON OPTICKS. those which enter your eyes; therefore it is the rays which are reflected by the house to you, and not those which proceed from the sun to the house, that are visible to you. Caroline, Why then does one side of the house ap- pear to be in sunshine, and the other in the shade ? for if I cannot see the sun shine upon it, the w^hole 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 illumined 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 absorbed 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 objects, 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 why the sun appears to shine on one part of it only ? Caroline, No, indeed ; for the whole of it is equally exposed to the sun. This partial brilliancy of water has often excited my wonder ; but it has struck me more par- ticularly by moon-light. I have frequently observed a vivid streak of moon-shine on the sea, while the rest of the water remained in deep obscurity, and yet there was no apparent obstacle to prevent the moon from shining on every part of the water equally. * Mrs, B. By moon-light the effect is more remarkable, on account of the deep obscurity of the other parts of the water ; while by the sun's light the effect is too strong for the eye to be able to contemplate 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 1 Mrs, B. The reflected rays are not attracted out of th^ir natural course by your eyes. The direction of a 789. What does one side of an opaque body appear to be in the sun-shine and the other in the shade, when by not seeing the rays that fall upon the object, both sides of it would appear shaded ? 790. What illustration is given to show that we only see the reflected light which falls upon different objects ' ON OPTICKS. 191 reflected ray, you know, depends on that of the incident ray ; the sun's rays, therefore, which fail with various de- grees of obliquity upon the water, are reflected in direc- tions 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 different 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. Enitly. 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 towards us, ap- pear equally in shadow ? Mrs. B. Certainly ; for we see them both illumined 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 must be by those reflected on it from other objects, and which it again reflects to us. Caroline. But if we all see terrestrial objects by re- flected light, (as we do the moon,) why do they appear so bright and luminous ? I should have supposed that re- flected 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 day-light and on which the sun shines. The rays of the moon are doubtless feeble, when compared with those of the 791. Why is it that the whole surface of water on which the sun or moon shines does not appear illumined ? 79'2. How does the case of the sheet of water named, differ from that of the house on which the sun shines? 793. How are we enabled to see thp moon ? 1^ ON OPTICKS. sun ; but that would not be a fair comparison, lor the for- mer are incident, the latter reflected rays. Caroline, True ; and when we see terrestrial objects 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 observed, that near the sur- face 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 on 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 vapours in an elevated situation, and the reflected rays being conse- quently 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 pro- ceed. Mrs. B, The rays of light enter at the pupil of the eye, and proceed to the retina, or optick nerve, which is situated at the back part of the eye-ball ; and there they describe the figure,colour, and (excepting size) form a per- fect representation of the object from which they proceed. We shall again close the shutters, and admit the light through the small aperture, and you will see a picture on the wall, opposite the aperture, similar to that which is delineated on the retina of the eye. Caroline, Oh, how wonderful ! there is an exact pic- ture in miniature of the garden, the gardener at work, the 794. What effect is produced on the sun and moon's rays from traversing the atmosphere ? 795. What is there in the atmo- sphere that has a tendency to absorb the rays of light .' 796. Why is it that objects on a hill appear more distinct than at an equal distance from us in a valley .'' 797. How is it that the rays of light give us an idea of the objects from which they pro- ceed .' 798. What experiment illustrates the manner in which objects are delineated on the retina of the eye ? QK OPTICKS. 193 trees blown about by the wind* The landscape would be perfect, if it were not reversed ; the ground being above and the sky beneath. Mrs, B, It is not enough to admire, you must under- stand this phenomenon, which is called a camera obscura, from the necessity of darkening the room, in order to ex- hibit it. This picture is produced by the rays of light reflected from the various objects in the garden, and which are ad- mitted through the hole in the window shutter. The rays from the glittering weathercock at the top of the alcove A, (pi. 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 descending 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 low- er part of the wall opposite the aperture, and represent the weathercock reversed in that spot, instead 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. 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, coming in different directions, and proceeding always in right lines, cross each other at their entrance through the aperture : those which come above proceed below, those from the right go to the left, those from the left towards the right ; thus every object is represented in the picture, as occupying a situation the very reverse of that which it does in nature. Caroline, Excepting the flower-pot E F, which, though 799. What is this illustration called ? 800. From what cir- cumstance does the camera obscura derive its name ? 801» How would you explain Figure 1, plate XVI, as illustrating the camera obscura ? 802. Why do the objects exhibited by the eamera obscura appear inverted '' 17 194 ON OPTICKS. 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 which the rays of light enter, represents the aperture in the window-shutter ; and the image delineated 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 on 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 to the mind. Now it is known, that our nerves can be affected only by contact ; and for ^his reason the organs of sense cannot act at a distance ; for instance, we are capable of smell- ing 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 effluvia, composed of very minute particles, which penetrate the nostrils, and ** Take off the sclerotica from the back part of the eye of an ox, or other animal, and place the eye in the hole of the window-shut- ter of a dark room, with its fore part towards the external objects ; a person in the room will, through the transparent coat, see the inverted image painted upon the retina. 803. What part of the eye is represented by the aperture in the window-shutter ? — —804. And to wliat is the picture on the wall in the camera obscura similar ? 805. Do we receive the sensa- tion of objects before us, from the images formed on the retina of the eye, or direct from the objects themselves ?—t — 806. How is *n i^ea of visible objects conveyed to the mind ^ ON OPTICKS. *\ 196 Strike upon the olfactory 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 excited 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 optick nerve, the image of them is conveyed thither by the rays of light proceeding from real objects, which actually strike upon the optick nerve, and form that image which the mind perceives. Caroline, While I listen to your reasoning, I feel con- vinced ; 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 staggered. I can- not reconcile myself to the idea, that I 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 extraordinary, that you never beheld your own face. Caroline. No ; because I so frequently see an exact representation of it in the looking-glass. Mrs, B, You see a far more exact representation of objects on the retina of your eye : it is a much more per- fect mirror than any made by art. Emily, But is it possible, that the extensive landscape which I now behold from the window, should be repre- sented on so small a space as the retina of the eye ? Mrs, B, It would be impossible for art to paint ^ small and distinct a miniature ; but nature works with a surer hand and a more delicate pencil. That power, which forms the feathers of the butterfly, and the flowerets of the daisy, can alone portray so admirable and perfect 607. How may the nerves which constitute the sense of sight be considered ? 196 ON OPTICKS. a miniature as that which is represented on the retina of the eye. Caroline. But, Mrs. B., if we see only the image of objects, why do we not see them reversed, as you showed us they were, in the camera obscura ? Is not that a strong argument against your theory ? Mrs. B. Not an unanswerable one, I hope. The image on the retina, it is true, is reversed, like that in the camera obscura ; as the rays, unless from a very small object, intersect each other on entering the pupil, in the same manner as they do on entering the camera obscura. The scene, however, does not excite the idea of being in- verted, because we always see an object in the direction of the rays which it sends to us. Emily. I confess I do not understand that. Mrs. B. It is, I think, a difficult point to explain clearly. A ray which comes from the upper part of an ob- ject describes the image on the lower part of the retina ^ but experience having taught us that the direction of that ray is from above, we consider that part of the object it represents as uppermost. The rays proceeding from the lower part of an object fall upon the upper part of the re- tina ; but as we know their direction to be from below, we see that part of the object they describe as the lowest. Caroline. When I want to see an object above me, I look up ; when an object below me, I look down. Does not this prove that I see the objects themselves ? for if I beheld only the image, there would be no necessity for looking up or down, according as the object was higher or lower than myself Mrs. B. I beg your pardon. When you look up to an elevated object, it is in order that the rays reflected from it should fall upon the retina of your eyes ; but the very circumstance of directing your eyes upwards con- vinces you that the object is elevated, and teaches you to consider as uppermost the image it forms on the retina, though it is, in fact, represented in the lowest part of it. When you look down upon an object, you draw your conclusion from a similar reasoning ; it is thus that we see all objects in the direction of the rays which reach our eyes. 808. If objects are seen only by their pictures on the retina of ihe eye, why do they not appear reversed, as in the camera obsctt- ra? * ON THE ANGLE OF VISION. 197 But I have a further proof in favour of what I have ad- vanced, which I hope will remove your remaining doubts ; I shall, however, defer it till our next meeting, as the les- son has been sufficiently long to-day. CONVERSATION XV. OPTICKS CONTINUED. 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, CAROLINE. Well, Mrs. B., I am very impatient to hear what fur- ther proofs you have to offer in support of your theory. You must allow that it was rather provoking to dismiss us as you did at our last meeting. Mrs, B. You press so hard upon me with your objec- tions, that you must give me time to recruit my forces. Can you tell me, Caroline, why objects at a distance ap- pear smaller than they really are ? Caroline. I know no other reason than their distance. Mrs. B. I do not think I have more cause to be sa- tisfied with your reasons than you appear to be with mine. We must refer again to the camera obscura to account for this circumstance ; and you will find, that the different apparent dimensions of objects at different distances pro- ceed from our seeing, not the objects themselves, but merely their image on the retina. Fig. I, plate XVII. represents a row of trees, as viewed in the camera obscura. I have expressed the direction of the rays, from the ob- jects to the image, by lines. Now, observe, the ray which comes from the top of the nearest tree, and that which comes from the foot of the same tree, meet at the aperture, 609. Why do objects appear smaller at a distance than they really are ? 810. What is an angle of vision ? 811. Which figure illustrates the angle of vision ? 812. How would you explain that figure in reference to the effect that distance has op the apparent size of an object ? 17 ♦ 196 ON THE ANGLE OP VISION. forming an angle of about 25 degrees ; this is called the an- gle of vision, under which we see the tree. These rays cross each other at the aperture, forming equal angles on each side of it, and represent the tree inverted in the camera obscura. The degrees of the image are conside- rably smaller than those of the object, but the proportions are perfectly preserved. Now let us notice the upper and lower ray, from the ■K)st distant tree ; they form an angle of not more than twelve or fifteen degrees, and an image of proportional dimensions. Thus, two objects of the same size, as the two trees of the avenue, form figures of different sizes in the camera obscura, according to their distance ; or, in other words, according to the angle of vision under whioh they are seen. Do you understand this ? Caroline, Perfectly. Mrs* B. Then you have onfy to suppose that the re- presentation in the camera obscura is similar to that on the retina. Now since objects in the same magnitudes appear to be of different dimensions, when at different distances from us, let me ask you, which it is that we see ; the real objects, which we know do not vary in size, or the images, which we know do vary according to the angle ol vision under which we see them ? Caroline. I must confess, that reason is in favour of the latter. But does that chair at the further end of the room form an image on my retina much smaller than this which is close to me ? they appear exactly of the same size. Mrs, B, 1 assure you they do not. The experience we acquire by the sense of touch corrects the errours of our sight with regard to objects within our reach. You are so perfectly convinced of the real size of objects which you can handle, that you do not attend to their apparent difference. Does that house appear to you mueh smaller than when you are close to it ? Caroline. No, because it is very near us. Mrs. B. And yet you can see the whole of it through one of the windows of this room. The image of the house, on your retina, must, therefore, be smaller than that of 813 To what is the size of the angle of vision proportioned ^ ON THE ANGLE OP VISION. 199 the window through which you see it. It is your know- ledge of the real size of the house which prevents your attending to its apparent magnitude. If you were accus- tomed to draw from nature, you would be fully aware of this difference. Emily. And pray, what is the reason that, when we look up an avenue, the trees not only appear smaller as they are more distant, but seem gradually to approach each other till they meet in a point ? Mrs. B. Not only the trees, but the road which sepa- rates the two rows, forms a small visual angle, in propor- tion as it is more distant from us ; therefore the width of the road gradually diminishes as well as the size of the trees, till at length the road apparently terminates in a: point, at which the trees seem to meet. But this effect of the angle of vision will be more fully illustrated by a little model of an avenue, which I have made for that purpose. It consists of six trees, leading to a hexagonal temple, and viewed by an eye, on the retina of which the picture of the objects is delineated. I beg that you will not criticise the proportions ; for though the eye is represented the size of life, while the trees are not more than three inches high, the dispropor- tion does not affect the principle, which the model is in- tended to elucidate. Emily. The threads which pass from the objects through the pupil of the eye to the retina, are, I suppose, to represent the rays of light which convey the image of the objects to the retina ? Mrs. B. Yes. I have been obliged to limit the rays to a very small number, in order to avoid confusion ; there are, you see, only two from each tree. Caroline. But as one is from the summit, and the other from the foot of the tree, they exemplify the diffe- rent angles under which we see objects at diflferent dis- tances, better than if there were more. Mrs. B. There are seven rays proceeding from the temple, one from the summit, and two from each of the an- gles that are visible to the eye, as it is situated ; from 814. Why are we not deceived as to the size of objects if the size of their images on the retina of the eye is varied by the dis- tance the objects are from us ? 815. Why does a road or any avenue appear to diminish in width, till at length it apparently terminates in a point ? 816. What is the reason that objects viewed in front appear larger than when viewed obliq^uely ^ 200 ON THE ANGLE OF VISION. these you may form a just idea of the difference of the an- gle of vision of objects viewed obliquely, or in front ; for though the six sides of the temple are of equal dimen- sions, that which is opposite to the eye is seen under a much larger angle than those which are viewed obliquely. It is on this principle that the laws of perspective are founded. Emily, I am very glad to know that, for I have lately begun to learn perspective, which appeared to me a very dry study ; but now that I am acquainted with the princi- ples on which it is founded, I shall find it much more in- teresting. Caroline. In drawing a view from nature, then, we do not copy the real objects, but the image they form on the retina of our eyes 1 Mrs, B. Certainly. In sculpture, we copy nature as she really exists ; in painting, we represent her as she ap- pears to us. It was on this account that I found it diffi- cult to explain by a drawing the effects of the angle of vision, and was under the necessity of constructing a mo- del for that purpose. Emily. I hope you will allow us to keep this model some time, in order to study it more completely, for a great deal may be learned from it ; it illustrates the na- ture of the angle of vision, the apparent diminution of distant objects, and the inversion of the image on the re- tina. But pray, why are the threads that represent the rays of light, coloured, the same as the objects from which they proceed 1 Mrs, B, That is a question which you must excuse my answering at present, but I promise to explain it to you in due time. I consent very willingly to your keeping the model, on condition that you will make an imitation of it, on the same principle, but representing different objects. We must now conclude the observations that remain to be made on the angle of vision. If an object, with an ordinary degree of illumination, does not subtend an angle of more than two seconds of a 817. On what principle are the laws of perspective founded ? 