T*w,v 
 
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 /*
 
 DIALOGUES, 
 
 ILLUSTRATIVE CF THE FIRST PRINCIPLES OF 
 
 MECHANICS AND ASTRONOMY, 
 
 DESIGNED TO FORM 
 
 A PRIZE BOOK IN SCHOOLS, 
 
 AND 
 
 A HELP TO NATIVES DESIROUS OF SCIENTIFIC KNOWLEDGE. 
 
 Reprinted, ivith some Alterations, from the 1st and 2d 
 
 Volumes of the REV, J. JOYCE'S "Scientific 
 
 Dialogues, intended for the Instruction and. 
 
 Entertainment of Young People" 
 
 
 
 EIGHT PLATES, RE ENGRAVED BY CASHEE NATH. 
 
 " Conversation, with the habit of explaining the meaning of words, and 
 structure of common domestic implements to Children, is the sure and most 
 effectual method of preparing the mind for the acquirement of science/' 
 
 EDGEWORTH'S PRACTICAL EDUCATION, 
 
 CALCUTTA, 
 
 REPRINTED FOR THE CALCUTTA SCHOOL-BOOK SOCIETY. 
 1819.
 
 CALCUTTA: 
 
 PRINTED AT THE MISSION PRESS. 
 
 2000 Copies. 
 
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 ADVERTISEMENT, 
 
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 Some few additions have also been introduced, in 
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 republished to the present state of physical know- 
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 IV ADVERTISEMENT. 
 
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 miMK*! W&vlm suit 'to 0oii<K><{ sifi ai fa
 
 SCIENTIFIC DIALOGUES, 
 
 PART I.-MECHANIC3,
 
 CONTENTS TO PART I. 
 
 ON MECHANICS. 
 
 Conversation Page 
 
 I. Introduction t \ 
 
 II. Of Matter. Of the Divisibility of Matter t 6 
 
 III. Of the Attraction of Cohesion *....< 10 
 
 IV. Of the Attraction of Cohesion , t 15 
 
 V. Of the Attraction of Gravitation . * 21 
 
 VI. Of the Attraction of Gravitation ,.* 4 27 
 
 VII. Of the Attraction of Gravitation < . 35 
 
 VIII. Of the Attraction of Gravitation 40 
 
 IX. Of the Centre of Gravity 45 
 
 X. Of the Centre of Gravity..,.. .. it 49 
 
 XI. Of the Laws of Motion * 53 
 
 XII. Of the Laws of Motion . . . . * * . 61 
 
 XIII. Of the Laws of Motion , 66 
 
 XIV. Of the Mechanical Powers 71 
 
 XV. Of the Lever , 77 
 
 XVI. Of the Lever ..,,82 
 
 XVII. Of the Wheel and Axis 89 
 
 XVIII. Of the Pulley 95 
 
 XIX. Of the Inclined Plane.... 99 
 
 XX. Of the Wedge < 104 
 
 XXI. Of the Screw * 107
 
 SCIENTIFIC DIALOGUES 
 
 CONVERSATION I. 
 
 INTRODUCTION. 
 FATHER CHARLES EMMA. 
 
 CHARLES. Father, you told sister Emma and 
 me, that yon would explain^to us some of the prin- 
 ciples of Natural Philosophy; will you begin this 
 morning- ? 
 
 Father. Yes, i am quite at leisure ; and JLsliall. 
 indeed at_ all times take a -delight ^n com municati ng 
 to you the elements of useful knowledge ; and the 
 more so in proportion to the desire which you have 
 of collecting and storing those facts that may ena-^ 
 ble you to understand the operations of nature, as 
 well as the works of ingenious artists. These, I 
 trust, will lead you, insensibly, to admire the \ns- 
 dom and goodness by means of which the whole sy- 
 stem of the universe is constructed and supported. 
 
 Emma. But can philosophy be comprehended by 
 children so young as we are ? I thought that it had 
 been the business of men, and of old men too. 
 B
 
 2 MECHANICS. 
 
 Father. Philosophy is a word which, in its original 
 sense, signifies only a love or desire of wisdom ; and 
 you will not allow that you and your brother are too 
 young to wish for knowledge. 
 
 Emma. So far from it, that the more knowledge 
 I get, the better I seem to like it. 
 
 Father. You will find very little in the introduc- 
 tory parts of natural and experimental philosophy, 
 that with a little attention you will not easily under- 
 stand. Besides, tlie_stndy of natural philosophy im- 
 proves and elevates the mind by unfolding the mag- 
 nificence, the order, .and the beauty manifested in 
 the construction of the material world; while it 
 offers the most striking proofs of the beneficence, 
 the wisdom, and the power of the Creator. 
 
 Charles. But in some books of natural philoso- 
 phy, which I have occasionally looked into, a num- 
 ber of new and uncommon words have perplexed 
 me : I have also seen references to figures by means 
 of large letters and small, the use of which I did 
 not comprehend. 
 
 Father. It is frequently a dangerous practice for 
 young minds to dip into subjects before they are pre- 
 pared, by some previous knowledge, to enter upon 
 them; since it may create a distaste for the most 
 interesting topics. Thus those books which you 
 now read with so much pleasure would not have 
 afforded you the smallest entertainment a few years 
 ago, when you must have sprit out almost every
 
 INTRODUCTION. 3 
 
 word in each page. The same sort of disgust will 
 naturally be felt by persons who attempt to read 
 works of science before the leading terms are ex- 
 plained and understood. The word angle is con- 
 tinually recurring in subjects of this sort; do you 
 know what an angle is ? 
 
 Emma. I do not think I do ; will you explain 
 what it means ? 
 
 Father. An angle is made by the opening of 
 two straight* lines that me,et at a point. In this 
 figure (Plate I. Fig. 1.) there are two straight lines 
 AB and CB meeting at the point B, and the open- 
 ing made by them is called an angle. 
 
 Charles. Whether that opening be small or great, 
 is it still called an angle ? 
 
 Father. It is ; your drawing compasses may fa- 
 miliarize to your mind the idea of an angle ; the lines 
 in this figure will aptly represent the legs of the 
 compasses, and the point B the joint upon which 
 they move or turn. Now you may open the legs to 
 any distance you please, even so far that they shall 
 from one straight line; in that position only they 
 do not form an angle. In every other situation an 
 angle is made by the opening of these legs, and the 
 angle is said to be greater or less, as that opening 
 is greater or less. 
 
 Straight lines, in works of science, nre mnally denominated riprht lines.
 
 4 MECHANICS. 
 
 Emma. Are not some angles called right angles? 
 
 Father. Angles are either right \ acute, or obtuse. 
 When the line AB (Plate 1. Fig. 2.) meets another 
 straight line DC, in such a manner as to make the 
 angles ADD and ABC equal to one another, then those 
 angles are called right angles. And the line AB is 
 said to be perpendicular to DC. Hence to be perpen- 
 dicular to, or to make right angles with a line, means 
 one and the same thing. 
 
 Charles. Does it signify how you call the letters 
 of an angle ? 
 
 Father. It is usual to call every angle by three 
 letters, and that at the angular point must be always 
 the middle letter of the three. There are cases, how- 
 ever, where an angle may be denominated by a single 
 letter, as in figures 1 and 3, the angle ABC may be 
 called simply the angle at B, for in these figures 
 there is no danger of mistake, because there is but a 
 single angle at the point B. 
 
 C/iarles. I understand this, for if in the second 
 figure I were to describe the angle by the letter B 
 only, you would not know whether I meant the an- 
 gle ABC or ABD. 
 
 Father. That is the precise reason why it is ne- 
 cessary in most descriptions to make use of three 
 letters. An acute angle (Fig. 1.) ABC is less than a 
 right angle ; and an obtuse angle (Fig. 3.) ABC is 
 greater than a right angle. 
 
 Emma. You see the reason now, Charles, why
 
 INTRODUCTION. 5 
 
 letters are placed against or by the figures, which 
 puzzled you before. 
 
 Charles. I do, they are intended to distinguish the 
 separate parts of each, in order to render the descrip- 
 tion of them easier to both the author and the reader. 
 
 Emma. What is the difference between an angle 
 and a triangle ? 
 
 Father. An angle being made by the opening of 
 two lines, and, as you know, that two straight lines 
 cannot enclose a space, so a triangle ABC (Fig. 4.) 
 is a space bounded by three straight lines. It 
 takes its name from the property of containing three 
 angles. There are various sorts of triangles, but it 
 is not necessary to enter upon these particulars, as I 
 do not wish to burthen your memories with more 
 technical terms than we have occasion for. 
 
 Charles. A triangle then is a space or figure con- 
 taining three angles, and bounded by as many straight 
 lines. 
 
 Father. Yes, that description will answer our 
 present purpose. 

 
 MECHANICS. 
 
 CONVERSATION II. 
 
 Of Matter. Of the Divisibility of Matter. 
 
 FATHER. Do you understand what philoso- 
 phers mean when they make use of the word mat- 
 ter? 
 
 Emma. Are not all things which we see and feel 
 composed of matter ? 
 
 Father. Every thing which is the object of our 
 senses is composed of matter differently modified or 
 arranged. But in a philosophical sense matter is 
 denned to be an extended, solid, inact ive, -and move- 
 able substance. 
 
 Charles. If by extension is meant length, breadth, 
 and thickness, matter, undoubtedly, is an extended 
 substance. Its solidity is also manifest by the re- 
 sistance it makes to the touch. 
 
 Emma. And the other properties nobody will 
 deny, for all material objects are, of themselves, 
 without motion ; and yet it may be readily conceiv- 
 ed that by the application of a proper force there is 
 no body which cannot be moved. But I remem- 
 ber, that you told us something strange about the 
 divisibility of matter, which you said might be con- 
 tinued without end.
 
 OF DIVISIBILITY OP MATTER. 7 
 
 Father. I did, some time ago, mention this as a 
 curious and interesting subject, and this is a very 
 fit time for me to explain it. 
 