818. In drawing a picture of any object what are we to fol- low ? 819. How is nature to be exhibited in sculpture ? 820. How is it to be represented in painting .^ 821. "Wbe» arc objects invisible ? ON THE ANGLE OF VISION. 201 degree, it is invisible. There are consequently two cases in which objects may be invisible, either if they are too small, or so distant as to form an angle less than two se- conds of a degree. In like manner, if the velocity of a body does not ex- ceed 20 degrees in an hour, its motion is imperceptible. Caroline! A very rapid motion may then be imper- ceptible, provided the distance of the moving body is suffi- ciently great. Mrs, B, Undoubtedly ; for the greater its distance, the smaller will be the angle under which its motion will appear to the eye. It is for this reason that the motion of the celestial bodies is invisible, notwithstanding their immense velocity. Emily, I am surprised that so great a velocity as 20 degrees an hour should be invisible. Mrs, B, The real velocity depends altogther on the space comprehended in each degree ; and this space de- pends on the distance of the object, and the obliquity of its path. Observe, likewise, that we cannot judge of the velocity of a body in motion unless we know its distance ; for supposing two men to set off at the same moment from A and B, (fig. 2.) to walk each to the end of their respec- tive lines C and D : if they perform their walk in the same space of time, they must have proceeded at a very different rate, and yet to an eye situated at E, they will appear 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 extremely 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 ; indeed our senses would be very liable to lead us into errour, 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 sufficiently so for the general pur- poses of life. To convince you how requisite experience 822. What must be the velocity that its motion be perceptible ? 323 Why is the motion of the celestial bodies imperceptible ? — r-^624. What is necessary for us to know in order to judge of the A elocity of a moving body ? 825. In what respects may the sense of sight deceive us ? .826. By what are the errours into which we may bo led by the senses to be corrected ? 202 ON THE ANGLE OF VISION. is to correct the errours of sight, I 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 ope- ration of couching. At first he had no idea either of the size or distance of objects, but imagined that every thing he saw touched his eyes ; and it was not till after having repeatedly felt them, and walked from one object to ano- ther that he acquired an idea of their respective dimen-* sions, their relative situations, and their distances. Caroline, 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 e}'es. Mrs. B, That is doubtless the reason of the opinion he formed, before the sense of touch had corrected 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 optick 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 ob- ject to be single. Caroline. This is difficult to comprehend, and, I should think, can be but conjectural. 3Irs, B, I can easily convince you that you have 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 1 Caroline. A little to the right of it. Mrs. B. Then shut your right eye, and you will set 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 sensation, we should see 827. How would objects appear as to distance, to one who had always been blind, on first being made to see r 828. Why would they seem to touch the eye ? 829. If the image of an object is formed on the retina of each eye, why does not the object double ' REFLECTING MIRRORS. 203 double, and we find that to be the case with many persons who are afflicted with a disease in one eye, which pre- vents the rays of light from affecting it in the same man- ner as the other. Emily, Pray, Mrs. 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 yoif 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 ob- ject before it. Emily, Yes, I see that 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 see the whole of your person in it (fig. 3.) The ray of light C D from your eye, which falls perpendicularly 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 order to reach it ; it will therefore be re- flected in the line D A : and since we view objects in the direction 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 continue 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 reflected ; 830. AVhen we see the image of an object in a looking-glass^ why does it not appear inverted, as in the camera obscura ? 831. What must be the heii^htof a looking glass, in order for one to see his whole person in it ? 832. How would you explain Fig" 3, of plate XVII. ? 833. Why may we not see ourselves entire, in a looking-glass less than half our height? ^04 RELFtCTING MIRRORS. the ray would therefore he reflected above your head, and you could not see it. This is shown by the dotted hne. (fig. 3.) Now stand a little to the right of the mirror, so that the rays of light from your figure may fall obliquely 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 obliquely on the mirror will be reflected obliquely in the opposite direc- tion, the angles of incidence and of reflection being equal. Caroline, place yourself in the direction of the reflected rays, and tell me whether you do not see Emily's image in the glass ? Caroline, Let me consider. In order to look in the direction of the reflected rays, I must place myself as much to the left of the glass as Emily stands to the right of it. Now I 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 ob- jects 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 ray 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 re- flects the rays of light : for glass is a transparent body which should transmit them. Mrs, 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. 834. How is this shown by the figure ? 835. Why cannot a person see his own image in a looking-glass, if he stand to the right or left of it ? 836. If you stand obliquely to the right of the glass, why must another person stand just as much to the left ol it, in order to see your image } 8^37. When you stand at the right of the glass, and I stand at the left of it, why does your image appear directly opposite to yourself? 83S. How would you illustrate this by the Fiirure ^- 839. If glass is a transpa- rent body, why will looking-glasses reflect light ? REFLECTION OF MIRRORS. 205 {yaroUne. Why then should not mirrors be made sim- ply of mercury 1 Mrs. B, Because mercury is a fluid. By amalgamat- ing 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 transpa- rent ; some of the rays therefore are lost during their pas- sage through it, by being either absorbed, or irregularly reflected. This imperfection of glass mirrors has introduced the use of metallick mirrors, for optical purposes. Emily, But since all opaque bodies reflect the rays of light, I do not understand why they are not all mir- rors. 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 reflect 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 understand better, when I shall explain to you the nature of vision, and the struc- ture of the eye. You may easily conceive the variety of directions in which rays would be reflected by a nutmeg grater, on ac- count 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 susceptible 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 n-ake the best mirrors ; none therefore are so well calculated for this purpose as metals. Caroline. But the property of regular reflection is not 840. If the mercury reflect the light, why should not mirrors be made of that material ? 841. What description of mirrors more perfect than glass have been introduced ^ 842. If all opaque bodies reflect light, why cannot we see ourselves as well when lookincr at any other object, as when viewing a mirror ? r843. What substances make the most perfect mirrors ? IS 206 REFLECTION OP CONVEX MIRRORS. confined to this class of bodies ; for I have often seen my- self in a highly polished niahogany table. Mrs. J5. Certainly ; but as that substance is less du- rable, and its reflection less perfect, than that of metals, I believe it would seldom be chosen for the purpose of a mirror. There are three kinds of mirrors used in opticks ; 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 different from that of the former. The plain mirror, we have seen, does not alter the direction of the reflected rays, and forms an image behind the glass exactly similar to the object be- fore it. A convex mirror has the peculiar property of making the reflected rays diverge, by which means it di- minishes the image ; and a concave mirror makes the rays converge, and, under certain circumstances, magni- fies the image. Emily. We have a convex mirror in the drawing- room, vvbich forms a beautiful miniature picture of the ob- jects in the room ; and T have often amused myself with looking at my magnif.od face in a concave mirror. But I hope you will explain to us why the one enlarges, while the other diminishes the objects it reflects. Mrs. B. Let us begin by examining the reflection of a convex mirror. This is formed of a portion of the ex- teriour surface of a sphere. When several parallel rays fall upon it, that ray only, which, if prolonged, would pass through the centre or axis of the mirror, is perpen- dicular to it. In order to avoid confusion, I have in fig. 1, plate XVIII. drawn only thre^ parallel lines, A B, CD, E F, to represent rays falling on the convex mirror M N ; the middle ray, you will obcerve, 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 844. How many kinds of mirrors are there used in opticks ? 845. What are they ? 846. How does a plain mirror exhibit an object ? 847. How does a convex mirror exhibit. an object .'' — --848. How does a concave mirror exhibit an ob- ject .'■ 849. Of what is the convex mirror formed .'' 850. What does Fig. 1, plate XVHI. represent.' 851. When seve- ral rays fall upon a convex mirror, which one will be perpendicu- lar to it ? REFLECTION OF CONVEX MIRRORS, 207 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 fall per- pendicularly to the mirror at B and F, the rays must be in the direction of the dotted lines, which, you may ob- serve, 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 per- pendicularly 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. This point is equally distant from the surface and centre of the sphere, and is called the imagi- nary focus of the mirror. Caroline. Pray what is the meaning of a focus l 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 mir- ror, since they are reflected by it. Emily. I do not yet understand why an object ap- pears smaller when viewed in a convex mirror. Mrs. B. It is owing to the divergence of the reflected rays. You have 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 852. In what direction must rays fall on the convex mirror M, N, at the points B, T, so as to be perpendicular to it ? 853. Why will the rays A, E, in Fig. 1, plate XVIII. be reflected to the points G, H ? 854. Why would the image formed from these rays be seen at the point L ? 855. What is the relative situa-^ tion of the point L, and what is it called ? 856. What is a fo- cus ? 857. Why is the point L called an imaginary focus .'' — — S58. Why does an object appear s-maller when viewed in a convex mirror ? 208 REFLECTION OP CONCAVE MIRRORS. by reflection, and convergent rays are reflected either parallel, or less convergent. If then an object be placed before any part of a convex 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 conver- gent, and will not come to a focus 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 sup- posed that, on the contrary, they converged more, since they meet in a point. Mrs. B, They would unite sooner than they actually do, if they were not less convergent than the incident rays : for observe, that if the incident rays, instead of being re- flected 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 distant the latter is from the mirror, the less is the image reflected by it. You will now easily understand the nature of the re- flection of concave mirrors. These are formed of a por- tion of the internal surface of a hollow sphere, and their peculiar property is to converge the rays of light. Can you discover, Caroline, in w hat direction the three parallel rays, A B, C D, E F, which fall on the concave mirror M N, (f:g. 3.) are reflected ? Caroline. I believe I can. The middle ray i& 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 obliquely on the mirror. I must now draw two dotted lines perpendicular 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. 859. How would you explain by the Figure, the manner in which a convex mirror makes an object appear smaller than it is ? 860. Of what is a concave mirror formed ? 861. How would you explain Fig. 3, plate XVHI. as illustrating the manner jn which parn.Uel ray(?\vill be reflected ? REFLECTION OF CONCAVE MIRRORS. ^ 209 Mrs, B, Very well explained. Thus you see that, when any number of parallel rays fall on a concave mir- ror, they are all reflected to a focus ; for in proportion as the rays are more distant from the axis of the mirror, they fall more obliquely upon it, and are more obliquely reflect- ed ; in consequence of which they come to a focus in the direction of the axis of the mirror, at a point equally dis- tant 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 1 Mrs. B. Yes. If rays fall convergent on a concave mirror, (fig. 4.) they are sooner brought to a focus, L, than parallel rays ; their focus is therefore nearer to the mir- ror M N. Divergent rays are brought to a more distant focus than parallel rays, as in fig. 5. where the focus is at L ; but the true focus of mirrors, either convex or con- cave, is that of parallel rays, which is equally distant from the centre, and the surface of the sphere. I shall now show you the reflection of real rays of light, by a metallick concave mirror. This is one made of polished tin, which I expose to the sun, and as it shines bright, we shall be able to collect the rays into a very brilliant focus. I hold a piece of paper where I 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 be- coming closer together. I think you hold the paper just in the focus now, the light is so small and dazzling — Oh, Mrs. B., the paper has taken fire ! 8()2. Upon what does the obliquity depend with which paraJIeJ rays fall upon the surface of a concave mirror P 863. What is the focus of a concave mirror ? 864. What is the relative po- sition of the focus to a concave mirror ? 865. Is the focus of a concave mirrof real, or only imaginary as in the convex mirror .'* 866. Will the focus be in the same place whether the rays fall parallel or converginsj upon the mirror ? 867. Which is most distant from the mirror J 868. Which figure illustrates tiiis '. How is this illustrated by the figure ? 212 THE REFRACTION OF LIGHT. Mrs. B, It is the effect which transparent mediums produce on light in its passage through them. Opaque bodies, you know, reflect the rays, and transparent bodies transmit them ; but it is found, that if a ray, in passing from one medium into another of different 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 water, it is more strong- ly attracted by the latter on account of its superiour den- sity. Emily. In what direction does the water attract the ray? Mrs. B. It must attract it perpendicularly towards it in the same manner as gravity acts on bodies. If then a ray A B, (fig. 1, plate XIX.) fall perpendicu- larly 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 proceed straight on ta 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 affected by its attraction ; this attraction, if not counteracted by some other power, would draw it perpendicularly 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 be- tween 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 1 880. What is meant by the refraction of light ^ 881. When does refraction in hght take place ? 882. What power causes the refraction of light ? 883. How would you illustrate the re- fraction of light by an explanation of Fig. 1, plate XIX. .'' 884 Why does the ray C B desceBd to F instead of D or E in tlH^^ figure ' THE RErRACTION OF LIGHT. 213 Mrs, B, It is owing to the refraction of the rays re- flected by the oar ; but this is in passing from a dense to a rare medium, for you know that the rays, by means of which you see the oar, pass from water into air. E,mU.y. Bat 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 rather 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 ob* liquely from glass into water : glass being the denser me- dium, the ray will be more strongly attracted by that which it leaves than by that which it enters. The attraction of the glass acts in the direction A B, while the impulse of projection would carry the ray to F ; it moves therefore between these directions towards D. Emily, So that a contrary refraction takes place when a ray passes from a dense into a rare medium. 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 insen- sible ; 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 refraction, 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 v/ater, and you will see the flower again. Emily, I do indeed ! Let me try to explain this : when you drew the cup from me so as to conceal the flow- er, 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. 885. Why does a straight stick appear crooked when one end of it is immersed obliquely in the water ? 88(). How would you explain Fi«T. 2, plate XIX. ^ 887. Does the attraction of the denser medium affect the ray before it touches it ? 214 THE REFRACTION OF LIGHT. will help to imprint it on your memory. You must ob- serve tiiai when the flower becomes visible by the refrac- tion 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 iBMirection 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 refracted in their passage from the water into the air, will make the bottom appear higher than it really is. 3Irs, B. And the water will consequently appear more shallow. Accidents have frequently been occasion- ed by this circumstance ; and boys who are in the habit of bathing should be cautioned not to trust to the appa- rent shallowness of water, as it will always prove deeper than it appears ; unless indeed, they view it from a boat on the water, which will enable them to look perpendicu- larly upon it ; v*'hen the rays from the bottom passing per- pendicularly, no refraction will take place. The refraction of light prevents our seeing the heaven- ly bodies in their real situation ; the light they send to us being refracted in passing into the atmosphere, we see the sun and stars in the direction of the refracted ray ; as de- scribed in fig. 4, plate XIX. ; the dotted line represents the extent of the atmosphere, above a portion of the earth E B E : a ray of light coming from the sun S falls ob- liquely on it, at A, and is refracted to B : then since we see the object in the direction of the refracted ray, a spec- tator at B will see an image of the sun at C, instead of the real object as S. Emily. But if the sun were immediately over our heads, its rays falling perpendicularly on the atmosphere 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 vertical only to the inhabitants of the torrid zone ; its rays, there- 888. How would you describe the experiment represented in Fig. 3, plate XIX. ? 