 Charles. Can matter indeed be infinitely divided, 
 for I suppose that this is what is meant by a divi- 
 sion without end. 
 
 Father. Difficult as this may at first appear, yet 
 I think it very capable of proof. Can you conceive 
 of a particle of matter so small as not to have an 
 upper and under surface ? 
 
 Charles. Certainly, every portion of matter, how- 
 ever minute, must have two surfaces at least, and 
 then I see, that it follows of course that it is divi- 
 sible ; that is, the upper surface may be separated 
 from the lower. 
 
 Father. Your conclusion is just, and though there 
 may be particles of matter too small for us actu- 
 ally to divide, yet this arises from the imperfection 
 of our instruments; they must nevertheless, iu their 
 nature, be divisible. 
 
 Emma. But you were to give us some remark- 
 able instances of the minute division of matter. 
 
 Father. A few years ago a lady spun a single 
 pound of wool into a thread 168,000 yards long. 
 And Mr. Boyle mentions, that two grains and a half 
 of silk were spun into a thread 300 yards in length. 
 If a pound of silver, which, you know, contains 5760 
 grains, and a single grain of gold be melted toge- 
 ther, the gold will be equally diffused through the
 
 8 MECHANICS. 
 
 whole silver, insomuch that if one grain of the mass 
 be dissolved in a liquid called Aqua Fortis, which 
 is diluted nitric acid, the gold -will fall to the bot- 
 tom. By this experiment it is evident that a grain 
 may be divided into 5761 visible parts, for only the 
 5761st part of the gold is contained in a single 
 grain of the mass. 
 
 Gold-beaters can spread a grain of gold into a 
 leaf containing 50 square inches, and this leaf may 
 be readily divided into 500,000 parts, each of 
 which is visible to the naked eye : and by the help 
 of a magnifying glass or microscope, which makes 
 the area or surface of a body appear 100 times grea- 
 ter than it is, 100th part of each of these becomes 
 visible ; that is, the 50 millionth part of a grain of 
 gold will be visible, or a single grain of that metal 
 may be divided into 50 million of visible parts. But 
 the gold which covers the silver wire used in mak- 
 ing what is called gold lace,, is spread over a much 
 larger surface ; yet it preserves, even if examined 
 by a microscope, an uniform appearance. It has 
 been calculated that one grain of gold under these 
 circumstances would cover a surface of nearly thirty 
 square yards. 
 
 The natural divisions of matter are still more sur- 
 prising. In odoriferous bodies, such as camphor, 
 musk, and asafcetida, a wonderful subtilty of parts 
 is perceived, for though they are perpetually filling 
 a considerable space with odoriferous particles, yet
 
 OF DIVISIBILITY OF MATTER. 9 
 
 these bodies lose bat a very small part of their 
 weight in a great length of time. 
 
 Again, it is said by those who have examined the 
 subject with the best glasses, and whose accuracy 
 may be relied on, that there are more animals in the 
 milt of a single cod-fish, than there are men on the 
 whole earth, and that a single grain of sand is larger 
 than four millions of these animals. Now if it be 
 admitted that these little animals are possessed of 
 organized parts, such as a heart, stomach, muscles, 
 veins, arteries, &c., and that they are possessed of a 
 complete system of circulating fluids,.similar to what 
 is found in larger animals, we seem to approach to an 
 jdea of the infinite divisibility of matter. It has in- 
 deed been calculated that a particle of blood of one 
 of these animalcula is as much smaller than a globe 
 one-tenth of an inch in diameter, as that globe is 
 smaller than the whole earth. Nevertheless, if these 
 particles be compared with the particles of light, it 
 is probable, that they would be found to exceed 
 them in bulk as much as mountains do single grains 
 of sand. 
 
 1 might enumerate many other instances of the 
 same kind, but these, I doubt not, will be sufficient 
 to convince you into what very minute parts matter 
 is capable of being divided : and with these we will 
 put an end to our present conversation.
 
 10 MECHANICS. 
 
 CONVERSATION ILL 
 
 Of the Attraction of Cohesion. 
 
 FATHER. Well, my children, have you re- 
 flected upon what we last conversed about? Do 
 you comprehend the several instances which I enu- 
 merated as examples of the minute division of 
 matter? 
 
 Emma. Indeed, the examples which you gave us 
 very much excited my wonder and admiration : and 
 yet from the thinness of some leaf-gold which I once 
 had, I can readily admit all you have said on that 
 part of the subject. But I know not how to con- 
 ceive of such small animals as you described ; and 
 I am still more puzzled in imagining, that animals 
 so minute, actually possess all the properties of the 
 larger ones, such as a heart, veins, blood, &c. 
 
 Father. 1 can, the next bright morning, by the 
 help of the solar microscope,show you very distinct- 
 ly, the circulation of the blood in a flea, which you 
 may get from your little dog ; and with better glass- 
 es than those of which I am possessed, the same 
 might be shown in animals still smaller than the 
 flea, perhaps, even in those which are themselves 
 invisible to the naked eye. But we shall converse
 
 ATTRACTION OF COHESION. 11 
 
 more at large on this matter when we come to con- 
 sider the subject of optics, and the construction and 
 uses of the solar microscope. At present we will 
 turn our thoughts to that principle in nature, which 
 philosophers have agreed to call gravity or attrac- 
 tion. 
 
 Charles. If there be no more difficulties in phi- 
 losophy than we met with in our last lecture, 1 do 
 not fear but that we shall, in general, be able to un- 
 derstand it. Are there not several kinds of attrac- 
 tion? 
 
 Father. Yes, there are; two of which it will be 
 sufficient for our present purpose to describe; the 
 one is the attraction of cohesion; the other that of 
 gravitation. The attraction of cohesion is that pow r er 
 \^hich keeps the parts of bodies together when they 
 touch, and prevents them from separating; or which 
 inclines the parts of bodies to unite, when they are 
 placed sufficiently near to each other. 
 
 Charles. Is it then by the attraction of cohesion 
 that the parts of this table, or of the pen-knife, are 
 kept together? 
 
 Father. The instances which you have selected 
 are accurate, but you might have said the same of 
 every other solid substance in the room, and it is in 
 proportion to the different degrees of attraction with 
 which different substances are affected, that some 
 bodies are hard, others soft, tough, &c. A philoso- 
 pher iu Holland, almost a century ago, took great
 
 12 MECHANICS. 
 
 pains in ascertaining the different degrees of cohe- 
 sion, which belonged to various kinds of wood, me- 
 tals, and many other substances. A short account 
 of the experiments made by M. Musschenbroek, 
 you will hereafter find in your own language, in the 
 second edition of Dr. Enfield's Institutes of Na- 
 tural Philosophy. 
 
 Charles. You once showed me that two leaden 
 bullets, having a little scraped from the surfaces, 
 might be made, with a sort of twisting pressure, to 
 stick together with great force ; you called that, I 
 believe, the attraction of cohesion ? 
 
 Father. I did: some philosophers, who have 
 made this experiment with great attention and ac^ 
 curacy, assert, that if the flat surfaces, which are 
 presented to one another, be but a quarter of an 
 inch in diameter, scraped very smooth, and for- 
 cibly pressed together with a twist, a weight of a 
 hundred pounds is frequently required to separate 
 them. 
 
 As it is by this kind of attraction that the parts of 
 solid bodies are kept together, so when any sub- 
 ^^tance is separated or broken, it is only the attrac- 
 tion of cohesion that is overcome in that particular 
 part. 
 
 Emma. Then when I had the misfortune this 
 morning at breakfast, to let my saucer slip from my 
 hands, by which it was broken into several pieces, 
 \vas it only the attraction of cohesion that was over-
 
 ATTRACTION OF COHESION. 13 
 
 come by the parts of the saucer being separated in 
 its fall on the ground ? 
 
 Father. Just so ; for whether you unluckily break 
 the china, or cut a stick with your knife, or melt 
 lead over the fire, as your brother sometimes does, 
 in order to make plummets; these, and a thousand 
 other instances, which are continually occurring, are 
 but examples in which the cohesion is overcome by 
 the fall, the knife, or the fire. 
 
 Emma. The broken saucer being highly valued 
 by mamma, she has taken the pains to join it again 
 with white lead ; was this performed by means of 
 the attraction of cohesion? 
 
 Father. It was, my dear ; and hence you will 
 easily learn that many operations in cookery are in 
 fact nothing more than different methods of over^ 
 coming this attraction.- 
 
 C/iarles. How are we to understand this ? 
 
 Father. I will endeavour to remove your diffi- 
 culty. Heat expands almost all bodies, as you 
 shall see before we have finished our lectures. Now 
 the fire applied to metals in order to melt them, 
 causes such an expansion, that the particles are 
 thrown out of the sphere, or reach of each other's at- 
 traction. 
 
 Emma. When the cook makes broth, it is the 
 heat then which overcomes the attraction which the 
 Jparticles of meat have for each other, for I have seen 
 
 K
 
 14 MECHANICS. 
 
 her pour off the broth, and the meat is all in rags. 
 But will not the heat overcome the attraction which 
 the parts of the bones have for each other ? 
 
 Father. The heat of boiling water will never effect 
 this, but a machine was invented several years ago, 
 by Mr. Papin, for that purpose. It is called 
 Papin's digester, and is used in taverns, and in 
 many large families, for the purpose of dissolving 
 bones, as completely as a lesser degree of heat will 
 liquefy jelly. On some future day I will show jou 
 an engraving of this machine, an-d explain its diflet- 
 ent parts, which are extremely simple*. 
 
 * Se Eng.ed. Vol. IV- Conver. XIX. p. 18i~8.
 
 ATTRACTION OF COHESION. 15 
 
 CONVERSATION IV. 
 
 Of the Attraction of Cohesion. 
 