889. Why does water appear more shal- low than it really is ? 890. In what situation may the bottom of water be viewed so as to appear of its real depth ? 891. Do we see the heavenly bodies in their real situation .•' 892. Why do we not ? 893. By which Figure is this illustrated, and how would you describe the illustration given ? 894. In what si- tuation may the sun be seen in ils true place ? THE REFRACTION OF LIGHT. 215 fore, are always refracted in these climates. 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 reac' us, the sun must have quitted the spot he occupied their departure ; yet we see him in the direction of thosS rays, and consequently in a situation which he had aban- doned eight minutes and a half before. Etnily, When you speak of the sun's motion, you mean, I suppose, his apparent motion, produced by the diurnal motion of the earth 1 Mrs, B. No doubt ; the effect being the same, whether it is our earth, or the heavenly bodies which move : it ife more easy to represent things as they appear to be, than as they really are. Caroline, During the morning, then, when the sun is rising towards the meridian, we must (from the length of time the light is in reaching us) see an image of the sun below that spot whic]^ it really occupies. Emily. But the refraction of the atmosphere counter- acting this effect, w^e may perhaps, between the two, see the sun in its real situation. Caroline, And in the afternoon, when the sun is sink- ing 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 at- mosphere 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 refracted to the earth. So like- wise we see an image of the sun before he rises, the rays that previously fall upon the atmosphere being reflected to the earth.* " It is entirely owing to the reflection of the atmosphere that the heavens appear bright in the day time. For without it, oaly that part would be luminous in which the sun is placed ; and if 805. How long is light in coming from the sun to the earth ? 896. How would you explain the effect this has on the ap- parent situation of that luminary ? 897. What effect does the refraction of light from the atmosphere have on the length of our days .'' 898. What would he the appearance of the heavens were it not for the atmosphere f ^16 THE REFRACTION OF LIGHT. Carolint, On the other hand we must recollect thai iight 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 percep- tible, because, in passing through a pane of glass, the rays suffer two refractions, which being in contrary directions, produce the same effect, as if no refraction had taken place. Emily, I do not understand that. Mrs. B. Fig. 5, plate XIX. will make it clear to you : A A represents a thick pane of glass seen edgeways. When the ray B approaches the glass at C, it is refracted by it ; and instead of continuing its course in the same di- rection, 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 glass, but in a contrary direction to the first refraction, and in consequence proceeds to E. Now you must observe that the ray B C and the ray D E being parallel, the light 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 its quitting it. Or, to express myself more scientifically, when a ray of light passes from one medium into another, and through that into the first again, the two refractions being equal and in opposite directions, no sensible effect is produced. Mts. B. This 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 di- rection, as I shall show you. We could live without air, and should turn our backs to the sun, the whole heavens would appear as dark as in the night. In this case, also, we should have no twilig^ht, but a sudden transition from the brightest sunshine to dark, immediately upon the setting of the sun. 899. In what manner wovld the changes of day and night then take place ? 900. Is light refracted in passing throngli com- mon vi^indow-glass ? 901. Why then is not the refraction per ceptible ? 902. Which figure illustrates this ? THE REFRACTION OP LIGlfT* 217 When parallel rays (fig. 6.) fall on a piece of glass hav- ing a double convex surface, and which is called a Lens^ that only which falls in the direclion of the axis of the lens is perpendicular to the surface ; the other rays fall* ing obliquely, are refracted towards the axis, and will meet at a point beyond the lens, called its focus. { Of the three rays, ABC, which fall on the lens D E, the rays A and C are refracted in their passage through it, to a and c, and on quitting the lens they undergo a se- cond refraction in the same direction which unites them with the ray B at the focus F. Emihj, 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 sub- stance of which it is made ; in a glass lens, both sides of which are equally convex, the focus is situated nearly at the centre of the sphere of which the surface of the lens forms a portion ; it is at the distance, therefore, of the ra- dius of the sphere. There are lenses of various forms, as you will find de- scribed 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 thenu For the rays A C falling on the concave lens X Y, (fig. 7, plate XIX. ,) instead of con- verging towards the ray B, which falls on the axis of the lens, will each be attracted towards the thick edges of the lens, both on entering and quitting it, and will, therefore, by the first refraction, be made to diverge to a, c, and by the second to d, e, Caroline, And lenses which have one side flat and the other convex or concave, as A and B, fig. 1, plate XX. are, I suppose, less powerful in their refractions. Mrs, B. Yes ; they are called plano-convex, and plano-concave lenses ; the focus of the former is at the 903. What is a lens ? 904 In parallel rays that pass through a lens what ones will be refracted ? 905. In what place \yill the refracted rays meet ? 906. Which figure illustrates this ^ — — 907. What is the distance of the focus from the surface of the lens ? 908. What is the property of a convex lens ? 909. What is the property of a concave lens = 910. What does Figure 7, Plate six illustrate .? 911. What is a plano-con- vex lens .' 19 218 ON REFRACTION AND COLOURS. distance of the diameter of a sphere, of which the convex surface of the lens forms a portion ; as represented in fig. 2, plate XX. The three parallel rays, ABC, are brought to a focus by the plano-convex lens, X Y at F. I must now explain to you the refraction of a triangular 'piece of glass, called a prism. (Fig. 3.) Eniihj, The three sides of this glass are flat; it can- not therefore bring the rays to a focus ; nor do I suppose that its refraction will be similar to that of a flat pane of glass, because it has not two sides parallel ; I cannot therefore conjecture what effect the refraction of a prism can produce. Mrs, B, The refractions of the light, on entering and on quitting the prism, are both in the same direction. (Fig. 3.) On entering the prism P, the ray A is refracted from B to C, and on quitting it from C to D. I will show you this in nature ; but for this purpose it will be adviseable to close the window-shutters, and ad- mit, through the small aperture, a ray of light, which I shall refract by means of this prism. Caroline, Oh, what beautiful colours are represented on the opposite w'all ! There are all the colours of the rain- bow, and with a brightness I never saw equalled. (Fig. 4, plate XX.) Emily, I have seen an effect, in some respect similar to this, produced by the rays of the sun shining upon glass lustres ; but how is it possible that a piece of white glass can produce such a variety of brilliant colours ? Mrs, B, The colours are not formed by the prism, but existed in the ray previous to its refraction. Caroline, Yet, before its refraction, it appeared per- fectly white. Mrs, B. The white rays of the sun are composed of coloured rays, which, when blended together, appear co- lourless or white. Sir Isaac Newton, to whom w^e are indebted for the most important discoveries respecting light and colours, 912. What is a plano-concave lens? 913. Where will be the focus of a plano-convex lens ' 914. What is illustrated by- figure 2, plate XX. => 915. What is a prism .^ 916. What does figure 3, plate XX. represent ^ 917. What is the design of figure 4, plate XX. : 918. Are the different colours exhibited in that figure formed by the prism .^ 919. Of what are the white rays of the sun composed ? 920. To whom arc we inuebt- ed for the most important discoveries respecting light and colours .' ON REFRACTION AND COLOURS. 219 was the first who divided a white ray of light, and found it to consist of an assemblage of coloured rays, which formed an image upon the wall, such as you now see ex- hibited, (fig. 4.) in which are displayed the following se- ries of colours : red, orange, yellow, green, blue, indigo^ . and violet. ^'0 Emily, But how does a prism separate these coloured rays ? Mrs. B. By refraction. It appears that the coloured rays have different degrees of refrangibility ; in passing through the prism, therefore, they take different direc- tions according to their susceptibility of refraction. The violet rays deviate most from their original course ; they appear at one of the ends of the spectrum A B : contigu- ous to the violet, are the blue rays, being those which have somewhat less refrangibility : then follow, in succes- sion, the green, yellow, orange, and, lastly, the red, which are the least refrangible of the coloured rays. Caroline, I cannot conceive how these colours, mixed together, can become white. Mn, B, That I cannot pretend to explain ; but it is a fact that the union of these colours, in the proportions in which they appear in the spectrum, produce in us the idea of whiteness. If you paint a card in compartments with these seven colours, and whirl it rapidly on a pin, it will appear white. But a more decisive proof of the composition of a white ray is afforded by re-uniting these coloured rays, and form- ing with them a ray of white light.* * The same conclusion may be drawn from the experiment of mixing together paints of the colours exhibited in the prism, and in proper proportions, which will form white. It is true the white will not be of the resplendent kind ; but this will be owing to the colours mixed being less bright than those produced from the prism. 921. What is the order of the colours displayed in the prism ? 922. How does the prism separate these rays ? 923. To what is the different directions, taken by the different rays in pass- ing through a prism, owing ? 924. Which rays deviate most and which least from their original course in passing through a prism? 925. What fact is mentioned respecting a painted card, as proving that these seven colours united make white .'' 926. What experiment relating to this subject is mentioned in the note f 220 ON REFRACTION AND COLOURS. Caroline. If you can take a ray of white light to pieces, and put it together again, I shall be quite satisfied. Mrs. B. This can be done by letting the coloured rays, which have been separated by a prism, fall upon a lens, which will converge them to a focus ; and if, when w^ thus re-united, we find that they appear white as they did before refraction, I hope that you will be convinced that the white rays are a compound of the several coloured rays. The prism P, you see, (fig. 5.) separates a ray of white light into seven coloured rays, and the lens L L brings them to a focus at F, where they again appear white. Caroline. You succeed to perfection : this is indeed a most interesting and conclusive experiment. Emily. Yet, Mrs. B., I cannot help thinking, that there may perhaps be but three distinct colours in the spectrum, red, yellow, and blue ; and that the four others may consist of two of these colours blended together ; for in painting, we find that by mixing red and yellow, we pro- duce orange ; with different proportions of red and blue, we make violet or any shade of purple ; and yellow and blue form green. Now it is very natural to suppose, that the refraction of a prism may not be so perfect as to se- parate the coloured rays of light completely, and that those which are contiguous in order of refrangibility may en- croach on each other, and by mixing produce the inter- mediate colours, orange, green, violet, and indigo. Mrs. B. Your observation is, I believe, neither quite wrong, nor quite right. Dr. Wollaston, who has refract- ed light in a more accurate manner than had been pre- viously done, by receiving a very narrow line of light on a prism, found that it formed a spectrum, consisting of rays of four colours only ; but they were not exactly those you have named as primitive colours, for they consisted of red, green, blue, and violet. A very narrow line of yellow was visible, at the limit of the red and green, which Dr. Wollaston attributed to the overlapping of the edges of the red and green light. 927. How can these colours once separated be again united ? 928. Which figure illustrates this ? 929. Who has been very successful and accurate in experiments upon the refrac- tion of light ? 930. Wlmt did he suppose to be the primitive colours ? I ON REFRACTION AND COLOURS. 231 Caroline, But red and green, mixed together, do not produce yellow. Mrs, B. Not in painting ; but it may be so in the primitive rays of the spectrum. Dr. WoUaston observed that, by increasing the breadth of the aperture by which the line of light was admitted, the space occupied by each coloured ray in the spectrum was augmented in proportion as each portion encroached on the neighbouring colour and mixed with it ; so that the intervention of orange and yellow, between the red and green, is owing, he supposes, to the mixture of these two colours, and the blue is blend- ed on the one side with the green, and on the other with the violet, forming the spectrum as it was originally observed by Sir Isaac Newton, and which I have just shown you. The rainbow, which exhibits a series of colours so ana- logous to those of the spectrum, is formed by the refraction of the sun's rays in their passage through a shower of rain, every drop of which acts as a prism, in separating the coloured rays as they pass through it.* Emily, Pray, Mrs. B., cannot the sun's rays be col- lected to a focus by a lens in the same manner as they are by a concave mirror ? Mrs, B, No doubt the same effect is produced by the refraction of a lens as by the reflection of a concave mir- ror : in the first, the rays pass through the glass and con- verge to a focus behind it ; in the latter, they are reflect- ed from the mirror, and brought to a focus before it. A lens, when used for the purpose of collecting the sun's rays, is called a burning glass. The sun now shines very bright; if we let the rays fall on this lens you will per- ceive the focus. * That this is the true account of the formation of the rainbow appears from the following considerations — 1. That a bow is never seen "but when rain is falling, and the sun shining at the same time, and that the sun and bow are always in opposite parts of the heavens ; and, secondly, that the same appearance can be artificially represented by means of water thrown into the air, when the spectator is placed in a proper position with his back towards the sun. 931. How is the rain-bow formed ? 932. From what COU' sidcrations does it appear that the rain-bow is formed by the re- fraction of the sun's rays in their passage through a shower of rain ? ^933 When is a lens called a burning glass ? 19* 222 ON REFRACTION AND COLOURS. Emily. Oh yes ; the point of union of the rays is very luminous. I will hold a piece of paper in the focus, and see if it will take fire. The spot of light is extremely brilliant, but the paper does not burn. Mrs, B. Try a piece of brown paper ; — that you see takes fire almost immediately. Caroline, This is surprising ; for the light appeared to shine more intensely on the white than on the brown paper. Mrs. B. The lens collects an equal number of rays to a focus, whether you hold the white or the brown paper there ; but the white paper appears more luminous in the focus, because most of the rays, instead of entering into the paper, are reflected by it ; and this is the reason that the paper is not burnt ; whilst on the contrary, the brown paper, which absorbs more light than it reflects, soon be- comes heated and takes fire. Caroline. This is extremely curious; but why should brown paper absorb more rays than white paper ? Mrs. B. I am far from being able to give a satisfac- tory answer to that question. We can form but mere conjecture on this point ; and suppose that the tendency to absorb, or reflect rays, depends on the arrangement of the minute particles of the body, and that this diversity of arrangement renders some bodies susceptible of reflecting one coloured ray, and absorbing the others ; whilst other bodies have a tendency to reflect all the colours, and others again, to absorb them all. Emily, And how do you know which colours bodies have a tendency to reflect, or which to absorb ? Mrs. B. Because a body always appears to be of tne colour which it reflects ; for as we see only by reflected rays, it can appear but of the colour of those rays. Caroline, But we see all bodies of their own natural colour, Mrs, B, ; the grass and trees, green ; the sky, blue ; the flowers, of various hues. Mrs* B. True : but why is the grass green ? because it absorbs all except the green rays ; it is therefore these only which the grass and trees reflect to our eyes, and 934. Why will a piece of brown paper placed beneath a lens, which collects the sun's rays, take fire sooner than a piece of white paper r 935. What conjecture is given for the brown paper's absorbing more rays than the white ? 936. How do we know which colours bodies have a tendency to reflect, and which to ab^ sorb ? ON REFRACTION AND COLOURS. '22'S ^hich makes them appear green. The sky and flowers, in the same manner, reflect the various colours of which they appear to us ; the rose, the red rays ; the violet, the blue ; the jonquil, the yellow, &lc. Caroline. But these are the permanent colours of the grass and flowers, whether the sun's rays shine on them or not. Mrs, B. Whenever you see those colours, the flowers must be illumined by some light ; and light, from what- ever source it proceeds, is of the same nature, composed of the various coloured rays, which paint the grass, the flowers, and every coloured object in nature. Caroline, But, Mrs. B., the grass is green, and the flowers are coloured, whether in the dark or exposed to the light ? Mrs, B, Why should you think so ? Caroline, It cannot be otherwise. Mrs, B, A most philosophical reason indeed ! Butj as I never saw them in the dark, you will allow me to dis- sent from your opinion. Caroline, What colour do you suppose them to be. then, in the dark ? Mrs, B, None at all ; or black, which is the same thing. You can never see objects without light. Light is composed of colours, therefore there can be no light without colours ; and though every object is black, or without colour in the dark, it becomes coloured, as soon as it becomes visible. It is visible, indeed, but by the coloured rays which it reflects ; therefore we can see it only when coloured. Caroline, All you say seems very true, and I know not what to object to it ; yet it appears at the same time in- credible ! What, Mrs. B., are we all as black as negroes, in the dark ? you make me shudder at the thought. Mrs, B, Your vanity need not be alarmed at the idea, as you are certain of never being seen in that state. Caroline, That is some consolation, umioubtedly ; but what a melancholy reflection it is, that all nature which appears so beautifully diversified with colours should be one uniform mass of blackness ! Mrs, B, Is nature less pleasing for being coloured, as well as illumined by the rays of light ; and are colours less 937 Are colours essential properties of bodies ? -938. On. what do they depend ? 939. What colour do objects^ have in the dark ? 224 ON REFRACTION AND COLOURS. beautiful for being accidental, rather than essential pro- perties of bodies ? Providence appears to have decorated nature with the enchanting diversity of colours which we so much admire, for the sole purpose of beautifying the scene, and render- ing it a source of pleasurable enjoyment : it is an orna- ment which embellishes nature whenever we behold her. What reason is there to regret that she does not wear it when she is invisible ? Emily, I confess, Mrs. B., that I have had my doubts as well as Caroline, though she has spared me the pains of expressing them ; but I have just thought of an experi- ment, which, if it succeeds, w^ill, I am sure, satisfy us both. It is certain, that we cannot see bodies in the dark, to know whether they have any colour. But we may place a coloured body in a ray of light, which has been refracted by a prism ; and if your theory is true, the body, of what- ever colour it naturally is, must appear of the colour of the ray in which it is placed ; for since it receives no other coloured rays, it can reflect no others. Caroline, Oh ! that is an excellent thought, Emily ; will you stand the test, Mrs. B. ? Mrs, B, I consent : but we must darken the room, and admit only the ray which is to be refracted ; other- wise, the white rays will be reflected on the body under trial from various parts of the room. With what do you choose to make the experiment ? Caroline, This rose : look at it, Mrs. B., and tell me whether it is possible to deprive it of its beautiful colour? Mrs, B, We shall see. — I expose it first to the red rays, and the flowT.r appears of a more brilliant hue ; but observe the green leaves — Caroline, They appear neither red nor green ; but of a dingy brown with a reddish glow ! Mrs, B, They cannot be green, because they have no green rays to reflect ; neither are they red, because green bodies absorb most of the red rays. But though bodies, from the arrangement of their particles, have a tendency to absorb some rays, and reflect others, yet it 940. What experiment is proposed to prove that bodies appear of the colour of the particular ray in which they are placed? 941. Why is it necessary to darken the room in which the experi- ment is to'^be made ? 942. How would a green object appear placed in a red ray ? ON REFRACTION AND COLOURS. 225 is not natural to suppose, that bodies are so perfectly uni- form in their arrangement, as to reflect only pure rays of one colour, and perfectly absorb the others ; it is found, on the contrary, that a body reflects, in great abundance, the rays which determine its colour, and the others m a greater or less degree, in proportion as they are nearer or further from its own colour, in the order of refrangibility. The green leaves of the rose, therefore, will reflect a few of the red rays which, blended with their natural black- ness, give them that brown tinge ; if they reflected none of the red rays, they would appear perfectly black. Now I shall hold the rose in the blue rays — Caroline, Oh, Emily, Mrs. B. is right ! look at the rose : it is no longer red, but of a dingy blue colour,- - Emily. This is the most wonderful of any thing we have yet learned. But, Mrs. B., what is the reason that the green leaves are of a brighter blue than the rose ? Mrs, B, The green leaves reflect both blue and yel- low rays, which produces a green colour. They are now in a coloured ray, which they have a tendency to reflect ; they, therefore, reflect more of the blue rays than the rose, (which naturally absorbs that colour,) and will, of course, appear of a brighter blue. Emily, Yet, in passing the rose through the different colours of the spectrum, the flower takes them more rea- dily than the leaves. Mrs, B, Because the flower is of a paler hue. Bodies which reflect all the rays are white ; those which absorb them all are black : between these extremes, the body appears lighter or darker, in proportion to the quantity of rays they reflect or absorb. This rose is of a pale red : it approaches nearer to white than black ; it therefore re- flects rays more abundantly than it absorbs them. Emily, But if a rose has so strong a tendency to re- flect rays, I should have imagined that it would be of a deep red colour. 943. Why would it appear of a brownish tinge P 944. If a red object be placed in a blue ray how will it appear ? 945. Why does an object that is green placed in a blue ray appear of a brighter blue, than an object that is red when placed in the same coloured ray ? 946. In passing a red and green object through the different colours of the spectrum, why does the red one take them more readily than the green one .' 947. What bodies re- flect all the rays that fall on them ' 948, What ones absorb them ? 226 ON REFRACTION AND COLOURS. Mrs, B. I mean to say, that it has a general tenden- cy to reflect rays. Pale coloured bodies reflect all the co- loured rays to a certain degree, which produces their pale- ness, approaching to whiteness ; but one colour they re- flect more than the rest ; this predominates over the white, and determines the colour of the body. Since, then, bo- dies of a pale colour in some -degree reflect all the rays of light, in passing through the various colours of the spec- trum, they will reflect them all with tolerable brilliancy ; but will appear most vivid in the ray of their natural co- lour. The green leaves, on the contrary, are of a dark colour, bearing a stronger resemblance to black, than to white ; they have, therefore, a greater tendency to ab- sorb, than to reflect rays ; and reflecting very few of any but the blue and yellow rays, they will appear dingy in passing through the other colours of the spectrum. Caroline, They must, however, reflect great quan- tities of the green rays to produce so deep a colour. Mrs, B, Deepness or darkness of colour proceeds rather from a deficiency than an abundance of reflected rays. Remember that bodies are, of themselves, black ; and if a body reflects only a few green rays, it will appear of a dark green ; it is the brightness and intensity of the colour which show that a great quantity of rays are re- flected. Emily, A white body, then, which reflects all the rays, will appear equally bright in all the colours of the spectrum. Mrs, B, Certainly ; and this is easily proved by pass- ing a sheet of white paper through the rays of the spec- trum. Caroline. What is the reason that blue often appears green by candle-light ? Mrs, B, The light of a candle is not so pure as that of the sun ; it has a yellowish tinge, and when refracted by the prism, the yellow rays predominate ; and as blue bodies reflect the yellow rays in the next proportion, (being next in order of refrangibility,) the superabundance of yellow rays gives to blue bodies a greenish hue. Caroline, Candle-light must then give to all bodies a yellowish tinge, from the excess of yellow rays ; and yet 949 To what is darkness of colour owing ? 950. What is the reason the blue often appears green by candle-light ? 951. Why do persons of a sallow complexion appear fairer or whiter by night, if the candle-light ^ives all objects a yellowish tinge - ex\ REFRACTION AND COLOUR. 227 it is a common remark, that people of a sallow complexion appear fairer or whiter by candle-light. Mrs. B, The yellovv cast of their complexion is not so striking, when every object has a yellovv tinge. Emily, Pray, why does the sun appear red through a fog ? Mrs, B. It is supposed to be owing to the red rays hav- ing a greater momentum, which gives them power to tra- verse so dense an atmosphere. For the same reason, the sun generally appears red at rising and sitting ; as the increased quantity of atmosphere, which the oblique rays must traverse, loaded with the mists and vapours which are usually formed at those times prevents the other rays from reaching us. Caroline, And, pray, why are the skies of a blue co- lour. 3Irs, B, You should rather say, the atmosphere ; for the sky is a very vague term, the meaning of which it would be difficult to dehne philosophically. Caroline, But the colour of the atmosphere should be white, since all the rays traverse it in their passage to the earth. 3Irs, B, Do not forget that we see none of the rays which pass from the sun to the earth, excepting those which meet our eyes ; and this happens only if we look at the sun, and thus intercept the rays, in which case, you know, the sun appears white. The atmosphere is a trans- parent medium, through which the sun's rays pass freely to the earth ; but when reflected back into the atm.osphere, their momentum is considerably diminished ; and they have not all of them power to traverse it a second time. The momentum of the blue rays is least ; these, there- fore, are the most impeded in their return, and are chiefly reflacted by the atmosphere : this reflection is performed in every possible direction ; so that whenever we look at the atmosphere, some of these rays fall upon our eyes ; hence we see the air of a blue colour. If the atmosphere did not reflect any rays, though the objects on the sur- face of the earth would be illumined, the skies would ap- pear perfectly black. Cdroline, Oh, how melancholy that would be ; and how pernicious to the sight, to be constantly viewing 052. Why does tlie san appear red in the morninfr and wh'^n seon throuirh ibfr or clonds ? 053. Why does the sky or at- ino3phere appear blue ? 054. How would the sky appear if tho atmosphere refiec.led none of the rays of light ? ^28 ON REFRACTION AND COLOURS. bright objects against a black sky ! But what is the reason that bu^K^s often change their colour; as leaves which wither in autumn, or a spot of ink which produces an iron- mould on linen ? Mrs, B, It arises from some chemical change, which takes place in the internal arrangement of the parts, by which they lose their tendency to reflect certain colours, and acquire the power of reflecting others. A withered leaf thus no 1 »iiger reflects the blue rays ; it appears, therefore, yellow, or has a slight tendency to reflect sevc' ral rays which produce a dingy brown colour. An ink-spot on linen at first absorbs all the rays ; bu^ exposed to the air, it undergoes a chemical change, anc the spot partially regains its tendency to reflect colours, but with a preference to reflect the yellow rays, and such, is the colour of the iron-mould. Emily. Bodies, then, far from being of the colour which they appear to possess, are of that colour which they have the greatest aversion to, which they will not in- corporate with, but reject and drive from them. Mrs, B, It certainly is so ; though I scarcely dare venture to advance such an opinion whilst Caroline is con- templating her beautiful rose. Caroline. My poor rose ! you are are not satisfied with 984. Of what does the retina consist ^ — — 985. How is the light which enters the pupil affected by the several humours ? 986. What would be the consequence if the light admitted by the pupil were not refracted bv the humours ? 232 opTrcKs^ Emily, These divergent rays, issuing from a single point, I believe you told us, were called a pencil of rays ? Mrs, jB. Yes. Now, divergent rays, on entering the pupil, do not cross each other ; the pupil, however, is sufficiently large to admit a small pencil of them ; and these, if not refracted to a focus by the humours, would continue diverging after they had passed the pupil, would fall dispersed upon the retina^ and thus the image of sl single point would be expanded over a large portion of the retina. The divergent rays from every other point of the object would be spread over a similar extent of space, and would interfere and be confounded with the first ; so that no distinct image could be formed, and the retina would represent total confusion both of figure and colour. Fig. 3 represents two pencils of rays issuing from two points of the tree A B, and entering the pupil C, refracted by the crystalline humour D, and forming dis- tinct images of the spot they proceed from, on the retina at a h. Fig. 4 differs from the preceding, merely from not being supplied with a lens ; in consequence of which the pencils of rays are not refracted to a focus, and no distinct image is formed on the retina. I have delineated only the rays issuing from two points of an object, and distinguished the two pencils in fig. 4, by describing one of them with dotted lines ; the interference of these two pencils of rays on the retina will enable you to form an idea of the confusion which would arise, from thousands and millions of points at the same instant pouring their divergent rays upon the retina. Emily, True ; but I do not yet well understand how the refracting humours remedy this imperfection, Mrs. B. The refraction of these several humours unite the whole of a pencil of rays, proceeding from any one point of an object, to a corresponding point on the retina, and the image is thus rendered distinct and strong. If you conceive, in fig. 3, every point of the tree to send forth a pencil of rays similar to those, A B, every part of the tree will be as accurately represented on the retina as the points a h. Emily, How admirably, how wonderfully, this is con- trived ! 987. What does Fi^. 3. plate XXI. represent ? 98S;'~\Vhat does Fig. 4. of that plate represent ? 989. How does the re- fraclinor hnmonr romodvthp drferts exlubited inthatfi<^nre ' OPTICKS. 233 Caroline. But since the eye requires refracting hu- mours in order to have a distinct representation formed on the retina, why is not the same refraction necessary for the image formed in the camera obscura ? Mrs, jB. Because the aperture through which we re- ceived the rays into the camera obscura is extremely small ; so that but very ^e\v of the rays diverging from a point, gain admittance ; but we will now enlarge the aperture, and furnish it with a lens, and you will find the landscape to be more perfectly represented. Caroline, How obscure and confused the image is now that you have enlarged the opening, without putting in the lens ! Mrs-, B, Such or very similar would be the representa- tion on the retina, unassisted by the refracting humours. But see what a difference is produced by the introduction of the lens, which collects each peacil of divergent rays into their several foci. Caroline, The alteration is wonderful : the represen- tation is more clear, vivid, and beautiful than ever. 3Irs, B, You will now be able to understand the na- ture of that imperfection of sight, which arises from the eyes being too prominent. In such cases, the crystalline humour, D, (fig. 5.) being extremely convex, refracts the rays too much, and collects a pencil, proceeding from the object A B, into a focus, F, before they reach the retina. From this focus the rays proceed diverging, and consequently form a very confused image on the retina at a h. This is the de- fect of short-sighted people ? Emily, I understand it perfectly. But why is this defect remedied by bringing the object nearer to the eye, as we find to be the case with short-sighted peopk ? Mrs. B. The nearer you bring an object to your eye, the more divergent the rays fall upon the crystalline hu- mour, and they are consequently not so soon converged to a focus ; this focus, therefore, either falls upon the retina, or at least approaches nearer to it, and the object is pro- portionally distinct, as in fig. 6. Emily, The nearer, then, you bring an object to a lens, the further the image recedes behind it. 990. Why is not something like the refiracting humours neces- sary in the camera obscura ? 991. What peculiarity of the eye causes some persons to be short-sighted ? 992. Which figure represents the eye of a short-sighted person ? 993. Why can short-sighted persons see better by bringing the objects near to the eye ? 994. By which figure is this illustrated ? 20 *♦ 234 tfPTICKs. Airs, B, Certainly. But short-sighted persons have another resource for objects which they cannot approach to their eyes ; this is to place a concave lens, C D, (fig. 1, plate XXII.) before the eye, in order to increase the di- vergence of the rays. The effect of a concave lens is, you know, exactly the reverse of a convex one : it renders parallel rays divergent, and those which are already diver- gent, still more so. By the assistance of such glasses, therefore, the rays from a distant object fail on the pupil, as divergent as those from a less distant object ; and, with short-sighted people, they throw the image of a dis- tant object back as far as the retina. Caroline, This is an excellent contrivance, indeed. Mrs, B, And tell me, what remedy would you devise for such persons as have a contrary defect in their sight ; that is to say, in whom the crystalline humour, being too flat, does not refract the rays sufficiently, so that they reaQh the retina before they are converged to a point 1 Caroline, I suppose that a contrary remedy must be applied to this defect ; that is to say, a convex lens, L M, fig. 2. to make up for the deficiency of convexity of the crystalline humour O P. For the convex lens would bring the rays nearer together, so that they would fall either less divergent, or parallel on the crystalline humour ; and, by being sooner converged to a focus, would fall on the retina. i>/?*5. B, Very well, Caroline. This is the reason why elderly people, the humours of whose eyes are decay- ed by age, are under the necessity of using convex specta- cles. And when deprived of that resource, they hold the object at a distance from their eyes, as in fig. 4., in order to bring the focus forwarder. Caroline, I have often been surprised, when my grandfather reads without his spectacles, to see him hold the book at a considerable distance from his eyes. But I now understand it ; for the more distant the object is from the crystalline, the nearer the image will be to it. 995. What other resouree have short-sighted persons, for reme- dying the defect of their eyes ? 