 FATHER. I will now mention some other in* 
 stances of this great law of nature. If two polish- 
 ed plates of marble, or brass, be put together, with 
 a little oil between them to fill up the pores of their 
 surfaces, they will cohere so powerfully as to require 
 a very considerable force to separate them. Two 
 globules of quicksilver, placed very near to each other, 
 will run together and form one large drop. Drops 
 of water will do the same. Two circular pieces of 
 cork placed upon water at about an inch distant 
 will run together. Balance a piece of smooth board 
 on the end of a scale beam ; then let it lie flat on 
 water, and five or six times its own weight will be 
 required to separate it from the water. If a small 
 globule of quicksilver be laid on clean paper, and a 
 piece of glass be brought into contact with it, the 
 mercury will adhere to it, and be drawn away from 
 the paper. But bring a larger globule into contact 
 with the smaller one, and it will forsake the glass, 
 and unite with the other quicksilver. 
 
 Charles. Is it not by means of the attraction of 
 cohesion, that the little tea which is generally left at
 
 16 MtCHANICS. 
 
 the bottom of the cup instantly ascends in the sugar* 
 when thrown into it? 
 
 Father. The ascent of water or other liquids in 
 sugar, sponge,and all porous bodies, is a species of* 
 this attraction, and is called capillary* attraction; 
 it is thus denominated from the property which 
 tubes of a very small bore, scarcely larger than to 
 admit a hair, have of causing water to stand above 
 its level. 
 
 Charles. Is this property visible in no other tubes 
 then those, .the bores of which are so exceedingly 
 fine? 
 
 Father. Yes, it is very apparent in tubes whose 
 diameters are one tenth of an inch or more in length, 
 but the smaller the bore, the higher the fluid rises ; 
 for it ascends, in all instances, till the weight of the 
 column of water in the tube balances, or is equal 
 to the attraction of the tube. By immersing tubes of 
 different bores in a vessel of coloured water, you 
 will see that the water rises as much higher in the 
 smaller tube, than in the larger, as its bore is less 
 than that of the larger. The water will rise a qurr- 
 ter of an inch, and there remain suspended in a 
 tube, whose bore is about one eighth of an inch in 
 diameter. 
 
 This kind of attraction is well illustrated by tak- 
 ing (Plate 1. Fig. 5.) two pieces of glass joined to-; 
 
 * I'rom cupillttt, the I-atin word for /.>.
 
 ATTRACTION OF COHESION. 17 
 
 gether at the side BC, and kept a little open at the 
 opposite side AD, by a small piece of cork E. In this 
 position immerse them in a dish of coloured water 
 FG, and you will observe that the attraction of the 
 glass at, and near BC, will cause the fluid to ascend 
 to B, whereas about the parts D it scarcely rises 
 above the level of the water in the vessel. 
 
 Charles. I see that a curve is formed by the water. 
 
 Father. There is, and to this curve there are 
 many curious properties belonging, as you will here- 
 after be able to investigate for yourself. 
 
 Emma. Is it not upon the principle of the attrac- 
 tion of cohesion, that carpenters glue their work 
 together ? 
 
 Father. It is upon this principle that carpenters 
 and cabinet-makers make use of glue ; that braziers, 
 tinmen, plumbers, &c., solder their metals ; and that 
 smiths unite different bars of iron by means of heat. 
 These and a thousand other operations, of which 
 we are continually the witnesses, depend on the 
 same principle as that which induced your mothev 
 to use the white lead in mending her saucer. And 
 you ought to be told, that though white lead is fre- 
 quently used as a cement for broken china, glass, 
 and earthen ware, yet if the vessels are to be brought 
 again into use, it is not a proper cement, being an 
 active poison; besides, one much stronger has been 
 discovered, I believe., by a very able and ingenious 
 philosopher, the late Dr. Ingenhouz, at least I had
 
 J8 MECHANICS. 
 
 it from him several years ago ; it consists simply of 
 a mixture of quick-lime and cheese, rendered soft 
 by warm water, and worked up to a proper con- 
 sistency. 
 
 Emma. What! do such great philosophers, as I 
 have heard you say Dr. Ingenhouz was, attend to 
 such trifling things as these ? 
 
 Father. He was a jnan deeply skilled in many 
 branches of science ; and I hope that you and your 
 brother will one day make yourselves acquainted 
 with many of his important discoveries. But no 
 real philosopher will consider it beneath his atten- 
 tion to add to the conveniencies of life. 
 
 Charles. This attraction of cohesion seems to 
 pervade the whole of nature. 
 
 Father. It does, but you will not forget that it acts 
 only at very small distances. Some bodies indeed 
 appear to possess a power the reverse of the attrac- 
 tion of cohesion. 
 
 Emma. What is that? 
 
 Father. It is called repulsion. Thus water 
 repels most bodies till they are wet. A small 
 needle carefully placed on water will swim, al- 
 though the iron of which it is made is much heavier 
 than water : flies walk upon water without wetting 
 their feet : 
 
 Or bathe unwct their oily forms, and dwell 
 "With feet repulsive on the dimpling well. 
 
 D
 
 ATTRACTION OF COHESION. 19 
 
 The drops of dew which appear in a morning on 
 plants, particularly on cahbage plants, assume a 
 globular form, from the mutual attraction between 
 the particles of water ; and upon examination it will 
 be found that the drops do not touch the leaves, 
 for they will roll off in compact bodies, which could 
 not be the case if there subsisted any degree of at- 
 traction between the water and the leaf. 
 
 If a small thin piece of iron be laid upon quicksil- 
 ver, the repulsion between the different metals will 
 cause the surface of the quicksilver near the iron to 
 be depressed. 
 
 If a glass or any hard substance be broken, the 
 parts cannot be made to cohere without first being 
 moistened, because the repulsion is too great to ad- 
 mit of a reunion. 
 
 The repelling force between water and oil is 
 likewise so great, that it is impossible to mix them 
 in such a manner that they shall not separate a- 
 gain. 
 
 If a ball of light wood be dipped in oil, and then 
 put into water, the water will recede so as to form 
 a sort of channel around the ball. 
 
 Charles. Why do cane, steel, and many other 
 things, bear to be bent without breaking, and, when 
 set at liberty, recover their original form ? 
 
 Father. That a piece of thin steel, or cane, reco- 
 vers its usual form, after being bent, is owing to a 
 certain power called elasticity; which may, per-
 
 20 MECHANICS. 
 
 haps, arise from the particles of those bodies, though 
 disturbed, not being drawn out of each other's at- 
 traction : therefore, as soon as the force upon them 
 ceases to act, they restore themselves to their for- 
 mer position. But our half hour is expired, I must 
 leave you.
 
 ATTRACTION OF GRAVITATION. 21 
 
 CONVERSATION V. 
 
 O/* <//e Alt faction of Gravitation. 
 
 FATHER. We will now proceed to discuss 
 another very important general principle in nature; 
 the attraction of gravitation, or, -as it is frequently 
 termed, gravity, which is that power by which dis- 
 tant bodies tend towards each other. Of this we 
 have perpetual instances in the falling of bodies to 
 the earth. 
 
 Charles. Am I -then to understand, that whether 
 this marble falls from my hand, or a loose brick 
 from the top of the house, or an apple from the tree 
 in the orchard, that all these happen by the attrac- 
 tion of gravity ? 
 
 Father. It is by the power which is commonly 
 expressed under the term gravity, that all bodies 
 whatever have a tendency to the earth, and, unless 
 supported, will fall in lines perpendicular.to its sur- 
 face. This tendency or disposition of bodies to fall 
 is commonly called their weight or heaviness. ;!ftvfrt>' 
 
 Emma. Then the reason why lead is so much 
 heavier than cork is because it has a stronger attrac- 
 tion of gravitation. Is there any way of accounting 
 for this difference ? 
 
 G
 
 22 MECHANICS. 
 
 Father. It is found that in bodies composed of 
 the same substance the weight is always in propor- 
 tion to the quantity of matter. Thus two pints of 
 water weigh just twice as much as one pint. I have 
 already mentioned that heat expands, or increases 
 the bulk of bodies. This is the case with respect to 
 mercury. So that a quantity of this fluid that mea- 
 sures exactly one pint in a cold day, will measure 
 f ths of an ounce more if heated so as nearly to 
 boil. Its weight however is not at all affected by 
 this increase of bulk. If you pour off the f ths of an 
 ounce it has expanded by heat, the remaining hot 
 pint will weigh less than the cold pint, proportionate- 
 ly to the quantity of matter you remove. Fluids 
 when turned to solids by freezing, and solids when 
 liquefied by heat, generally alter their bulk ; but as 
 the quantity of matter they contain is neither increas- 
 ed nor diminished by these changes of form, their 
 weight is not affected. Hence it is inferred that in 
 every form of matter the weight of a body indicates 
 the absolute quantity of matter of which it is com- 
 posed'. 
 
 Clturles. Then there one two ways in which the 
 wf-i'^ht of a body may be considered. Though I 
 call a cork light, it is only so when considered with 
 relation to such bodies as lead ; for I can easily 
 imagine a quantity of cork so great that it would be 
 too heavy for a man to carry. 
 
 Fat/ter. You are right, Charles, to make that dis-
 
 ATTRACTION OF GRAVITATION. 23 
 
 tinction. The relative weight of different bodies is 
 called their specific gravity; but the comparative 
 wight of different bulks of the same matter is 
 called absolute gravity. Thus mercury is said to 
 have 13 times the specific gravity of water, be- 
 cause one pint of mercury will weigh 13 pints of 
 water; or the absolute weight of 131 pints of water 
 and of one pint oi mercury are equal. 
 
 Emma. But are not smoke, steam, and other light 
 bodies, which we see ascend, exceptions to the ge- 
 neral rule? 
 