996. Why will a concave lens remedy this eifect ? 997. What is the design of Fig. 1, plate XXII. ? 998. What is the reason that elderly people usually lose their sight ? — ^ — 999. What remedy is there for the eyes when the humours are decayed or flattened ^ 1000. Which figure illustrates this? 1001. Why do old people without convex glasses hold the objects to be seen at a distance fiom the eye.'' oPTicKs. 235 Emily. I comprehend the nature of these two oppo- site defects very well ; but I cannot now conceive, how any sight can be perfect : for if the crystalline humour is of a proper degree of convexity, to bring the image of dis- tant objects to a focus on the retina, it will not represent near objects distinctly ; and if, on the contrary, it is adapt- ed to give a clear image of near objects, it will produce a very imperfect one of distant objects. Mrs. JB. Your observation is very good, Emily : and it is true, that every person would be subject to one of these two defects, if we had it not in our power to in- crease or diminish the convexity of the crystalline humour, and to project it towards, or draw it back from the object, as circumstances require. In a young well constructed eye, the two muscles to which the crystalline humour is attached, have so perfect a command over it, that the focus of the rays constantly falls on the retina, and an image is formed equally distinct both of distant objects, and of those which are near. Caroline. In the eyes of fishes, which are the only eyes I have ever seen separate from the head, the cornea does not protrude, in that part of the eye which is exposed to view. 3Irs. B. The cornea of the eye of a fish is not more convex than the rest of the ball of the eye ; but to supply this deficiency, thei? crystalline humour is spherical, and refracts the rays so much, that it does not require the as- sistance of the cornea to bring them to a focus on the re- tina. Emily. Pray, what is the reason that we cannot see an object distinctly, if we approach it very near to the eye 1 Mrs. B. Because the rays fall on the crystalline hu- mour too divergent to be refracted to a focus on the retina ; the confusion, therefore, arising from viewing an object too near the eye, is similar to that which proceeds from a flattened crystalline humour ; the rays reach the retina be- fore they are collected to a focus, (fig. 4.) If it were not for this imperfection, we should be able to see and distin- 1002. By what means can the same eye see distinctly distant objects and those which are near ? 1003. What peculiarity of structure is there in the eyes of fishes ? 1004. How is this seeming defect remedied ? 1005. What is the reason that we cannot sec an object distinctly when it is placed very near to the eye? — ^1000. Py which figure is this illustrated I 236 opTicKs. guish the parts of objects, which are now invisible to us, from their minuteness ; for could we approach them very near the eye, their image on the retina would be so much magnified as to render them visible. Emily, And could there be no contrivance to convey the rays of objects viewed close to the eye, so that they should be refracted to a focus on the retina. Mrs. B. The microscope is constructed for this pur- pose. The single microscope (fig. 5.) consists simply of a convex lens, commonly called a magnifying-glass ; in the focus of which the object is placed, and through which it is viewed : by this means you are enabled to approach your eye very near the object, for the lens, A B, by di- minishing the divergence of the rays, before they enter the pupil C, makes them fall parallel on the crystalline humour D, by which they are refracted to a focus on the retina, at R R. JEmihj, This is a most admirable invention, and no- thing can be more simple, for the lens magnifies the ob- ject merely by allowing us to bring it nearer to the eye. Mrs, B. Those lenses, therefore, which have the shortest focus, will magnify the object most, because they enable us to bring the object nearest to the eye. Emily. But a lens, that has the shortest focus, is most bulging or convex ; and the protuberance of the lens will prevent the eye from approaching very near to the object. Mrs, B, This is remedied by making the lens ex- tremely small : it may then be spherical without occupy- ing much space, and thus unite the advantages of a short focus, and of allowing the eye to approach the object. Caroline, We have a microscope at home, which is a much more complicated instrument than that you have described, Mrs. B. It is a double rarcroscope, (fig. 6.) in which you see not the object A B, but a magnified image of it, ah. In this microscope, two lenses are employed, the one L M, for the purpose of magnifying the object, is 1007. In what way can objects be seen distinctly when placed near the eye? 1008. Of what does a single microscope con- sist? 1009. What is the object of Fig. 5, plate XXII. .? 1010. What lenses will magnify objects most ? 1011. What kind of lenses has the shortest focus ? 1012. What is repre- sented by Y\g. 6, plate XXII. ^ 1013. How would you explaini the use of the double microscope; by the aid of that figure ? opTicKs. 237 called the object-glass ; the other N O, acts on the prin- ciple of the single microscope, and is called the eye-glass. There is another kind of microscope, called the solar microscope, which is the most wonderful from its great magnifying power ; in this we also view an image formed by a lens, not the object itself. As the sun shines, I can show you the effect of this microscope : but for this pur- pose, we must close the shutters, and admit only a small portion of light, through the hole in the window-shutter, which we used for the camera obscura. We shall now place the object A B, (plate XXIII. fig. I.) which is a small insect, before the lens, C D, and nearly at its fo- cus ; the image E F, will then be represented on the op- posite wall in the same manner as the landscape was in the camera obscura ; with this difference, that it will be mag- nified, instead of being diminished. I shall leave you to account for this, by examining the figure. Emily, I see it at once. The image E F is magnified, because it is further from the lens, than the object A B ; while the representation of the landscape was diminished because it was nearer the lens, than the landscape was. A lens, then, answers the purpose equally well, either for magnifying or diminishing objects 1 Mrs, B. Yes ; if you wish to magnify the image,you place the object near the focus of the lens ; if you wish to produce a diminished image, you place the object at a distance from the lens, in order that the image may be formed in or near the focus. Caroline, The magnifying power of this microscope is prodigious, but the indistinctness of the image for want of light, is a great imperfection. Would it not be clearer, if the opening in the shutter were enlarged, so as to ad- mit more light ? Mrs. B, If the whole of the light admitted does not fall upon the object, the effect will only be to make the room lighter, and the image consequently less distinct. Emily. But could you not by means of another lens bring a large pencil of rays to a focus on the object, and thus concentrate the whole of the light admitted upon it 1 1014. WhatdoesFig.l, plate XXTII. represent? 1015. How would you describe a solar microscope by the use of this figure .'' lOlG. Where must an object be placed in regard to a lens, so that the r.bject be magnified ? 10 i 7. Where, so that the ob- ject be diminished ? 1018. Where must all the light fall, used in the solar microscope, so that the effect be the most favourable ? 238 opTicKs. Mrs, B. Very well. We shall enlarge the opening and place the lens X Y (fig. 2.) in it, to converge the rays to a focus on the object A B. There is but one thing more wanting to complete the solar microscope, which I shall leave to Caroline's sagacity to discover. Caroline. Our microscope has a small mirror attached to it, upon a moveable joint, which can be so adjusted as to receive the sun's rays, and reflect them upon the ob- ject ; if a similar mirror were placed to reflect light upon the lens, would it not be a means of illuminating the ob- ject more perfectly ? Mrs, B, You are quite right. P Q, (fig. 2.) is a small mirror placed on the outside of the window-shutter, which receives the incident rays S S, and reflects them on the lens X Y. Now that we have completed the appara- tus, let us examine the mites on this piece of cheese, which I place near the focus of the lens. Caroline, Oh ! how much more distinct the image now is, and how wonderfully magnified ; the mites on the cheese look like a drove of pigs scrambling over rocks. Emily, I never saw any thing so curious. Now an immense piece of cheese has fallen : one would imagine it an earthquake : some of the poor mites must have been crushed ; how fast they run, — they absolutely seem tb gallop. i But this microscope can be used only for transparent objects ; as the light must pass through them to form the image on the wall. Mrs, B, Very minute objects, such as are viewed in a microscope, are generally transparent; but when opaque objects are to be exhibited, a mirror M N {^g, 3. ) is used to reflect the light on the side of the object next the wall : the image is then formed by light reflected from the object, instead of being transmitted through it. Emily, Pray is not a magick lantern constructed on the same principles ?* ^ The magick lantern is an instrument used for magnifying paintings on glass, and throwing their images upon a white screen in a darkened chamber. 1019. What does fig. 2, plate XXIII. represent .? 1020. What is the use of the mirror in the solar microscope .^ 1021. For what objects can the solar microscope be used .' 1022. How can opaque objects be exhibited .' 1023. Which figure illus- trates this ? 1024. What is a magich lantern ? opTicKs. 239 Mrs, B, Yes ; with this difference, that the light is supplied by a lamp, instead of the sun. The microscope is an excellent invention, to enable us to see and distinguish objects, which are too small to be visible to the naked eye. But there are objects which, though not really small, appear so to us, from their dis- tance ; to these we cannot apply the same remedy ; for when a house is so far distant, as to be seen under the same angle as a mite, which is close to us, the effect produced on the retina is the same : the angle it subtends is not large enough for it to form a distinct image on the retina. Emily. Since it is impossible, in this case, to approach the object to the eye, cannot we by means of a lens bring an image of it nearer to us ? Mrs. B. Yes ; but then the object being very distant from the focus of the lens, the image would be too small to be visible to the naked eye. Emily. Then, why not look at the image through ano- ther lens, which will act as a microscope, enable us to bring the image close to the eye, and thus render it visi- ble ? Mrs. B. Very well, Emily ; I congratulate you on having invented a telescope. In figure 4, the lens C D, forms an image E F, of the object A B ; and the lens X Y, serves the purpose of magnifying that image ; and this is all that is required in a common refracting telescope. Emily. But in fig. 4, the image is not inverted on the retina, as objects usually are : it should therefore appear to us inverted ; and that is not the case in the telescopes 1 have looked through. Mrs. B. When it is necessary to represent the image erect, two other lenses are required ; by which means a second image is iormed, the reverse of the first and conse- quently upright. These additional glasses are used to view terrestrial objects ; for no inconvenience arises from seeing the celestial bodies inverted, 1025. How does a inagick lantern differ from a solar micro- scope? 1026. What is the reason that the solar microscope may not be used with objects at a great distance with equal effect .' 1027. What does Fig. 4, plate XXIII. represent ? 1028. How would you explain the principle of the common refracting tele- scope by the use of that figure ? 1029. What is necessary when the image of an object is to be exhibited erect ? 1030. Why are not these additional glasses used in viewing celestial objects ? ^0 OPTICKS. Emily, The difference between a microscope and a telescope seems to be this : — a microscope produces a mag- nified image, because the object is nearest the lens ; and a telescope produces a diminished image, because the ob- jects farthest from the lens. Mrs, B, Your observation applies only to the lens C D, or object glass, which serves to bring an image of the object nearer the eye ; for the lens X Y, or eye-glass, is in fact a microscope, as its purpose is to magnify the image. When a very great magnifying power is required, tele- scopes are constructed with concave mirrors, instead of lenses. Concave mirrors, you know, produce, by reflec- tion, an effect similar to that of convex lenses by refrac- tion. In reflecting telescopes, therefore, mirrors are used in order to bring the image nearer the eye ; and a lens or eye-glass the same as in tlie refracting telescope to mag- nify the image. The advantage of the reflecting telescope, is, that mir- rors whose focus is six feet, will magnify as much as lenses of a hundred feet. Caroline, But I thought it was the eye-glass only which magnified the image ; and that the other lens served to bring a diminished image nearer to the eye. Mrs, B, The image is diminished in comparison to the object, it is true ; but it is magnified if you compare it to the dimensions of which it would appear without the intervention of any optical instrument ; and this magni- fying power is greater in reflecting than in refracting telescopes. We must now bring our observations to a conclusion, for I have communicated to you the ^hole of my very limited stock of knowledge of Natural Philosophy. If it will enable you to make further progre^^^ in that science, my wishes will be satisfied ; but remember that, in order that the study of nature may be productive of happiness, it must lead to an entire confidence in the wisdom and goodness of its bounteous Author. 1031. What part of the telescope exhibited in the figure may be considered as a simple microscope ? 1032. When a very great magnifying power is required, how must telescopes be con- structed ? 1033. In the reflecting telescopes why are mirrors used ? 1034. How great is the advantage of the reflecting telescope ? A DICTIONARY OF PHILOSOPHICAL TERMS. ABERRATION, in astronomy, an appa- rent motion of the heavenly bodies, pro- duced by the progressive motion of light and the earth's annual motion. ACCELERATION, in mechanicks, de notes tlie augmentation or increase of mo- tion in accelerated bodies. ACOUSTICKS is the science whicli treat: pole, 66 1-2 degrees from the equator and parallel to it. AREOMETER, an instrument by which the density and gravity of fluids are mea- sured. ARIES, in astronomy, a constellation of fixed stars, drawn on the globe in the figure of a ram. It is the first of the twelve signs of the nature, phenomena, and laws of the; of the zodiac from which a twelfth part of sense of sound. It extends to the theory of jthe ecliptick takes its name. It consists of musical concord and harmony, and is, there-, sixty-six stars. fore, a valuable and interesting science. | ASCENSION, in astrononfi}', the rising AIR, a thin, elastick fluid, surrounding thelof the sun or star, or any part of the equi- globe of the earth. The air, together withjnoctial with it, above the horizon, the clouds and vapours that float in it, is ASTERIODS, a nam-^ given by Dr. Her- called the atmosphere. The height to whichjschel to the new planets, Ceres, Juno, Pal- the atmosphere extends has never been as- las, and Vesta, lately discovered. certained ; but, at a greater height than 45 miles, it ceases to reflect the rays of light from the sun. AIR-PUMPS are machines made for ex- hausting the air from certain glass vessels, adapted to the purpose of experiments on air. ANGLE is the inclination of two linos ASTRONOMY is the science which teaches the motions of the earth, the sun, moon, planets, comets, and stars, and ex- plains the phenomena occasioned by those motions. ATMOSPHERE, or atmospherickair, the fluid that surrounds our earth. Without this fluid no animal could exist ; vegetation meeting one another in a point, and called] would cease, and there would be neither the legs of the angle. Angles, in geometry, 'rain nor refreshing dews to moisten the are called rights acute, and obtii?c. A right angle contains just 90 degree.:; or tlie quar- ter part of a circle. Acute nngles contain Ies3,and obtuse angles more tlian 90 degrees. ANGLE OF INCIDENCE is that which is contained between the lino described by the incident ray, and a line perpendicular to the surface on which the ray ptrikes, raised from the point of incidence. ANGLE OF REFLECTION is contain- ed between the line described by the re- face of the ground ; and though the sun and stars might be seen as bright specks, yet there would be little enjoyment of light, could we exist v/ithout it. ATTRACTION, a general term, used to denote the power or principle by v.'hich bo- dies mutually tend towards each other, without regarding the cause or action that niav he the means of producing the eflTect. ATTRACTION OF COHESION takes place between the confrtituent particles of fleeted rav; and a lino perpendicular to the jthe same body. By this principle bodies reflecting surface, at the point from whif"h preserve their forms and arc prevented from the ray is reflected. ifalling to piece*. ANGLE OF REFRACTION is thalj ATTRACTION OF GRAVITATION, which is contained between tlie line descrili- or gravity, i.^ the name of that force by ed by the refracted ray, and a lino perpendi-; which distant bodies tend towards one cular to the refracting surface at the point another. in which the ray passes through that sur ANGLE OF VISION is th'at which is contained between lines coming from oppo- site parts of an object and meeting in the AXIS of a planet is an imaofinnry line which passes through its centre, and on which it turns ; and it is this motion which produces day and niglit. V/ith that side of the planet fHcin.^ the snn it is day ; and with the opposite si(?(j, which remains in 'ANTARCTICK CIRCLE, in astronomy.idarkness, it is night, is an imaginary Ivio exteiiding round the' AXIS OP MOTION, in mechanicks, is the south pole, 661--i degrees from tiie equator, line about which a revolving boc'y moves, and parallel to it. j Philosophically =peaking. the axis of mo- APHELION, in astronomy, is that pointitinn is said to be at reat, whilst the other in any planet's orbit in which the orbit is'parts of a body move round it; and the most distant from the sun. Ifurth'"'- any part af a body is from the axis AQ,U£OUS HUiuOUR, or watery hu-|of motion, the greater is its velocity, mour of the eye ; it is the first and outermost, j AXIS OF THE EARTH is an imagina- and tint which is less dense than ciiheriry line conceived to pass through the centre the vitreous or crystalline. It i-,' transpa-joV it from one pole to the other, u.'