 Father. It appears so at first sight, and it was for- 
 merly received as a general opinion, that smoke, 
 steam, &c., possessed no weight: the discovery of 
 the air-pump has shown the fallacy of this notion ; 
 for in an exhausted receiver, that is, in a glass jar 
 from which the air is taken away by means of the 
 air-pump, smoke and steam descend by their own 
 weight as completely as a piece of lead. When we 
 come to converse on the subject of pneumatics and 
 hydrostatics, you will understand that the reason 
 why smoke and other bodies ascend is simply be- 
 cause they are lighter than the atmosphere which 
 surrounds them, and the moment they reach that 
 part of it which has the same gravity with them- 
 selves they cease to rise. 
 
 Charles. Is it then by this power that all terrestri- 
 al bodies remain firm on the earth ? 
 
 Father. By gravity, bodies on all parts of the earth 
 (which you know is of a globular form) are kept on
 
 24 MECHANICS* 
 
 its surface, because they all, wherever situated, tend 
 to the centre; and, since all have a tendency to the 
 centre, the inhabitants of New Zealand, although 
 nearly opposite to our feet, stand as firm as we do 
 in Great Britain. 
 
 Charles. This is difficult to comprehend : neverthe- 
 less, if bodies on all parts of the surface of the earth 
 have a tendency to the centre, there seems no rea- 
 son why bodies should not stand firni on one part 
 as well as another. Does this power of gravity act 
 alike on all bodies ? 
 
 Father. It does, without any regard to their figure, 
 or size; for as attraction or gravity acts equally oii 
 every particle of matter which they contain, all 
 bodies at equal distances from the earth fall with 
 equal velocity. 
 
 Emma. What do you mean, papa, by velocity? 
 
 Father. I will explain it by an example or two; 
 if you and Charles set out together, and you walk a 
 mile in half an hour, but he walk and run two miles 
 in the same time, how much swifter will he go than 
 you? 
 
 Emma. Twice as swift. 
 
 Father. He does, because, in the same time, he 
 passes over twice as much space ; therefore "we say 
 his velocity is twice as great as yours. Suppose a 
 ball, fired from a cannon, pass through 800 feet in 
 a second of time ; and in the same time your bro- 
 ther's arrow pass through 100 feet only, how much 
 swifter does the cannon ball fly than the arrow ?
 
 ATTRACTION OF GRAVITATION. 25 
 
 Emma. Eight times swifter. 
 Father. Then it has eight times the velocity of the 
 arrow; and hence you understand that swiftness 
 and velocity are synonymous terms, and that the 
 velocity of a body is measured by the space it pas- 
 ses over in a given time, as a second, a minute, an 
 hour, Sec. 
 
 Emma. If I let a piece of metal, as a penny-piece 
 and a feather, fall from my hand at the same time, 
 the penny will reach the ground much sooner than 
 the feather. Now how do you account for this, if 
 all bodies are equally affected by gravitation, and 
 descend with equal velocities, when at the same dis- 
 tance from the earth ? 
 
 Father. Though the penny and feather will not, 
 in the open air, fall with equal velocity, yet, if the 
 air be taken away, which is easily done, by a little 
 apparatus connected with the air-pump, they will 
 descend in the same time. Therefore the true rea- 
 son why light and heavy bodies do not fall with e- 
 qual velocities is, that the former, in proportion to 
 its weight, meets with a much greater resistance 
 from the air than the latter. 
 
 Charles. ' It is then, I imagine, from the same 
 cause, that, if I drop the penny and a piece of 
 light wood into a vessel of water, the penny shall 
 reach the bottom, but the wood, after descending a 
 small way, rises to the surface. 
 
 Father. In this case the resisting medium is water 
 instead of air, and the copper being about nine times
 
 20 MECHANICS. 
 
 heavier than its bulk of water, falls to the bottom 
 without apparent resistance. But the wood, being 
 much lighter than water, cannot sink in it ; therefore, 
 though by its momentum * it sinks a small distance, 
 yet as soon as that is overcome by the resisting me- 
 dium, that is the water, it rises to the surface, be- 
 ing the lighter substance. 
 
 The explanation of this term will be found in the next Conversation. 
 
 r *.*'; 
 
 ;*>, i%r j|fiafq -* ; ! 
 
 -. < 
 
 ,-iia yqo SIM in 
 r-v *ulfi < u.4tfi 

 
 ATTRACTION OP GRAVITATION. 27 
 
 ' 
 
 * 
 
 CONVERSATION VI. 
 
 Of the Attraction of Gravitation. 
 
 EMMA. The term momentum, which you made 
 use of yesterday, is another word which I do not 
 understand. 
 
 Father. If you have understood what I have said 
 respecting the velocity of moving bodies, you will 
 easily comprehend what is meant by the word mo- 
 mentum. 
 
 The momentum is the moving force of a body, and 
 is measured by its weight multiplied into its veloci-. 
 ty. You may, for instance, place this pound weight 
 upon a china plate without any danger of breaking, 
 but if you let it fall from the height of only a few 
 inches, it will dash the china to pieces. In the first 
 case, the plate has only the pound weight to sustain ; 
 in the other the weight must be multiplied into the 
 velocity, or, to speak in a popular manner, into the 
 distance of the height from which it fell. 
 
 If a ball a (Plate 1. Fig. 6.) lean against the ob? 
 stacle b, it will not be able to overturn it, but 'if it 
 be taken up to c and suffered to roll down the in-, 
 clined plane A it against /;, it will certainly overthrow 
 it ; in the former case b would only have to resist
 
 28 MECHANICS. 
 
 the weight of the ball a, in the latter it has to re 
 si^t the weight multiplied into its motion, or ve- 
 locity. 
 
 Charles. Then the momentum of a small body, 
 whose velocity is very great, may be equal to that 
 of a very large body with a slow velocity. 
 
 Father* It may ; and hence you see the reason 
 why immense battering rams, used by the ancients, 
 in the art of war, have given place to cannon balls of 
 but a few pounds weight. 
 
 Cltarles. I do ; for what is wanting in weight is 
 made up by velocity. 
 
 Father. Can you tell me what velocity a cannon 
 ball of 28 pounds must have to effect the same pur- 
 poses as would be produced by a battering ram 
 oT 15,000 pounds .weight, and which, by manual 
 strength, could be moved at the rate of only two 
 feet in a second of a time? 
 
 Charles. I think I can ; the momentum of the 
 battering ram must be estimated by its weight, mul- 
 tiplied into the space passed over in a second, 
 which is 15,000 multiplied by two feet equal to 
 30,000 ; now if this momentum, which must also 
 be that of the cannon ball, be divided by the weight 
 of the ball, it will give the velocity required ; and 
 30,000 divided by 28, will give for the quotient 
 10,072 nearly, which is the number of feet which the 
 cannon ball must pass over in a second of time in 
 order that the momenta of the battering ram and 
 the ball may be equal, or in other words, that they
 
 ATTRACTION OF GRAVITATION. 33 
 
 may have the same effect in beating down an ene- 
 my's wall. 
 
 Emma. I now fully comprehend what the mo- 
 mentum of a body is, for if I let a common trap-ball 
 accidentally fall from my hand, upon my foot, it oc- 
 casions more pain than the mere pressure of a 
 weight several times heavier than the ball. 
 
 Charles. If the attraction of gravitation be a 
 power by which bodies in general tend towards each 
 other, why do all bodies tend to the earth as a cen- 
 tre? 
 
 Father. I have already told you that, by the 
 great law of gravitation, the attraction of all bodies 
 is in proportion to the quantity of matter which they 
 contain. Now the earth* being so immensely large 
 in comparison with the detached bodies on its sur- 
 face, destroys the effect of this attraction between 
 smaller bodies, by bringing them all to itself. If 
 two balls are let fall from a high tower at a small 
 distance apart; though they have an attraction for 
 one another, yet it will be as nothing when compar- 
 ed with the attraction by which they are both impell- 
 ed to the earth, and consequently the tendency which 
 they mutually have to approach one another will 
 not be perceived in the fall. Near large and steep 
 mountains, however, the attraction of the matter they 
 contain can be measured by their effect in draw- 
 ing a plummet towards themselves from the perpendi- 
 cular line in which it would naturally hang. And
 
 34 MECHANICS. 
 
 when two bodies are placed so as to move freely in- 
 dependently of the earth's attraction, they will ap- 
 proach each other; as in the instance already men- 
 tioned of two pieces of cork placed upon water. In 
 these cases the bodies move towards each other with 
 increased velocity as they come nearer. If the bo- 
 dies were equal, they would meet in the middle point 
 between the two ; but if they were unequal, they would 
 then meet as much nearer the larger one as that con- 
 tained a greater quantity of matter than the other. 
 
 Charles. According to this, the earth ought to 
 move towards falling bodies, as well as they move 
 to it. 
 
 Father. It ought, and, in just theory, it does ; but 
 when you calculate how many million of times larger 
 the earth is than any thing belonging to it, and if 
 you reckon, at the same time, the small distances 
 from which bodies can fall, you will know that 
 the point where the falling bodies and the earth will 
 meet, is removed only to an indefinitely small dis- 
 tance from its surface ; a distance much too small 
 to be conceived by the human imagination. 
 
 As all bodies on or near the earth tend to the 
 centre of that body; so the earth, and all the pin- 
 nets, with their several moons, as we shall see by 
 and by, tend to the centre of the sun, as the point 
 to which the whole and every part of the solar sy- 
 stem is attracted. 
 
 We will resume the subject of gravity to-morrow.
 
 ATTRACTION OP GRAVITATION. 35 
 
 CONVERSATION VII. 
 
 Of the Attraction of Gravitation. 
 
 EMMA. Has the attraction of gravitation the 
 same effect on all bodies, whatever be their distance 
 from the earth? 
 
 Father. No ; this, like every power which pro- 
 ceeds from a centre, decreases as the squares of the 
 distances from that centre increase. 
 