.ont v/hich rent and colourless like water, and hlls uplls performnd its diurnal rotation. :he spaco that lies between tht cornea and' AXIS, in opticks. is that raj', among all ihe crystalline humour. lotherg that arc oont to the eye^ which falls * ARCTICK CIRCJ iE, in astronomy, is an! perpendicularly upon it, and which consc- anaginary line expending round the northi quently passes through the centre of the eye. ' 21 242 A DICTIONARY OF AXIS OF A GLASS, OR LENS, is a Tight line joining the middle points of the two opposite surfacos of the glass. BALANCE, or BALLANCE, in mecha- nicks, one of the simple powers which serves to find out the equality or difference of weight in heavy bodies. BALLOON, a machine used in naviga- tion through the air. It takes its name from the K)rm of the machine, the word balloon signifying any spherical hollow bo- that point about which all th« parts of a body do, in any situation, balance each other. CENTRE OF MOTION, that point which remains at rest, while all the oth«r I parts of a bfulv move about it. CENTRAL FORCES, the poAvers which cause a moving body to tend towards, or recede from, the centre of motion. CENTRIFUGAL FORCE, that by which all bodies, that move round any dy, of whatever matter it be composed, orjothor body in a curve, endeavour to fly off for whatever purposes it be designed. from the axis of their motion in a tangent. BAROMETER, an instrument for mea- CENTRIPETAL FORCE, that force by suring the weight or pressure of the at- which a body is every where impelled, or mosphere; and by that means measuring any how tends towards some point as a heights and depths, determining variations centre ; such as gravity, or that force in the state of the air, and foretelling the changps in the weather. BASE, in geometry, the lowest side of the perimeter of a figure. Thus, the base of a triangle may be said of any of its sides, but more properly of the lov/est, or that which is parallel to the horizon. In rec- tangled triangles, the base is properly that side opposite to the right angle. BASS, in musick, that part of a concert hereby bodies tend towards the centre of the earth ; magnetical attraction, whereby the loadstone draws iron ; and that force, whatever it be, whereby the planets are continually drawn back from right-lined motions, and made to move in curves, CHROMATICKS is that part of opticks which explains the several properties of tlie colours of light and of natural bodies. CIRCLE, in geometry, a plane figure which is most heard, which consists of thejcomprehended by a single curve line, called gravest and deepest sounds, and which isjits circumference, to wnich right lines or played on the largest pipes or strings of the iradii, drawn from a point in the middle, instrument. called the centre, are equal to each other. BODY, in physicks, an extended solid sub- CIRCUMFERENCE, in a general sense, stance,of itself utterly passive and inactive, jdenotes the line or lines bounding a plane indifferent either to motion or rest ; but ca-jfigure. However, it is generally used in a pable of any sort of motion, and of all figures ;more limited sense, for the curve line which and forms. Body, or substance, which isjbounds a circle, and otherwise called a pe- the same thing, is usually denoted by the - general term matter. BREADTH, in geometry, one of the three dimensions of bodies, which, multi- plied into their length, constitutes a sur- face. BUBBLE, in philosophy, small drops or vesicles of any fluid filled with air, and either formed on its surface, by an addition riphery ; the boundary of a right lined figure being expressed by the term perime- ter. CLOUDS are a collection of misty va- pours suspended in the air. Their various colours and appearances are owing to their particular situation in regard to the sun, to the different reflection of the sun's rays, and to the effects produced on them by of more of the fluid, or in its substance, by! wind. an intestine motion of its component parts. | COHESION, one of the species of attrac- BURNING-GLASS, a convex or concavejtion, denoting that force by which the parts glass, commonly spherical, which, beingiof bodies stick together. exposed directly to the sun, collects all the COLOUR means that property of bodies rays falling thereon into a very small space. called the focus, where wood, or any other combustible substance, being put, will be set on fire. CAMER A-OBSCURA, in opticks, a ma- chine representing an artificial eye. It is which affects the sight only ; thus the grass in the fields has a green colour, blood has a red colour, the sky generally appears of a blue colour, and thus of others that might be named. The variety of colours, as they are presented to us by the substances that made by placing a convex glass in a hole .surround us, is immense, and from them of a window shutter, and if no light enters arises the admirable beauty of the works theroombutthroujh the glass, the pictures of nature in the animal, in the vegetable, of all objects on the outside may be distinct- and in the mineral kingdom, or, more pro- ly seen in an )nverted position, on any perly speaking, in the universe, white surface placed at the focus of the COLURES, in astronomy and geogra- lens. phy» ^ wo great circles, supposed to inter- CAPILLARY TUBES, in physicks, little sect each other at right angles in the poles pij)e9, whose canals are extremely narrow, 'of the world, and to pass through the sol- used for experiments in illustrating cohe-'stitial and equinoctial points of the eclip- sive attraction. jtick. CAPPTCORN, in astronomy, one of thej COMETS are opaque and solid bodieg. twelve signs of the zodiack, represented onjAcomet, atagiven distance from the earth, globes in the form of a 2 oat. jshines much brighter when it is on the CENTREOFGRAVlTYjinmechanickSj'samesideof the earth with the sun than PHILOSOPHICAL TEEMS- 24$ when it is on the contrary side; from ing to make that refraction of the rays of whence it appears that it owes its bright-^ light, necessary to make them meet in the ness to the sun. [retina, and form an image thereon, where- COMPLEMENT, in astronomy, the dis-jby vision may be performed, tance of a star from the zenith ; or the arch] CYLINDER, in geometry, a solid body, comprehended between the place of the supposed to be generated by the rotation star above the horizon and the zenith. j of a parallelogram. COMPRESSION, the act of pressing or] DAY. In common language, the day is squeezing some matter, so as to set its the interval of time which elapses from the parts nearer to each other, and make iti rising to the setting of the sun. The astro- possess less space. nomical day embraces the whole interval CONCAVE, an appellation used in which passes during a complete revolution speaking of the inner surface of hollow bo- of the sun. dies, but more especially of spherical ones. I DECLINATION, in astronomy, the dis- CONCORD,in musick, the relation of two| tance of any celestial object from the equi- sounds that are always agreeable to the noctial, either northward or southward. It ear, whether applied in succession or con-, is either true or apparent, according as the sonance. jreal or apparent place of the object is con- CONDENSER, a pneumatick engine or,sidered. syringe, whereby an uncommon quantity! DEGREE, in geometry, a division of a of air may be crowded into a given space ;[ circle, including a three hundred and six- 80 that sometimes ten times as much air as, tieth part of its circumference. Every there is at the same time in the same space, circle is supposed to be divided into three without the engine, may be thrown in by hundred and sixty parts, called degrees, means of it, and its egress prevented by and each degree divided into sixty other valves properly disposed. I parts called minutes ; and each of these CONDUCTORS, in electricity, are long minutes is again divided into sixty seconds, metal rods, whose points are raised above] DENSITY denotes the degree of close- the buildings to which the conductors arc ness and compactness of the particles of a affixed, for the purpose of attracting or re-: body ; and is that property directly oppo- ceiving the electrick fluid, and of coaduct-isite to rarity. ing it into the earth, or into water, thereby | DEPRESSION OF THE POLE. When to prevent such buildings from being struck^ person sails or travels towards the equa- by lightning. I tor, he is said to depress the pole, because CONE, in geometry, a solid figure, hav- as many degrees as he approaches nearer ing a circle for its base, a^id its top termi- nated in a point or vc'^ex. CONJUNCTION^ in astronomy, is the meeting of twost-^rs or planets in the same degree of the r-odiack. CONSTFi^LATION, in astronomy, system ©''"several stars that are seen in the heaver^ near to one another. Astronomers not only mark out the stars, but they dis trioute them into asterisms, or constella- tions, allowing several stars to makeup one constellation ; — and for the better dis- tinguishing and observing them, they re- duce the constellations to the forms of ob- jects with which we are well acquainted. CONVERGING, or convergent lines, in geometry, are such as continually approach nearer one another ; or whose distance be- comes still less and less. CONVERGING RAYS, in opticks, are those rays, that, issuing from diverse points of an object, incline towards one another, till, at last, they meet and cross, and then become diverging rays. CONVEX, an appellation given to the the equator, so many degrees will the pole be nearer the horizon. The phenomenon arises from the spherical figure of the earth. DIAGONAL, in geometry, a right line drawn across a quadrilateral figure, from one angle to another, by some called the diameter of the figure. DIAMETER, in geometry, a right line passing through the centre of a circle, and terminated at each side by the circumfe- rence thereof DIGIT, in astronomy, the twelfth part of the diameter of the sun or moon, is used to express the quantity of an eclipse. Thus an eclipse is said to be six digits, when six of these parts are hid. DIMENSION, in geometry, is either breadth, length, or thickness ; hence a line has one dimension, viz. length ; a superfi- cies, two, viz. length and breadth ; and a body, or solid, has three, to wit, length, breadth, and thickness. DIRECTION, inmechanicks, signifies the line or path of a body's motion, along which it endeavours to proceed, according to the exteriour surface of gibbous or globular bo-i force impressed upon it. dies, in opposition to the hollow inner sur- DISK, in astronomy, the body and face faceof such bodies, which is called concave, of the sun and moon, such as it appears to Thus we say a convex lens, a convex mir- us on the earth, or the body or face of the ror, and convex superficies. earth, such as it appears to a spectator in CORNEA, the second coat of the eye, so the moon. The disk in eclipses is supposed called from its substance, which resembles, to be divided into twelve equal parts, the horn of a lantern. DISCORD, in musick, a dissonant and un- CRYSTALLINE HUMOUR,a thick com-|harmonious combination of sounds, so call- pact humour, in form of a fljittish convex ed in opposition to concord, lens, situated in the middle of the eye, se.rv-j DIVERGENT RA,YS, in opticks, are 244 A DICTIONARY OP those, which, going from a point of the vi- sible object, are dispersed, and continually depart one from another, in proportion as they are removed from the object ; in which •ensc it is opposed to convergent. DIVISIBILITY, that property by which the particles of matter in all bodies are ca- pable of a separation, or disunion from each other. DIURNAL, in astronomy, something re- lating to the day, in opposition to noctur- nal, which regards the night. The diurnal motion of a planet, is so many degrees and minutes as any planet moves in twenty- four hours. Hence the motion of the earth about its axis is called its diurnal motion. DROPS, in meteorology, small spherical bodies, into which the particles of fluids spontaneously form themselves, when let fall from any height. DUCT denotes any tube or canal. DUCTILITY, in physicks, a property of certain bodies, whereby they are capable of being expanded, or stretched forth by means of a hammer or press. DYNAMICKS. Tliis branch of mecha- nicks relates to the action offerees that give motion to solid bodies ; which forces are cal- culated, both by their active powers, and by the proportion of time in which those powers become efficient. EARTH, the vast mass or planet which we inhabit. The ancients supposed the earth flat or cylindrical ; but from the ge- neral appearance of the planetary system, from the circular shadow of the earth in eclipses of the moon, and from the fact that the earth has been circumnavigated, it is concluded by the moderns, that it is sphe- rical. EARTHaUAKE is a sudden motion of the earth, occasioned, it is supposed, either by the discharge of some electrical power, or by large quantities of inflammable air. which, on being rarefied by internal fires, forces its way through the parts that sur- round it. EAST, one of the four cardinal points of the world ; being that point of the horizon, ■where the sun is seen to rise when in the equinoctial. ECCEN TRICK, in geometry, a term ap- plied to circles and spheres which have not the same centre, and consequently are not parallel, in opposition to concentrick, where they are parallel, having one common cen- tre. ECCENTRICITY, in astronomy, is the distance of the centre of the orbit of a pla- net from the centre of the sun, that is, the distance between the centre of the ellipsis and the focus. ECHO, a sound reverberated or reflected to the ear from some solid body. ECLIPSE, the deprivation of the light of the sun, or of some heavenly body, by the interposition of another neavenly body be- tween it and our sight. ECLIPTICK, in astronomy, a great circle of the sphere, supi)0sed to be drawn through the middle of thv zodiack ; or it is that path among the fixed stars, that the earth ap- pears to describe, to an eye placed in the sun. ELASTICITY, that disposition in bo- dies by which they endeavour to restore themselves to the posture from whence they were displaced by an external force. ELECTRICITY is an invisible, subtile fluid, that appears to pervade all nature^ and among other interesting phenomena, is the cause of thunder and lightning. Elec- tricity is of two kinds — positive and nega- tive. The positive is that state of a body which contains more than its due propor- tion ; and the negative is that state of a body which contains less than its due pro- portion. When two bodies, one charged with positive electricity and the other with negative, come in contact with each other, so much passes from the former to the lat- ter, as to produce an equilibrium — it passes thus with a flash and an explosion. Thus two clouds, charged in the above manner, coming together, or one cloud coming in contact with the earth, thunder and light- ning are produced. ELLIPSIS, in geometry, a curve line re- turning into itself, and produced from the section of a cone by a plane cutting both its sides, but not parallel to the base. EMERSION, in astronomy, is when any planet that is eclipsed begins to emerge or get out of the shadow of the eclipsing body. It is also used when a star, before nidden by the sun, as being too near him, begins to re-appear or etnerge out of his rays. E(iUATOR is aR imaginary circle equal- ly distant from the pUes, and dividing the earth into two equal pars, one being called the Northern hemisphere, a»{i the other the Southern hemisphere. , EaUINOCTI AL, in astrononrj, a great circle of the celestial globe, whose poles are the poles of the world. It is so called, be- cause, whenever the sun comes to this cir- cle, the days and nights are equal all over the globe ; being the same with that which the sun seems to describe at the time of the two equinoxes of spring and autumn. EQ,UINOX, the time when the sun en- ters either of the equinoctial points, where the ecliptick intersects the equinoctiah EXHALATION, a general term for all the effluvia or streams raised from the sur- face of the earth in form of vapour. Some distinguish exhalations from vapours, ex- pressing by the former all steams emitted from solid bodies, and by the latter, the steams raised from water and other fluids. EXPANSION, the enlargement or in- crease of bulk in bodies, chiefly by means of heat. EXPLOSION, a sudden and violent ex- pansion of an aerial or other elastick fluid, by which it instantly throws off" any obsta- cle that happens to be in the way, some- times with incredible force, and in such a manner as to produce the most astonishing effects. EXTENSION, in philosophy, one of the common and essential properties of body, Philosophical terms. 