 Emma. I fear that I shall not understand this, 
 unless you illustrate it by examples. 
 
 Father. Suppose you are reading at the distance 
 of one foot from a candle, and that you receive a 
 certain quantity of light on your book ; now if you 
 remove to the distance of two feet from the candle, 
 you will, by this law, receive four times less light 
 than you had before ; here then, though you have 
 increased your distance but twofold, yet the light is 
 diminished fourfold, because four is the square of 
 two, or two multiplied by itself. If instead of re- 
 moving two feet from the candle, you take your sta- 
 tion at 3, 4, 5, or 9 feet distance, you will then re- 
 ceive at ll.e different distances, 9, 16, 25, 36, times
 
 36 MECHANICS. 
 
 less light than when you were within a single foot 
 from the candle; for these, as you know, are the 
 squares of the numbers 3, 4, 5, 6. The same is ap- 
 plicable to the heat imparted by a fire ; at the dis- 
 tance of one yard from which, a person will enjoy 
 four times as much heat as he who sits or stands 
 two yards from it ; and nine times as much as one 
 that shall be removed to the distance of three 
 yards* 
 
 Charles. Is then the attraction of gravity four 
 times less at 2 yards distance from the earth than it 
 is at J yard from the surface? 
 
 Father. No ; whatever be the cause of attrac- 
 tion, which to this day remains undiscovered, it 
 acts from the centre of the earth, and not from 
 its surface, and hence the difference of the pow- 
 er of gravity cannot be discerned at the small 
 distances to which we can have access ; for a mile 
 or two, which is much higher than, in general, we 
 have opportunities of making experiments, is no- 
 thing in comparison of 4000 miles, the distance of 
 the centre from the surface of the earth. But could 
 we ascend 4000 miles above the earth, and of course 
 be double the distance that we now are from the 
 centre, we should there find that the attractive force 
 would be but one fourth of what it is here ; or, in 
 other words, that a body, which, at the surface of the 
 earth, weighs one pound, and ly the the force, of 
 gravity, falls through sixteen feet in a second of
 
 ATTRACTION OF GRAVITATION. 37" 
 
 time, would at 4000 miles above the earth weigh but 
 a quarter of a pound, and fall through only four feet 
 in a second*. 
 
 Emma. How is that known, papa, for nobody 
 ever was there ? 
 
 Father. You are right, my dear, for Garnerin, 
 who last summer astonished all the people of the 
 metropolis and its neighbourhood by his flight in a 
 balloon, ascended but a little way in comparison of 
 the distance that we are speaking of. However, I 
 will try to explain in what manner philosophers have 
 come by their knowledge on this subject. 
 
 The moon is a heavy body connected with the 
 earth by this bond of attraction, and, by the most 
 accurate observations, it is known to be obedient to 
 the same laws as other heavy bodies are : its dis- 
 tance is also clearly ascertained, being about 240,000 
 miles, or equal to about sixty semidiameters of the 
 earth, and of course the earth's attraction upon the 
 moon ought to diminish in the proportion of the 
 square of this distance, that is, it ought to be 60 
 times 60, or 3600 times less at the moon than it is 
 
 Ex. Suppose it were required to find the weight of a leaden ball, at 
 the top of a mountain three miles high, which on the surface of the earth 
 %veighs 20lb. 
 
 If the semi-diameter of the earth be taken at 4,000 ; then add to this 
 the height of the mountain, and say as the square of 4,003 is to the square 
 pf 4,000, so is 20lb. to a fourth proportional: or 16,024,009: 10,000,000 : : 
 20 : 19.97, or something more than I9lb. ISjoz. which is the weight of the 
 leaden ball at the top of the mountain. 
 L
 
 38 MECHANICS. 
 
 at the surface of the earth. This is found to be 
 the case. 
 
 Again, the earth is not a perfect sphere, but a 
 spheroid, that is, of the shape of an orange, rather 
 flat at the two ends called the poles, and the dis- 
 tance from the centre to the poles is about 13 or 14 
 miles less than its distance from the centre to the 
 equator; consequently, bodies ought to be some 
 thing heavier at and near the poles, than they 
 are at the equator, which is also found to be the 
 case. Hence it is inferred, that the attraction of 
 gravitation varies at all distances from the centre of 
 the earth, in proportion as the squares of those dis- 
 tances increase*. 
 
 Emma. And would a ball of twenty pounds 
 weight here, weigh half an ounce less on the top of 
 Ihe^nountain? 
 
 Father. Certainly : but you would not be able to 
 ascertain it by means of a pair of scales and another 
 weight, because both weights being in similar situa- 
 tions would lose equal portions of their gravity. 
 
 Emma. How, then, would you make the expe- 
 riment? 
 
 Father. By means of one of those steel spiral- 
 spring instruments which you have seen occasionally 
 used, the fact might be ascertained. 
 1 Charles. It seems very surprising that philoso- 
 phers who have discovered so many things have not 
 
 * Sec Eng. ed. Vol. II. Conver. VI.
 
 ATTRACTION OF GRAVITATION. 39 
 
 bees able to find out the cause of gravity. Had Sir 
 Isaac Newton been asked why a marble, dropped 
 from the hand, falls to the ground, could he not have 
 assigned a reason ? 
 
 Father. That great man, probably the greatest 
 man that ever adorned this world, was as modest as 
 he was great, and he would have told you he knew 
 not the cause. 
 
 The excellent and learned Dr. Price, in a work 
 which he published thirty years ago, asks, "Who 
 does not remember a time when he would have 
 wondered at the question, Why does water run down 
 hill? What ignorant man is there who is not per- 
 suaded that he understands this perfectly? But 
 every improved man knows it to be a question he 
 cannot answer." For the descent of water, like that 
 of other heavy bodies, depends upon the attraction 
 of gravitation, the cause of which is still involved in 
 darkness.
 
 40 MECHANICS. 
 
 CONVERSATION VIII. 
 
 O/' the Attraction of Gravitation. 
 
 EMMA. You said yesterday, that heavy bodies 
 by the force of gravity fall sixteen feet iu a second 
 of time is that always the case ? 
 
 Father. Yes, all bodies near the surface of the 
 earth fall at that rate in the first second of time, but 
 as the attraction of gravitation does not act by a 
 single impulse, but is always operating in a constant 
 and uniform manner, it must produce equal effects 
 in equal times, and consequently in a double or tri- 
 ple time a double or triple effect: and so must 
 accelerate the motion of a body proportionably to 
 the time of its descent. Thus if a body begin to fall 
 with a celerity constantly increasing in such a man- 
 ner as to carry it through 16 feet in one moment, 
 the velocity it has acquired at the end of that mo- 
 ment is sufficient to carry it through 32 feet the 
 next moment, though it should receive no new im- 
 pulse from the cause by which its motion has been 
 acceleratedT^but if the same accelerating cause con- 
 tinue to operate during the second moment, it will
 
 ATTRACTION OF GRAVITATION'. 41 
 
 carry the body 16 feet farther, in all 3. times 16 
 or 48 feet, which together with the 16 feet passed 
 through in the first moment makes 64 feet that 
 have been passed through in two moments. In the 
 same way the velocity acquired at the end of the 
 second moment would alone, without any continua- 
 tion of impulse, carry the body through double this 
 space or 128 feet the next two moments, or through 
 sixty four feet in the next or third moment. But 
 the additional impulse will carry it through 16 feet 
 further, or 80 feet, which is 5 times 16 feet. In the 
 same way it will move through 7 times 16 feet in 
 the fourth moment, 9 times 16 feet in the 5th mo- 
 ment, and so on, continually increasing as the odd 
 numbers 1, 3, o, 7, 9, 11, &c. The wlnole spaces 
 passed through are therefore as the squares of the 
 times. For the continued addition of the odd num- 
 ber yields the squares of all numbers from unity 
 upward. Thus 1 is the square of 1 ; 3 the next odd 
 member added to 1 makes 4, the square of 2; 5 the 
 third odd member added to 3 and 1 makes 9, the 
 square of 3 ; and so on. 
 
 Charles. I think, then, that with the assistance of 
 your stop-watch, I could tell the height of any place, 
 by observing the number of seconds that a marble 
 or other heavy body would take in falling from that 
 height. 
 
 Father. How would you perform the calculation? 
 
 Charles. I should go through the multiplications 
 M
 
 42 - . MECHANICS. 
 
 according to the number of seconds, and then 
 them together. 
 
 father. Explain yourself more particularly: 
 supposing you were to let a marble or penny-piece 
 fall down a deep well, and that it was exactly 
 five seconds in the descent, what would be the depth 
 of the well ? 
 
 Charles. In the first second it would fall 16 feet; 
 in the next 3 times .16 or 48 feet ; in the third 5 
 times 16 or 80 feet; in the fourth 7 times 16 or 112 
 feet; and in the fifth second 9 times 16 or 144 feet; 
 now if I add 16, 48, 80, 112, and 144 together, the 
 sum will be 400 feet, wjuch, according to your rule, 
 is the depth of the well. ., 
 
 Father. Though your calculation is accurate, 
 yet it was not done as nature effects her operations, 
 that is in the shortest way. 
 
 Charles. I should be pleased to know an easier 
 method ; this, however, is very simple, it required 
 nothing but multiplication and addition. 
 
 Father. True, but suppose I had given you an 
 example in which the number of seconds had been 
 fifty instead of five, the work would have taken you 
 an hour or more to have performed it; whereas, by 
 the rule which I am going to give, it might have 
 been done in half a minute. 
 
 Charles. Pray let me have it, I hope it will be 
 easily remembered. 
 
 Father. It will ; I think it cannot be forgotten af-
 
 ATTRACTION OF GRAVITATION. 43 
 
 ter it is once understood. The rule is this, "the 
 spaces described by a body falling freely from a state 
 of rest increase as the SQUARES of the times increase" 
 Consequently you have only to square the number 
 of seconds, that is, to multiply the number into it- 
 self; and then multiply that again by sixteen feet, 
 the space which it describes in the first second, and 
 you have the required answer. Now try the exam- 
 ple of the well. 
 
 Charles. The square of 5, for the time, is 25, which, 
 multiplied by 16, or the space passed through in 
 a second or moment gives 400, just as I brought it 
 out before. Now if the seconds had been 50, the 
 answer would be 50 times 50, which is 2,500, and 
 this multiplied by 16', gives 40,000 for the space 
 required. 
 
 Father. I will now ask your sister a question to 
 try how she has understood this subject. Suppose 
 you observe by this watch that the time of the flight of 
 your brother's arrow when shot directly upwards is 
 exactly six seconds, to what height does it rise? 
 
 Emma. This is a different question, because here 
 the ascent as well as the fall of the arrow is to be 
 considered. 
 
 Father. But you will remember, that the time of 
 the ascent is always equal to that of the descent ; for 
 as the velocity of the descent is generated by the 
 force of gravity, so is the velocity of the ascent de- 
 stroyed by the same force.
 
 44 MECHANICS. 
 
 Emma. Then the arrow was three seconds only 
 in falling ; now the square of 3 is 9, which multiplied 
 by 16, for the number of feet described in the first se- 
 cond, is equal to 144 feet, the height to which it 
 rose 
 
 Father. Now, Charles, if I get you a bow which 
 will carry an arrow so high as to be fourteen seconds 
 in its flight, can you tell me the height to which it 
 ascends. 
 
 Charles. I can now answer you without hesita- 
 tion : it will be 7 seconds in falling, the square of 
 which is 49, and this again multiplied by 16 will 
 give 784 feet, or rather more than 261 yards for the 
 answer. 
 
 Father. I have but a word or two more on the 
 subject : since the whole spaces described increase 
 as the squares of the times increase, so also the ve- 
 locities of falling bodies increase in the same pro- 
 portion ; for you know that the velocity must be 
 measured by the space passed through. Thus if a 
 person travels six miles an hour, and another person 
 travels twelve miles in the same time, the latter will 
 go with double the velocity of the former ; conse- 
 quently the velocities of falling bodies increase as 
 the squares of the times increase. 
 
 With this we conclude our present Conversation.
 
 CENTRE OF GRAVITY. 45 
 
 CONVERSATION IX. 
 
 On the Centre of Gravity. 
 
 7 ir 
 
 FATHER. We are now going to treat upon 
 the Centre of Gravity, which is that point of a body 
 in which its whole weight is, as it were, concen- 
 trated, and upon which, if the body be freely sus- 
 pended, it will rest; and in all other positions it 
 will endeavour to descend to the lowest place to 
 which it can get. 
 
 Charles. All bodies then, of whatever shape, have 
 a centre of gravity ? 
 
 Father. They have : and if you conceive a line 
 drawn from the centre of gravity of a body towards 
 the centre of the earth, that line is called the line 
 of direction, along which every body, not supported, 
 endeavours to fall. If the line of direction fall within 
 the base of any body, it will stand ; but if it does 
 not fall within the base, the body will fall. 
 
 If I place the piece of wood A (Plate I. Fig. 7) on 
 the edge of a table, and from a pin a at its centre of 
 gravity be hung a little weight b, the line of direc- 
 tion ab falls within the base, and therefore, though
 
 46 MECHANICS, 
 
 the wood leans, yet it stands secure. But if npon 
 A, another piece of wood E he placed, it is evident 
 that the centre of gravity of the whole will be now 
 raised to c, at which point, if a weight he hung, it 
 will be found that the line of direction falls out of the 
 base, and therefore the body must fall. 
 
 Emma. I think I now see the reason of the advice 
 which you gave me, when \ve were going across the 
 Thames in a boat. 
 
 Father. I told you that if ever you were overta- 
 ken by a storm, or by a squall of wind, while you 
 were on the water, never to let your fears so get the 
 better of you, as to make you rise from your seat, 
 because by so doing you w r ould elevate the centre of 
 gravity, and thereby, as is evident by the last expe- 
 riment, increase the danger : whereas, if all the per- 
 sons in the vessel were, at the moment of danger, 
 instantly to slip from their places to the bottom, the 
 risk would be exceedingly diminished, by bring- 
 ing the centre of gravity much lower within the ves- 
 sel. The same principle is applicable to those who 
 may be in danger of being overturned in any carriage 
 whatever. 
 
 Charles. I understand then, that the nearer the 
 centre of gravity is to the base of a body, the firmer 
 it will stand. 
 
 Father. Certainly; and hence you learn the rea- 
 son why conical bodies stand so sure on their bases, 
 for the tops being small in comparison of the lower
 
 CENTRE OF GRAVITY. 47 
 
 parts, the centre of gravity is thrown very low: 
 and if the cone be upright or perpendicular, the 
 line of direction falls in the middle of the base, 
 which is another fundamental property of steadiness 
 in bodies. For the broader the base, and the near- 
 er the line of direction is to the middle of it, the 
 more firmly does a body stand : but if the line of 
 direction fall near the edge, the body is easily 
 overthrown. 
 
 Charles. Is that the reason why a ball is so 
 easily rolled along a horizontal plane? 
 
 Father. It is ; for in all spherical bodies, the base 
 is but a point: consequently almost the smallest 
 force is sufficient to remove the line of direction out 
 of it. Hence it is evident, that heavy bodies situat- 
 ed on an inclined plane will, while the line of di- 
 rection falls within the base, slide down upon the 
 plane : but they will roll when that line falls with- 
 out the base. The body A (Plate I. Fig. 8) will 
 slide down the plane DE, but the bodies B and c will 
 roll down it. 
 
 Emma. I have seen buildings lean very much 
 out of a straight line ; why do they not fall ? 
 
 Father. It does not follow because a building 
 leans, that the centre of gravity does not fall within 
 the base. There is a high tower at Pisa, a town in 
 Italy, which leans fifteen feet out of the perpendicu- 
 lar; strangers tremble in passing by it; still it is 
 found by experiment that the line of direction falls 
 
 V
 
 48 MECHANICS. 
 
 within the base, and therefore it will stand while its 
 materials hold together. 
 
 A wall at Bridgenorth in Shropshire, which I have 
 seen, stands in a similar situation; but so long as a 
 line cb (Plate II. Fig. 9) let fall from the centre of 
 gravity c of the building AB, passes within the base 
 CB, it will remain firm, unless the materials with 
 which it is built go to decay. 
 
 Charles. It must be of great use in many cases to 
 know the method of finding the centre of gravity in 
 different kinds of bodies. 
 
 Father. There are many easy rules for this with 
 respect to all manageable bodies : I will mention 
 one which depends on the property which the centre 
 of gravity has, of always endeavouring to descend 
 to the lowest point. 
 
 If a body A (Plate II. Fig. 10) be freely suspend- 
 ed on a pin a, and a plumb line a B be hung by the 
 same pin, it will pass through the centre of gravity, 
 for that centre is not in the lowest point, till it fall in 
 the same line as the plumb line. Mark the line a B ; 
 then hang the body up by any other point, as D, with 
 the plumb line DE, which will also pass through the 
 centre of gravity for the same reason as before : and 
 therefore as the centre of gravity is somewhere in 
 a B, and also in some point of DE, it must be in the 
 point c where those lines cross.
 
 CENTRE OF GRAVITY. 49 
 
 CONVERSATION X. 
 
 itq ' Of the Centre oj Gravity. *&M 
 
 CHARLES. How do those people, who have 
 to load carts and waggons with light goods, as hay, 
 wool, &c., know where to find the centre of gravity ? 
 
 Father. Perhaps the generality of them never 
 heard of such a principle ; and it seems surprising 
 that they should nevertheless make up their loads 
 with such accuracy as to keep the line of direction 
 in or near the middle of the base'. 
 
 Emma. When our little brother James falls about, 
 is it because he cannot keep the centre of gravity 
 between his feet ? 
 
 Father. That is the precise reason why any per- 
 son, whether old or young, falls. And hence you 
 learn that a man stands much tinner with his feet a 
 little apart than if they were quite close, for by se- 
 parating them he increases the base. Hence also 
 the difficulty of sustaining a tall body, as a walk- 
 ing cane, UDOU a narrow foundation. Indeed the 
 most common actions of people in general 4re regu- 
 lated by this principle. 
 
 o
 
 50 MECHANICS. 
 
 *afc . ..^Ai.-iJ *' i*< i *'.,&*" 
 
 Charles. In what respects ? 
 
 Father. We bend forward, when we go up stairs, 
 or rise from our chair; for when we are sitting, our 
 centre of gravity is on the seat, and the line of di- 
 rection falls behind our base : we therefore lean for- 
 wards to bring the line of direction towards our 
 feet. For the same reason a man carrying a bur- 
 den on his back leans forward ; and backward if he 
 carries it on his breast. If the load be placed on 
 one shoulder he leans to the other. 
 
 This property of the centre of gravity always en- 
 deavouring to descend will account for appearances, 
 which are sometimes exhibited to excite the sur- 
 prise of spectators. 
 
 Emma. What are those ? 
 
 Father. One is, that of a double cone, appear- 
 iug to roll up two inclined planes forming an angle 
 with each other ; for as it rolls it sinks between them, 
 and by that means the centre of gravity is actually 
 descending. 
 