245 ofr that by which it possesses or takes up some part of universal space, which is call- ed the place of a body. FIGURE, in physicks, expresses the sur- face, or terminating extremities of any bo- dy ; and, considered as a property of body affecting our senses, is defined a quality which may be perceived by two of the outward senses. Thus a table is known to be square by the sight and by the touch. FLUID, in physiology, an appellation given to all bodies whose particles easily yield to the least partial pressure or force FOCUS, in geometry and conick sections, is applied to certain points in the parabola, ellipsis, and hyperbola, where the rays re- flected from all parts of these curves con- cur and meet. FOGS are clouds which float on the sur- face of the earth, and clouds are fogs in the higher regions of the atmosphere ; from many places they may be seen floating in the vallies, and often in the vallies they may be seen creeping along the sides of the mountains. FORCE, in mechanicks, denotes the cause of the change in the state of a body, when, being at rest, it begins to move, or has a motion which is either not uniform or not direct. Mechanical forces may be reduced to two sorts, one of a body at rest, the other of a bodj' in motion. FORCING-PUMP, in mechanicks, a kind of pump in which there is a forcer or piston without a valve. FOUNTAIN, in philosophy, a spring or source of water rising out of the earth. FRICTION, in mechanicks, the rubbing of the parts of engines and machines against each other, by which means a great part of their effect is destroyed. FRIGID ZONES, the spaces on the earth's surface between the polar circles and the poles. FULCRUM, in mechanicks, the press or support, by which a lever is sustained. GALAXY, in astronomy, a very into drops, and are frozen while they are falling. They assume various figures, be- ing sometimes round, at other times pyra- midal, cuniated, angular, thin and flat, and sometimes stellated with six radii like the small crystals of snow. HALO, in physiology, a meteor in the form of a luminous ring or circle, of vari- ous colours, appearing round the bodies of the sun, moon, or stars. HARDNESS, in physiology, is the resist- ance opposed by a body to the separation of its particles. This property depends on the force of cohesion ; and a body is con- sidered more hard in proportion as it pre- sents a greater resistance to the force which may be applied in order to separate its parts. HARMONY, in musick, the agreeable result, or union, of several musical sounds, heard at one and the same time, or the mix- ture of divers sounds, which together have an effect agreeable to the ear. As a con- tinued succession of musical sounds pro- duces melody, so does a continued combi- nation of these produce harmony. H ARxMONY OF THE SPHERES, a sort of musick much talked of by many of the ancient philosophers, supposed to be pro- duced by the sweetly tuned motions of the stars and planets. This harmony they at- tributed to the various proportionate im- pressions of the heavenly globes upon one another, acting at proper intervals. HEIGHT, ir geometry, is a perpendicu- lar let fall fr'jm the vertex, or top, of any right-lined ^Jgure, upon the base or side subtending It. It is likewise the perpendi- cular hein«t of any object above the hori- zon. HEMISPHERE, the half of a globe or spliere, when it is supposed to be cut throi'gh its centre in the plane of one of its great circles. KORIZON, in astronomy and geography, thit great circle which divides the heavens aid the earth into two equal parts or he- riispheres, distinguishing the upper from he lower. The horizon is either sensible markable appearance, sometimes double, or rational — t he sensible horizon is that cir- but for the most part single, surrounding the whole concave of the heavens, called the galaxy or milky way. GIBBOUS, in astronomy, a term used in reference to the enlightened parts of the moon, whilst she is moving from her first quarter to the full, and from the full to th' last quarter. GLOBE, a round or spherical body, pOie usually called a sphere, bounded h/ one uniform convex surface, every pc^nt of which is equally distant from a po't^t with- in called th«3 centre. GRAVITY, a term used >y physical writers to denote the cause by which all bodies move towards eac-'i other, unless prevented by some other ferce or obstacle. GREEN, one of the original colours ex- cited by the rays of light. HAIL, a compact mass of frozen water, consisting of such vapours as are united 21 * cle, which being discovered by our senses, limits oni prospect. HORIZONTAL, something relating to the "lorizon ; or that is taken in, or on a le- el with the horizon. Thus, we say, a lorizontal plane. HURRICANES are violent storms, fre- quent in South America and the West In- die3,^and other hot countries, in which the wind changes in a short time to every point of the compass, and blows with a violence which scarcely any thing can resist. HYADES, in astronomy, seven stars in the bull's head, famous among the poets for the bringing of rain. HYDRA, in astronomy, a southern con- stellation, imagined to represent a water serpent. HYDRAULICKS teach us to ascertain the velocity and impetus of fluids when in motion, and serves as the basis for comput- 246 A DICTIONARY OF ing the powers of various machinery acted|the place, whose latitude is spoken of, is om upon by running water. jthis or that side of the equator. HYDROMETKll, an instrument to mca-l LATITUDE, in astronomy, the distance sure the extent and specificit gravity of lof a star or planet from the ecliptick, in fluids. degrees, minutes, and seconds, measured on HYDROSTATICAL BALANCE, a kindia circle of latitude drawn through that star of balance contrived for the easy and exactjor planet, being either north or south, as ndingthe specitick gravities of bodies both j the object is situated either on the north or liquid and solid. isouth side of the ecliptick. HYDROSTATICAL PARADOX is thisj LEE, an epithet to distinguish that half — thatany quantity of riuid, however smalljiof the horizon to which the wind is direct- may be made to balance, or counterpoise led from the other part where it arises, any quantity, however large. which latter is accordingly called towind- HYDROriTATICKS treat of the nature, ward, gravity, }»res3ure, and motion of fluids inj LENS properly signifies a small round- general, and of the methods of weighingiish glass, of the figure of a lentil, but is ex- solids in them. jtended to any optick glass, not very thick, IMAGE, inopticks, is the appearance of i which either collects the rays of light into an object made either by reflection or re-'a point, in their passage through it, or dis- fraction. In all plane mirrors, the image iporses them further apart, according to the is of the same magnitude as the object, and laws of refraction. it appears as far behind the mirror as the! LEO, in astronomy, one of tlie twelve object is before it. In concave mirrors the signs of the zodiack, the fifth in order, object appears larger, and in those which I LEVEL, an instrument constructed for are convex, it appears less than the object, j the purpose of ascertaining the exact level IMMERSION, in astronomy, is wlien alof any fluid, building, or any other object, star or planet is so near the sun, with re-JLeveis are of two kinds — the horizontal, gard to our observations, that we cannot 'and the perpendicular, see it ; being as it v.ere enveloped or hidden! LEVER, in mechanicks, an inflexible in the rays of that luminary. It also de-jright line, rod, or beam, supported in a sin- notes the beginning of an eclipse of thesun gle point on a fulcrum or prop, and used or moon, when either of those bodies begins for the raising of weights; being either to be darkened by the siudowofthe oiher.jvoid of weight itself, or at least having IMPENETRABILITY, in philosophy,isuch a weight as may be commodiously that property of a body whs^reby it cannot counterbalanced. be pierced by another; thus, x body, whichi LIBRA, the balance, in astronomy, onfr 80 fills a space as to exclude ^J1 others, isjof the twelve signs of the zodiack, the sixth said to be impenetrable. jin order ; so called, because when the sun INCIDENCE, in mechanicks, denoteslenters it, the days and nights are equal, as the direction ia which, one body s^.rikes on, if weighed in a balance, another. ^ LIBRATION, in astronomy, an appa- INCLINATION, is a word frecf^ently'rent inequality of the moon's motion, used by mathematicians, and signitie? the! whereby she seems to librate about her mutual approach, tendency, or leaning of axis, sometimes from the east to the west, two lines, or planes, towards each other, so and now and then from the west to the as to make an angle. ' Jeast ; so that the parts in the western limb INCLINED-PLANE, in mechanicks, is ior margin of tlie moon sometimes recede merely a line or plane that makes an angk from the centre of the disk, and sometimes, with the horizon. It is frequently u.sed toVnove towards it, by which means they be- move Aveights from one level to anotlier. ^tome alternately visible and invisible ta INERTIA, or inactivity, isihat proi>er-!the inhabitants of the earth, ty of matter by which It would aHays con- 1 LIGHT is that principle, or thing, by tinue in the same state of rest, or ^»f mo- which objects are made perceptible to our tion, ill which it was put, unless cha»^ed sense of seeing ; or the sensation occasion- by some external force. led in the mind by the view of luminous ob- INTEGRAL, or integrant, appeilationsjgct?; given to parts of bodies which are of a si-, LIGHTNING, an electrical explosion, milar nature with the whole. Thus, filings! tjjve, in geometry, a quantity extended of iron have the same nature and properties in tyigth only, without any breadth or as bars of iron. ithick»ess. INTENSITY, in physieks, is the degree LiaviD, a fluid not sensibly elasticfc, or rate of power or energy of any quality, the part»of which move on each other, and as of heat and cold. lyield to th> smallest impression. JUPITER, in astronomy, one of the pri-! L0NGIT\IDE, in geography, is an arch mary planets remarkable for its great of the equate.-, intercepted between the brightness. first meridian passing through the propos- LATITUDE, the distance of a place ed place ; which n always equal to the an- froni the equator, or an arc of the meridi- gle at the pole, fonrved by the first meridian an intercepted between the zeiith of the and the meridian of the place, place and the equator. Hence latitude is] LOOKING-GLASSES are nothing but either northern tir southernj according as plain mirrors of glass, which, being impei* PHILOSOPHICAL Terms. 247 vious to the light, reflect the images of things placed before them. LUJ\AR, something belonging to the moon ; thus we say, lunar month, lunar year, lunar dial, or lunar eclipse. LUNATION, the time or period from one new moon to another — it is called the synodical month. MAGICK LANTERN is an instrument used for magnifying paintings on glass, and throwing their images upon a white screen in a darkened room. MAGNETLSM explains the properties of the loadstone, or natural magnet, which is a dark coloured and hard mineral body, and is found to be an ore of iron, being ge- nerally found in iron mines. MAGNITUDE, whatever is made up of parts locally extended, or that has s everal dimensions ; as a line, a surface, or a solid. MAN03IETER, an instrument to show or measure the alterations in the rarity or density of the air. MARS, in astronomy, the planet that re- volves next beyond the earth in our system, is of a red fiery colour, and always gives a much duller light than Venus, though some- times he equals her in size. MATHEMATICKS originally signified any discipline or learning ; but at present, denotes that science which teaches, or con- templates whatever is capable of being numbered or measured, in so far as it is computable or measurable; and according- ly is subdivided into arithmetick, which has numbers for its object, and geometry, which treats of magnitudes. MATTER is the general name of every substance, that has length, breadth, and thickness. MECHANICKS, is the science which and both zenith and nadir, crosses the equi- noctial at right angles, and divides the spliere into two hemispheres, the eastern and the western ; it has its poles in the east and west points of the horizon. It is called meridian, because, when the sun comes to the south part of this circle, it is then mid-day ; and then the sun has his greatest altitude for thn*. day. METEOR, in physiology, a moveable ig- neous body, congregated in the air by means not thoroughly understood, and varying reatly in size and raoidity of motion. METEOROLOGY* is the science of studying the phenomena of the atmo- sphere, and that term by which is expressed all the observations that tend to make them a system. MICROSCOPE, in opticks. By micro- scopes are understood instruments, of what- ever structure or contrivances, that can make small objects appear larger than they do to the naked eye. MINUTE, in geometry, the sixtieth part of a degree of a circle. Minutes are denot- ed by one acute accent, thus (') ; as the se- cond, or sixtieth part of a minute, is by two such accents, thus (") ; and the third by three ("'). MIRRORS, in catopticks, any polished body impervious to the rays of light, and which reflects them equally. Mirrors were anciently made of metal ; but at present they are generally smooth plates of glass, tinned or quick-silvered on the back part, and called looking-glasses. The doctrine of mirrors depends wholly on that funda- mental law, that the angle of reflection is always equal to the angle of incidence. MOBILITY is that property of matter by which it is capable of being moved from treats of the laws of the equilibrium andlone part of space to another, motion of solid bodies ; of the forces by' MOMENTUM, in mechanicks, signifies .vhich bodies, whether animate or inani- mate, may be made to act upon one ano- ther ; and of the means by which these may be increased, so as to overcome such as are most powerful. the same with impetus, or quantity of mo- tion in a moving body ; which is always equal to the quantity of matter multiplied into the velocity ; or, v/hich is the same thing, it may be considered as a rectangle MEDIUM, in philosophy, that space or[under the quantity of matter and velocity, region through which a body in n»otion MONSOON, in physiology, a species of passes to any point ; thus ether is siippos- wind, in the East Indies, which for six ed to be the medium through which the i months blows constantly the same way, heavenly bodies move; air, the medium and the contrary way the other six months.. •wherein bodies move near the eartk ; wa- ter, the medium wherein fishes live and move; and glass is also a medium of light, as it aflfords it a free passage. MELODY, in musick, the agreeable ef- MOON, in astronomy, a satellite, or se- condary planet, always attendant on our earth. MOTION is defined to be the continued and successive change of place. Nothir feet of different sounds, ranged and dispos- can be produced or destroyed without mo- ed in succession ; so that melody is the ef- fect of a single voice or instrument, by which it is distinguished from harmony. MERCURY, in astronomy, is a small star that emits a veiy bright white light — though, by reason of his always keeping near the sun, he is seldom to be seen ; and •when he does make his appearance, hi tion, and every thing that happens depends on it. MUSICK. Any succession of sounds, however much they may vary in regard to duration, or however much they may par- take of various modes or keys, provided that succession be agreeable, and excites, in a ■ell tuned ear, certain agreeable scnsa- motion towards the sun is so swift, that heitions, is called musick. ean only be discerned for a short time. NADIR, in astronomy, that point of the MERIDIAN, in astronomy, a great cir- heavens which is diametrically opposite to «le passing tlirough the poles of the world,! the zenith, or poiat directly over our heada^ 248 A DICTIONARY OP The zenith and nadir are the two poles of jing from the section of a cone, when cut by the horizon. la plane parallel to one of its sides. NATURAL PHILOSOPHY, otherwise! PARADOX, in philosophy, a proposition called physicks, is that science which con-!seemingly obscure, as being contrary to siders the powers of nature, the properties some received opinion, but yet true in fact. of natural bodies, and their actions upon one another. NEBULA, in astronomy, luminous spots in the heavens, some of which consist of clusters of telescopick stars, others appear as luminous spots of different forms. Some of them form a round compact system, others are more irregular, of various forms, and some are long and narrow. NIGHT, that part of the natural day during which the sun is underneath the PARALLAX, in astronomy, denotes i change of the apparent place of any hea- venly body, caused by being seen from dif- ferent points of view; or it is the difference between the true and apparent distance of any heavenly body from the zenith. PARALLEL straight lines, whose least distances from each other are every where equal, are said to be parallel. PARALLELOGRAM, in geometry, a quadrilateral right lined figure, whose op- horizon ; or that space wherein it is dusky, jposite sides are parallel and equal to each NODES, in astronomy, the two points lother. wherein the orbit of a planet intersects the j PARHELIUM, or PARHELION, in ccliptick, whereof the node, where the node, physiology, a mock sun, or meteor, in form ascends northwards, above the plane of the! of a very bright light, appearing on one ecliptick, is called the ascending node; andjside of the sun. the other, where the planet descends to the] PEGASUS, in astronomy, a constellation south, is called the descending node. |of the northern hemisphere, in form of a OBLATE, flattened, or siiortened, as an 'flying horse, oblate spheroid, having its axis shorter] PENDULUM, in mechanicks, denotes than its middle diameter, being formed by any heavy body so suspended as that it the rotation of an ellipse about the shorter jmay vibrate or swing backwards and for- axis. The oblateness of the earth refers to I wards, about some fixed point, by the force the diminution of the polar axis in respect of gravity. The vibrations of the pendu- of the equatorial, OBTUSE, signifies hlunt or dull, in op- position to sharp or acute. Thus we say an angle is obtuse if it measures more than ninety degrees. lum are called its oscillations. PENUMBRA, in astronomy, a partial shade observed between the perfect shadow and the full light, in an eclipse. PERCUSSION, in mechanicks, the im- OCCIDENT, in geography, the westernlpression a body makes in falling or striking quarter of the horizon, or tliat part of the|upon another, or the shock of two bodieg horizon where the ecliptick, or the sun in motion. therein, descends into the lower hemi- PERIHELIUM,in astronomy, that point sphere, in contradistinction to orient. |of a planet's or comet's orbit wherein it is OCCULT ATION, in astronomy, thean its least distance from the sun; iu which time a star or planet is hidden from our sense it stands in opposition to aphelium. sight, by the interposition of the moon or} PERIMETER, in geometry, the boundr of some other planet. lor lim.its of any figure or body. The peri- OPACITY, in philosophy^ a quality of jmeter of surfaces or figures are lines, those bodies which renders them impervious to of bodies are surfaces. In circular figures, the rays of light. [instead of perimeter, we say circumference, OPTICKS, the science of vision, includ-jor periphery, ing Catoptricks and Dioptricks, and evenj PERIOD, in astronomy, the time taken Perspective ; as also the whole doctrine of up h/ a star or planet in making a revolu- light and colours, and all the phenomena ition round the sun ; or the duration of its of visible objects. course till it return to the same point of its* ORBIT, in astronomy, the path of a pla-jorbit. net or comet, or the curve that it describes] PERIPHERY, m geometry, the circum- in its revolution round its central body, ference of a circle, ellipsis, or any other re- Thus the earth's orbit is the curve whichjgular curvilinear figure, it describes in its annual course, and usu-i PERPENDICULAR, in geometry, aline, ally called the ecliptick. jfalling directly on another line, so as to ORION, in astronomy, a constellation of make equal angles on each side; called the southern hemisphere, consisting of also a normal line. thirty-seven stars, according to Ptolemy; PERSPECTIVE, the art of represent- of sixty-two, according to Sycho ; aiul of ing. upon a plane surface, the appearance no leas than eighty, in the Britannick cata-lof objects, however diversified, similar to logue. jthat tiiey assume upon a glass-pane, inter- ORRERY, a curious machine for repre- 'posed between them and the eye at a given sent ing the motions and appearances of the {distance, heavenly bodies. PHASES, in astronomy, the several ap OSCILLATION, in mechanicks, the vi-jpearances or quantities of illumination of brat icn or reciprocal ascent and descent of jthe Bloon, Venus, Mercury, and the othei a pendnlnm. planets ; or the several mar.ners whereir PARABOLA, in geometry, a figure aris-lthey appear illuminated by the sim. PHILOSOPHICAL TERMS. 