 Let a body EF (Plate II. Fig. 13.), which is thick 
 in the centre, and round, and tapersoft'to a point at 
 each end, be placed upon the edges of two straight 
 smooth rulers, AH and CD, which at one end meet 
 in an angle at A, and rest on a level plane, and at 
 the other "are raised a little above the plane ; the 
 body will roll towards the elevated end' of the 
 rulers, and appear to ascend: for when the body, 
 EF, is placed near the angle at A, it must rest there
 
 CENTRE OF GRAVITY. 51 
 
 en its middle or thickest part ; so that the whole of 
 the body is above the rulers that support it. But 
 when it moves forward to where the rulers are wide 
 asunder, the small ends rest upon the rulers, and 
 the thick part of the body at the centre is conse- 
 quently half sunk below their edges, 'the centre 
 of gravity has of course now come to a position 
 lower than xvhen it was near the angle of the rulers. 
 But this experiment can succeed only when the 
 difference of level between the ends of the rulers is 
 less than half the thickness of the body at its centre. 
 Charles. Is it upon this principle that a cylinder 
 is msde to roll up hill? 
 
 Father. It is ; but this can be effected only to a 
 small distance. If a cylinder of pasteboard, or very 
 light wood AB (Plate II. Fig. 11.), having its centre 
 of gravity at c, be placed on the inclined plane CD, 
 it will roll down the inclined plane, because a line 
 of direction from that centre lies out of the base. 
 If I now fill the little hole o above with a plug of 
 lead, it will roll up the inclined plane, till the lead 
 gets near the base, where it will lie still: because 
 the centre of gravity by means of the lead is remov- 
 ed from c towards the plug, and therefore is de- 
 scending though tlie cylinder is ascending. 
 
 Before I put an end to this subject, I will show 
 you another experiment, which without nnderstaud- 
 ing the principle of the centre of gravity cannot be 
 explained. Upon this stick A (Plate II. Fig 12.)
 
 _- 
 
 52 MECHANICS. 
 
 "" .VLQ/iv. *vfj i ' * 03 ' t-'>J le*^Ji-Oiiijf tO 9'f^J^itn *i.ti fff* 
 
 which, of itself, would fall, because its centre of 
 
 gravity hangs over the table EF, I suspend a bucket 
 B, fixing another stick a, one end in a notch between 
 A and k, and the other against the inside of the 
 pail at the bottom. Now you will see that the 
 bucket will, in this position, be supported, though 
 filled with water. For the bucket being pushed a 
 little out of the perpendicular by the stick a, the 
 centre of gravity of the whole is brought under the 
 table, and is consequently supported by it. 
 
 The knowledge of the principle of the centre of 
 gravity in bodies, will enable you to explain the 
 structure of a variety of toys wliich are put into the 
 
 hands of children, such as the little sawyer* rope 
 
 
 dancer, tumbler, &? ^ ^ j .. { 
 
 .,0:1 s/iiik| ^tuiifUiu 9flJ no liipslq ^ .$ ^ yji 
 bsujft^i 9fU owoh Hoi 
 
 fi fW yo Q frOf 9 f>fiJ !l I 7/Oif 1 H . 
 
 i Uii '*i)i'i b* sjii. Wont )! I 
 
 
 WRtf* flif*-' .p!*>i<i 8l| Qt 
 
 dv; 
 
 ad Jeui : ' 9J> 
 
 !|iJ rjrfi roqll ,
 
 LAWS OF MOTION. 53 
 
 CONVERSATION XI 
 
 CHARLES. Are you. now going, papa, to de- 
 scribe those machines, which you call niec/ianical 
 powers ? 
 
 Father. We must, I believe, defer that a day 
 or two longer, as I have a few more general princi- 
 ples with which I wish you previously to be ac- 
 quainted. t/jtilUb v, 
 
 Emma. What are these ? 
 
 Father. In the first place, you must well under- 
 stand what are denominated the three general laws 
 of motion : the first of which is, " that every body 
 will continue in its state of rest or of uniform motion, 
 until it is compelled by some force to change its state" 
 This constitutes what is denominated the inertia or 
 inactivity of matter. And it may be r observed, that 
 a change never happens in the motion of any body, 
 without an equal and opposite change in the motion 
 of some other body. 
 
 Charles. There is no difficulty of conceiving that 
 
 a bodv, as this inkstand, in a state of rest amst al- 
 *
 
 51 MECHANICS. 
 
 ways reinaip so, if no external force be impressed 
 upon it to give it motion. But I know of no exam- 
 ple which will lead me to suppose, that a body 
 once put into motion would of itself continue so. 
 
 Father. You will, I think, presently admit the 
 latter part of the assertion as well as the former, al- 
 though it cannot be established by experiment. 
 Emma. I shall be glad to hear how this is. 
 
 Father. You will not deny that the ball which 
 you strike from the trap, has no more power either 
 to destroy its motion, or cause any change in its ve- 
 locity, then it has to change its shape. 
 
 Charles. Certainly; nevertheless, in a few se- 
 conds after I have struck the ball with all my force* 
 it falls to the ground, and then stops. 
 
 Father. Do you find no difference in the time 
 that is taken up before it comes to rest, even suppos- 
 ing your blow the same ? 
 
 Charles. Yes, if I am playing on the grass it rolls 
 to a less distance than when I play 011 the smooth 
 gravel. 
 
 Father* You find a like difference when .you are 
 playing at marbles, if you play in the gravel court, 
 or on the even floor of the verandah. 
 
 Charles. The marbles run so easily on the smooth 
 terrace of the verandah, that we can scarcely shoot 
 with a force small enough. 
 
 Father. Now these instances properly applied 
 will convince you, that a body once put into motion,
 
 LAWS OF MOTION. 66 
 
 would go on for ever, if it were not compelled by 
 some external force to change its state. 
 
 Charles. I perceive what you are going- to say: it 
 is the rubbing or friction of the marbles against the 
 ground which does the business. For on the ter- 
 race there are fewer obstacles than on the gravel, 
 and hence you would lead us to conclude, that if 
 all obstacles were removed they might proceed On 
 for ever. But what are we to say of the bail, what 
 stops that? 
 
 Father. Besides friction, there is another and 
 still more important circumstance to be taken into 
 consideration, which affects the ball, marbles, and 
 every body in motion. 
 
 Charles. I understand you, that is the attraction 
 of gravitation. 
 
 Father. It is ; for from what we said when we 
 conversed on that subject, it appeared that gravity 
 has a tendency to bring every body in motion to 
 the earth; consequently, in a few seconds, your 
 ball must come to the ground by that cause alone : 
 but besides the attraction of gravitation, there is 
 the resistance which the air, through which the ball 
 moves, makes to its passage. 
 
 Emma. That cannot be much, I think. 
 
 Father. Perhaps, with regard to the ball struck 
 from your brother's trap, it is of no great considera- 
 tion, because the velocity is but small ; but in all 
 great velocities, as that of a ball from a musket- or
 
 50 MECHANICS. 
 
 cannon, there will be a inateriaLdiflference between the 
 theory and practice, if it be neglected iu the calcu- 
 lation. Move my riding-whip through the air slow- 
 ly, and you observe nothing to remind you that 
 there is this resisting medium; but if you swing 
 it with considerable swiftness, the noise which 
 it occasions will inform you of the resistance it 
 meets with from something, which is the atmo- 
 sphere. 
 
 Charles. If I now understand you, the force 
 which compels a body in motion to stop, is of three 
 kinds; (1.) the attraction of gravitation; (2.) the 
 resistance of the air; and (3.) the resistance it 
 meets with from friction. 
 
 Father. You are quite right. 
 
 Charles. I have no difficulty in conceiving, that 
 a body in motion will not come to a state of rest, 
 till it is brought to it by an external force acting up- 
 on it in, some way or other. I have seen a gentleman, 
 when skaiting on very slippery ice, go a great way 
 without any exertion to himself; but where the ice 
 was rough, he could not go half the distance without 
 making fresh efforts. 
 
 Father. I will mention another instance or two 
 of this law of motion. Put a bason of water into 
 your little sister's cart on even ground, and when the 
 water is perfectly still, move the cart, and the water, 
 resisting the motion of the vessel, will at first rise up 
 in the direction contrary to that in which the vessel
 
 LAW8;OF MOTION. 57 
 
 moves. If, when the motion of the vessel is com- 
 municated to the water, you suddenly stop the cart, 
 the water, in endeavouring to continue the state of 
 motion, rises up on the opposite side, j^&i $tf% 
 
 In like manner, if while you are sitting quietly 
 on your horse, the animal starts forward, you will 
 be in danger of. falling off backward; but if, while 
 you are galloping along, the animal stops on a sud- 
 den, you will he liable to be thrown forward. 
 
 Charles. This I know" by experience, but I was 
 not aware of the reason of.it till to-day. 
 
 Father. One of the first, and not least important 
 uses of the principles of natural philosophy is, that 
 they may be applied to, and will explain many of 
 the common concerns of life. 
 
 \Ve now come to the second law of motion, which 
 is; " that the change of motion is proportional 
 to the force impressed, and in the direction of that 
 force" 
 
 Charles. There is no difficulty in this : for if while 
 my cricket-bail is rolling along after Henry has 
 struck it, I strike it again, it goes on with increased 
 velocity, and that in proportion to the strength which 
 I exert on the occasion; whereas, if r while it is roll- 
 ing,! strike it back again, or give it a side blow, I 
 change the direction of its course. ,&?& 
 
 Father. In the same way. gravity, and the resist- 
 ance of the atmosphere, change the direction of a 
 cannon-ball from its course in a straight line, and 
 
 Q
 
 58 MECHANICS. 
 
 bring it to the ground ; and the ball goes to a farther 
 or less distance in proportion to the quantity of 
 powder used. 
 
 The third law of motion is ; u that to every ac- 
 tion of one body upon another, there is an eqval and 
 contrary re-action." If I strike this table, I commu- 
 nicate to it (which you perceive by the shaking of 
 the glasses) the motion of my hand : and the table 
 re-acts against my hand, just as much as my hand 
 acts against the table. 
 
 If you press with your finger one scale of a ba- 
 lance, to keep it in equilibrio with a pound weight 
 in the other scale, you will perceive, that the scale 
 pressed by the finger acts against it with a force 
 equal to a pound, with which the other scale endea- 
 vours to descend. 
 