249 ^ PHOENIX, in astronomy, one of the constellations of the southern hemisphere, unknown to the ancients, and invisible in our northern parts. It is said to consist of thirteen stars. PHYSICKS, a term made use of for na- tural philosophy, explains the doctrines of natural bodies, their phenomena, causes, and effects, with the various effections, motions, and operations. PISTON, in pump-work, is a short cylin- der of metal, or other solid substance, fitted exactly to the cavity of the barrel or body of the pump. There are two kinds of pistons used in pumps, the one with a valve, and the other without a valve, called a forcer. PLANE, in geometry, denotes a plain surface, or one that lies evenly between its bounding lines — and as a right line is the shortest extension from one point to ano- ther, so a plain surface is the shortest exten sion from one line to another. PLANET, a celestial body revolving round the sun, as a centre, and continually changing its position, with respect to the fixed stars ; whence the name planet, which is a Greek word signifying wander. PLEIADES, in astronomy, an assem blage of seven stars in the neck of the con stellation Taurus, the bull ; although there are now only six of them visible to the na ked eye. The largest is of the third mag nitude, called " Lucido pleiadum." PNEUMATICKS is that branch of natural philosophy which treats of the weight, pressure, and elasticity of the air with the effects arising from them. POINT, in geometry, as defined by Eu did, is a quantity, which has no parts, or which is indivisible. Points are the ends or extremities of lines. If a point be sup posed to be moved any way, it will, by its motion, describe a line. — Point, in physicks, is the least sensible object of sight, marked with a pen, point of a compass, or the like. Of such points all physical magnitude consists. POLAR, in general, something relating to the poles of the world, or poles of arti- ficial globes. POLARITY, the quality of a thing con sidered as having poles ; but chiefly used in speaking of the magnet. POLE, in astronomy, one of the extre- mities of the axis, on which the sphere re- volves. These two points, each ninety de- grees from the equinoctial or equator, are by way of eminence called the poles of the world ; and the extremities of the axis of artificial globes, corresponding to these points in the heavens, are termed the poles thereof. POLLUX, in astronomy, a fixed star of the second magnitude in the constellation gemini, or the twins. The same name i- also given to the hindermost twin, or pos terior part of the same constellation. POWER, in mechanicks, denotes any force, whether of a man, a horse, a spring, the wind, or water, wnich Deing appiiea id a machine, tends to produce motion. PRECESSION OF THE EaUINOXES is a very slow motion of them, by which they change their place, going from east to west or contrary to the order of the signs. PROJECTION, in mechanicks, the art of communicating motion to a body, from thence called projectile. PULLEY, in mechanicks, one of the mechanical powers, called by seamen a tackle. PUMP, in hydraulicks, a machine formed on the model of a syringe, for raising water. PYROMETER, an instrument for mea- suring the expansion of bodies by heat. QUADRANT denotes a mathematical instrument, of great service in astronomy, and consequently, in navigation, for taking the altitudes of the sun and stars, as also for taking angles in surveying. QUADRATURE, in geometry, denotes the squaring or reducing a figure to a quare. QUADRILATERAL, in geometry, a figure whose perimeter consists of four right lines making four angles ; whence it is also called a quadrilateral figure. The quadrilateral figures are either a parallelo- gram, trapezium, rectangle, square, rhom- bus, or rhomboides. RADIATION, the act of a body emitting or diffusing rays of light all around, as from a centre. RADIUS, in geometry, the semi-diame- ter of a circle, or a right line drawn from the centre to the circumference. RAIN. Whatever suddenly disturbs the heat or density of the air, or the electricity of the clouds, occasions the particles of vapour to rush together, and form drops of water too heavy to continue suspended in the atmosphere. They then fall in the shape of rain, and increase in size as they fall by combining with the floating vapours as they pass through them. RAINBOW is a meteor in form of a party-coloured arch, or semicircle, exhibit- ed only at the time when it rains. It is always seen in that point of the heavens which is opposite to the sun, and is occa- sioned by the refraction and reflection of his rays in the drops of falling rain. RAREFACTION, in physicks, is the making a body to expand, or occupy more room or space, without the accession of new matter. RAY, in opticks, a beam of light, emitted from a radiant or luminous body. REACTION, in physiology, the resist- ance made by all bodies to the action or impulse of others, that endeavour to change its state, whether of motion or rest. RECEIVER, in pneumaticks, a glass vessel for containing the thing on which an experiment in the air pump is to be made. RECTANGLE, in geometry, the same with a right angled parallelogram. REFRACTION, is the deviation of a moving body from its direct course, occa- sluned by the di/TerenL density of the medi- um ill which it moves ; or, it is a pha.ngft 250 A DICTIONARY OF of direction, occasioned by a body's falling' at the equinox, where the San intersects obliquely out of one medium into anotheri and rises above the equator, have these of a different density. names and marks : REPULSION,inphysicks,that property A,- „ cko t ->« r\ a ..4. ■ *, in bodies, whereby. If Ihey are placed jus'tr^"^'' ^ ^^°' ^ Sagittarius, / ' ■ • ^ . . . Taurus, y Virgo, TTJ Capricornus,Vf Gemini, JJ Libra, £v Aquarius, -cji beyond the sphere of each other's attraction of cohesion, they mutually fly from each other. RESISTANCE, in philosophy, denotes, in general, any power which acts in an op- Cancer, (^2 Scorpio, rH Pisces, H Of these signs, the first six are called north- posite direction to another, so as to destroyern, lying on the north side of the equator ; or diminish its effects. |and the last six are called southern, being RETINA, the expansion of the optickj situated to the south of the equator, nerve on the internal surface of the eye,j SIPHON, or Syphon, in hydraulicks, a whereupon the images of objects being, bended pipe, one end of which being put painted, are impressed, and by that raeanS|into a vessel of liquor, and the other hang- conveyed to the common sensory in theling out of the said vessel over another, the brain, where the mind views and contem- liquor will nwi out from the first into the plates their ideas, ROTATION, in geometry, a term chiefly applied to the circumvolution of any sur- face round a fixed and immoveable line, which is called the axis of its rotation, anJ by such rotations it is that solids are con- ceived to be generated SAGITTARIUS, the archer, in astrono- my, the ninth sign of the zodiack. SATELLITES, in astronomy, are cer tain secondary planet.-^, moving round the other j)lanets, as the Moon docs round the Earth. They are so called, because they always attend them, and make the tour about the sun with them. SATURN is a very conspicuous planet, though not so brilliant as Jupiter. SEGMENT OF A CIRCLE, in geometry, that part of the circle contained between a chord and an arch of the same circle. SEMICIRCLE, in geometry, half a cir- cle, or that figure comprehended between the diameter of a circle and half the cir- cumference. SEMIDIAMETER, half the diameter, or a right line drawn from the centre of a circle, or sphere, to its circumference ; be ing the same with what is otherwise called the radius. SEXTANT, in mathematicks, denotes the sixth part of a circle, or an arch com prehending sixty degrees. The \vord sex tant is more particularly used for an astro- last, after the air has been sucked out of the external or lower end of the siphon, and that as long as the liquor in the upper vessel is above the upper orifice of the si- phon. SKY, the blue expanse of air and atmo- sphere. The azure colour of the sky is at- tributed, by Sir Isaac Newton, to vapours beginning to condense there, and which have got consistence enough to reflect the most dexible rays. SNOW, a v.e!! known substance, formed by the freezing of the vapours in the at- mosphere. It differs from hail and hoar- frost, in being as it were crystallized, which they are not. SOLID, in philosophy, a body whose parts are so firmly connected together, as not to give way or slip from each other up- on the smallest impression ; in which sense solid stands opposed to fluids. SOLAR, something belonging to the sun ; thus the solar system is that system of the world wherein the heavenly bodies are made to revolve round the sun as the cen- tre of their motion. SOLSTICE, in astronomy, that time when the sun is in one of the solstitial points ; that is, when he is at his greatest distance from the equator, thus called, be- cause he then appears to stand still, and not to change his distance from the equa- tor for some time ; an appearance owing nomical instrument made like a quadrant,! to the obliquity of our sphere, and to which excepting that its limb only comprehendskhose living under the equator are stran- sixty degrees. The use and application of [gers. the sextant is the same with that of the! SOUND. The sense of bearing is affect- quadrant. |ed by the pulsations or vibrations of the SHADOW, in opticks, a privation or di-| air, which are caused by its own expan- minution of light by the interposition of anjsion, or by the vibrations of sounding bo- opaque body; or it is a plane, where the dies. Theae sensations, or vibrations in light is either altogether obstructed, or the air, are called sounds, as are also the greatly weakened, by the interposition of Isensations which they produce, some opaque body between it and the lumi-j SPECIFICK, in philosophy, that which nary. lis peculiar to any thing, and distinguishes SIDEREAL DAY, is the time in whiclf it from all others. any star appears to revolve from the meri- dian to the meridian again. SIGNS, in astronomy. The ecliptick is SPECTRUM, in opticks. When a ray of light is admitted through a small hole, and received on a white surface, it forms a usually divided, by astronomers, into 12 luminous spot. If a dense, transparent bo- parts called signs, each of which of coursejdy 1m» intprpocorJ, tHn HgrKt will bo rofractpd, contains 30 degrees. They are usually 1 in proportion to the density of the medium : «all«d isigns of tho zodiaok ; aud begiuning'but if a triangular glass prism be inter- PHILOSOPHICAL TERMS. 251 posed, the light is not merely refracted, but it is divided into seven different rays. This image is called the spectrum, and from its being produced by the prism, the prismatick spectrum THUNDER, the noise occasioned by the explosion of a flash of lightning passing through the air ; or it is tliat noise which is excited by a sudden explosion of electri- cal clouds which are therefore called thun- SPHERE is a soli'l contained under onejder clouds, uniform round surface, such as woukl be| TORRID ZONE, among geographers, formed by the revolution of a circle aboutidenotes that space of the earth's surface the diameter thereof, as an axis. included between the tropicks. SPHEROID, in geometry, a solid, ap-l TRADE WINDS denote certain regular preaching to the figure of a sphere. Iwinds at sea, blowing either constantly SPOTS, in astronomy, certain places of the same way, or else alternately, a certain the Sun's or Moon's disk, observed to be length of time in one direction, and then either more bright or darker than the rest,|as long in an opposite one. They are call- and accordingly called facula and macula, ed trade winds from their use in navigation, SPRAY, the sprinkling or foam of the j and are very common in the Indian seas, sea, which is driven from the top of a TRANSIT, in astronomy, signifies the wave in stormy weather. 'passage of any planet just by, or over, a SQUARE, in geometry, a quadrilateral, fixed star, or sun, and of the moon in par- figure, both equilateral and equiangular. ticular, covering or moring over any planet. STAR, in astronomy, a general name for! TRANSMISSION, in opticks, the act of all the heavenly bodies which are dispersed! a transparent body passing the rays of throughout the whole heavens. I light through its substance, or suffering SUCTION, the act of sucking or draw-| them to pass; in which sense the word ing up a fluid, as air, water, milk, or the'stands opposed to reflection, like, by means of the mouth and lungs. I TRANSPARENCY, in physicks, a qua- SUN, in astronomy, the most conspicu-jlity in certain bodies, whereby they give ous of the heavenly bodies, which occupies passage to the rays of light, in contradis- the centre of the system which compre- tinction to opacity, or that quality of bo- hends the earth, the primary and secondary; dies which renders them impervious to the planet^, and the comets. |ravs of light. SUPERFICIES, or surface, in geometry,} TRIANGLE, in geometry, a figure of a Magnitude considered as having two di- three sides and three angles, meusions ; or extended in length and| TROPICKS, in astronomy, and geogra- breadth, but without thickness or depth, phy, are two circles supposed to be drawn SWiMMIxVG, the art or act of sustain-; round the earth on each side of the equa- ing ana moving the body in water. Brutes tor, and 23 deg, 29' distant from it. swim naturally, but men attain this art by, TWILIGHT, that light, whether in the practice and industry. It consists princi-' morning before sunrise, or in the evening pally in striking the water alternately withiafter sunset, which is occasioned by the the hands and feet, which, like oars, row a reflection of the sun's rays in passing person forward. 'through the atmosphere. SYRINGE, an inttrument serving to im-! VACUUM, in philosophy, denotes a hibe or suck in a quantity of any fluid, and'space empty or devoid of all matter or body, to squirt or expel the same with violence. | VALVE, in hydraulicks and pneuma- SYZYGY, in astronomy, a term equally Iticks, is a kind of lid or cover, of a tube or used for the conjunction and opposition of I vessel, so contrived as to open one way ; a planet with the sun. | but which the more forcibly it is pressed TANGENT, in geometry, is defined, inthe other way, the closer it shuts theaper- general, to be a right line, which touchesjture, so that it either admits the entrance any arch of a curve, in such a manner, asof a fluid into the tube or vessel, and pre- to make a right angle with the diameter of j vents its return, or admits its escape, and the circle of which that arch is a part. prevents its re-entrance. TANTALUS' CUP, in hydraulicks, a' VAPOUR, in meteorology, a thin, humid siphon, so adapted to a cup, thac the short matter, which, being rarefied to a certain leg being in the cup, the long leg may go degree by the action of heat, ascends to a down through the bottom of it. jparticular height in the atmosphere, where TAUilUS, in astronomy, one of the it is suspended, until it returns in the form twelve signs of the zodiack, the second in of dew, rain, snow, or hail, order, consisting of forty-four stars, accord-| VELOCITY, swiftness, or that affection ing to Ptolemy; of forty-one, according toof motion, whereby a moving body is dis- Tycho ; and of no less than one hundred posed to run over a certain space in a cer- and thirty-five, according to the Britannick tain time, catalogue. | VENUS, the most beautiful star in the TELESCOPE, an optical instrument, heavens, known by the names of the morn- which is used for discovering and viewinging and evening star, likewise keeps near distant objects, either directly by glasses, the sun, though she receies from him al- or by retiectior^. jmost double the dist^.^ice of ulercury. THERMOMETER, an instrument fori VESTA, one of the "^mall planetary bo- measuring the degree of heat gr cold in any, dies discovered lately lo revolve between y>odj. |the planets Mars and Jupiter, ^2 A DICTIONARY OF PHILOSOPHICAL TERMS. VIBRATION, in mechanicks, a regular jgular prism, whose bases are equilateral reciprocal motion of the body, as, for ex- acute angled triangles, ample, a pendulum, which, being freely SUS-; WEEK, in chronology, a division of pended, swings or vibrates from side to^time comprising seven days, aide. WEIGHT, in physicks, is a quality in VIRGK), in astronomy, one of the signs'natural bodies, by which they tend towards or constellations of the zodiack, and theUhe centre of the earth, sixth according to order. I WHEEL, one of the six powers of me- VISIBLE, something that is an object chanism ; and, without doubt, contributes of sight or vision, or something whereby more than any of the other live to the ge- the eye is affected, so as to produce a sen-iieral convenience of mankind, by the won- sation. 'derful variety of purposes, from a mill to a VISION is the act of seeing or of per-j watch, wherein it is employed, ceiving external objects by the organ ofj WHIRLWINDS are formed by opposite sight. j winds meeting and moving swiftly inacir- UNDJJLATION, in physicks, a kind of cle, raising sand and light bodies into the tremulous motion or vibration observable [air. In tlie deserts of Africa they some- in a liquid, whereby it alternately rises andjtimes draw up tlie sand into a moving pil- falls like the waves of the sea. liar, which buries all in its way. When UNISON, in musick, the eftoct of two'.they appear on the ocean, they draw up the sounds which are equal in degree of tune, water, and produce water-spouts. or in point of gravity and acuteness. | WIND. When the air over anyplace VOLCANOES, mountains which emit, is more heated than that around, it is rare- ignited matter and smoke through aper-|fied or expanded, and rises. The surround- tures, communicating with cavities in thejin^ air rushes in to supply its place, and depths of the earth. 'this produces a current called wind. VVATER, a transparent fluid, without] YEx\R, the time that the sun takes to go colour, smell, or taste, in a very small ue, through the twelve signs of the zodiack. gree compressible; and, when pure, not; ZENITH, in astronomy, the vertical liable to spontaneous change. j point ; or a point in the heavens directly WATER SPOUT, an extraordinary me- over our heads. The zenith is called the teor, in which a column of water is seen pole of the horizon, because it is ninety d«- hanging from the clouds, and descending grees distant from every point of that fir- until it meets with a column rising from cle. the ocean. They unite and ofteii^ move ZODIACK, in astronomy, abroad circle, with rapidity, until they meet with some whose middle is the ecliptick, and its ex- opposing wind, or other cause, which de-'tremes, two circles, parallel thereto, at stroys them, jsuch a distance from it, as to bound or WAVE, in physicks, a volume of water comprehend the excursions of the sun and elevated by the action of the wind, upon its'planets. surface, into a state of fluctuation, and ac-| ZONE, in geography and astronomy, a companied by a cavity. division of the terraqueous globe, with re- WEDGE, one of the mechanical powers, jspect to the different degrees of heat found as they are culled. The wedge is a trian-jin the diflferent parts of it. TLATE I h\f. J. 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