 In all cases the quantity of motion gained by 
 one body is always equal to that lost by the other 
 in the same direction. Thus, if a ball in motion 
 strike another at rest, the motion communicated to 
 the latter will be taken from the former, and the 
 velocity of the former will be proportionally dimi- 
 nished. 
 
 A horse drawing a heavy load is drawn back by 
 tlte load with a force exactly equal to what he 
 exerts in drawing it forward. 
 
 Emma. 1 do not comprehend how the cart draws 
 the horse. 
 
 Father. But the progress of the horse is impeded
 
 LAWS OF MOTION. 59 
 
 by the load, which is the same thing: for the force 
 which the horse exerts whoukl carry him to a greater 
 distance in the same time, were he freed from the 
 encumbrance of the load ; and therefore, as much as 
 bis progress falls short of that distance, so much is 
 
 he, in effect, drawn back by the re-action of the 
 
 i j j &&* 
 
 loaded cart. 
 
 Again, if you and your brother were in a boat, and 
 if, by means of a rope, you were to attempt to draw 
 another to you, the boat in which you were would 
 be as much pulled toward the empty boat as that 
 would be moved to you ; and if the weights of the 
 two boats were equal, they would meet in a point 
 half way between the two. 
 
 If you strike a glass bottle with an iron ham- 
 mer, the blow will be received by the hammer and 
 the glass ; and it is immaterial whether the hammer 
 be moved against the bottle at rest, or the bottle be 
 moved against the hammer at rest, yet the bottle 
 will be broken, though the hammer be not injured, 
 because the same blow, which is sufficient to break 
 glass, is not sufficient to break or injure a mass of 
 iron. 
 
 From this law of motion you may learn in what 
 manner a bird, by the stroke of its wings, is able to 
 support the weight of its body. v ^ 
 
 Charles. Pray explain this, papa. 
 
 Father. If the force with which it strikes the air 
 below it is equal to the weight of its body, then the
 
 MECHANICS. 
 
 re-action of the air upwards is likewise equal to it; 
 and the bird, being acted upon by two equal forces 
 in contrary directions, will rest between them. If 
 the force of the stroke is greater than its weight, 
 the bird will rise with the difference of these two 
 forces : and if the stroke be less than its weight, then 
 it will sink witK the difference.
 
 LAWS OF MOTION. 
 
 CONVERSATION XII. 
 
 On the Lates of Motion. 
 
 CHARLES. Are those laws of motion which 
 you explained yesterday of great importance in natu- 
 ral philosophy ? 
 
 l<al/ter> Yes, they are, and should be carefully com- 
 mitted to memory. They were assumed by Sir Isaac 
 jNewton, as the fundamental principles of mechanics, 
 and you will find them at the head of all books writ- 
 ten on these subjects. From these also, we are na- 
 turally led to some other branches of science, which 
 though we can only slightly mention, should not be 
 wholly neglected. They are, in fact, but corollaries 
 to the laws of motion. 
 
 Emma. What is a corollary, papa ? 
 
 Father. It is nothing more than some truth clear- 
 ly deducible from some other truth before demou- 
 8trated*or admitted. Thus, by the first law of mo- 
 tion, every body must endeavour to continue in the 
 state into which it is put, whether it be of rest, or 
 uniform motion in a straight line: from which it 
 follows, as a corollary, " that when we see a body 
 R
 
 62 MECHANICS. 
 
 move in a curved line, it must, be acted upon by at 
 least two forces." 
 
 Charles. When I whirl a stone round in a sling, 
 what are the two forces which act upon the stone? 
 
 Father. There is 'the force, by which, if you let 
 go the string, the stone will fly off in a right line ; 
 and there is the force j)f the. hand that holds the 
 string, which keeps it in a circular motion. 
 
 Emma. Are there any of these circular motions 
 in nature ? 
 
 Father. The moon, and all the planets move by 
 this law :_ to take the nioon.as an instance. It has 
 a constant tendency to the earth, by the attraction 
 pf gravitation, and it has also a tendency to pro- 
 ceed in a right line, by that projectile force impress- 
 ed upon it by the Creator, in the same manner as the 
 stone flies from your hand;; now, by the joint ac- 
 Jion of these two forces, it describes a circular mo- 
 tion. 
 
 Emma. . And what would be the consequence, sup- 
 posing the projectile force to cease ? 
 
 Father. The moon must ffcfl to the earth; and 
 if the force of gravity were to cease acting upon the 
 moon, it would fly off into infinite space, moving on 
 in a straight line, which is called a tangent to the 
 curve, from its just touching the curve at the point 
 from which it is drawn. Now the projectile force, 
 when applied to the plane, is called the centrifugal 
 force, a# having a tendency to recede or fly from the 
 
 1 v beds cm t 
 

 
 LAW'S OF MOTION. k 63 
 
 centre ; and the* other force is termed the centripetal 
 force, from its tendency to some point as a centre. 
 
 Charles. And all this is in consequence of the in- 
 activity of matter, by which bodies have a tendency 
 to continue in the same state they are in, whether of 
 rest or motion ? 
 
 Father. You are right; and this principle, which 
 Sir Isaac Newton assumed to be in all bodies, he 
 called their vis inertia, to which we have before 
 referred. 
 
 Cliarles. A few mornings ago, you showed us, that 
 the attraction of the earth upon the moon * is 3,600 . 
 times less than it is upon heavy bodies near the 
 earth's surface. Now, as this attraction is measured 
 by the space fallen through in a given time, I have 
 endeavoured to calculate the space which the moon 
 would fall through in a minute, were the projectile 
 force to cease. 
 
 Father. Well, and how have you brought it out? 
 
 Charles. A body falls here 16 feet in the first se- 
 cond, consequently in a minute, or 60 seconds, it 
 would fall 60 times 60 feet, multiplied by 16, that is 
 3,600 feet multiplied by 16 ; and as the moon would 
 fall through 3,600 times less space in a given time 
 than a body here, it would fall only 16 feet in the 
 first miyiute. 
 
 Father. You calculation is accurate. 1 will recal 
 to your mind the second law, by which it appears, 
 
 * See Conversation IV.
 
 64 MECHANICS. 
 
 that every motion or change of motion produced in a 
 body, must be proportional to and in the direction oj 
 the force impressed. Therefore, if a moving body re- 
 ceives an impulse in the direction of its motion, its 
 velocity will be increased ; if in the contrary direc- 
 tion, its velocity will be diminished ; but if the force 
 Ue impressed in a direction oblique to that in which 
 it moves, then its direction will be between that of 
 its former motion, and that of the new force im- 
 pressed. 
 
 Charles. This I know from the observations I 
 have made with my cricket-ball. 
 
 Father. By this second law of motion, you will 
 easily understand, that if a body at rest receives 
 two impulses, at the same time, from forces whose 
 directions do hot Coincide, it will by (heir joint 
 action be made to move in a line that lies between 
 the direction of the forces impressed. 
 
 Emma. Have you any machine to prove this sa- 
 tisfactorily to the senses? 
 
 Father. There are many such, invented by differ- 
 ent persons, descriptions of which you will hereaf- 
 ter find in various books on these subjects. But it is 
 easily understood by a figure. If on the ball A 
 (Plate II, Fig. 14) a force be impressed, sufficient to 
 make it move with an uniform velocity to the point u, 
 in a second of time ; and if another force be also im- 
 pressed on the ball, which alone would make it move 
 to the point c, in the same time ; the ball, by means of
 
 LAW* OF MOTION. 65 
 
 the two forces, will describe the line AD, which is a 
 diagonal of the figure whose sides are AC and AB. 
 
 Charles. How then is motion said to be produc- 
 ed in the direction of the force : according to the se- 
 cond law, it ought to be, in one case, in the direc- 
 tion AC, and, in the other, in that of AB, whereas it 
 is in that of AD. 
 
 Father. Examine the figure a little attentively, 
 and you will perceive that the body has moved to- 
 wards tlie side or direction c as far as if it had been 
 carried along the line AC ; and also towards the side 
 B as far as if it had moved on the line AB. 

 
 MECHANICS. 
 
 CONVERSATION XIII. 
 
 On the Latvs of Motion. 
 
 
 FATHER. If you reflect a little upon what 
 we said yesterday ou the second law of motion, and 
 compare it with the figure, you will readily deduce 
 the follpwing corollaries. (Plate II, Fig. 14.) 
 
 1. That, if the forces be equal, and act at right 
 angles to one another, the line described by the ball 
 will be the diagonal of a square. But in all other 
 cases it will be the diagonal of a parallelogram of 
 some kind. 
 
 2. By varying the angle and the forces, you vary 
 the form of your parallelogram. 
 
 Charles. Yes, papa; and 1 see another conse- 
 quence, viz. that the motion of two forces acting 
 conjointly in this way are not so great as when they 
 act separately. 
 
 Father. That is true, and you are led to the con- 
 clusion, I suppose, from the recollection, that in e- 
 very triangle any two sides taken together are greater
 
 LAWS OF MOTION*. 67 
 
 than the remaining side ; and therefore you infer,, and 
 justly too, that the motions which the ball A must 
 have received, had the forces been applied separate- 
 ly, would have been equal to AC and AJ$, or, which 
 is the same thing, to AC and CD, the two sides of the 
 triangle ADC ; but by their joint action the motion is 
 only equal to AD, the remaining side of the tri- 
 angle. 
 
 Hence then you will remember, that in the com- 
 position, or adding together of forces (as this is cal- 
 led), motion is always lost : and in the resolution of 
 any one force, as AD, into two other, AC, and AB, mo- 
 tion is gained. 
 
 Charles. Well, papa, but how is it that the hea- 
 venly bodies, the moon for instance, which is im- 
 pelled by two forces, performs her motion in a cir- 
 cular curve round the earth, and not in a diagonal 
 between the direction of the projectile force and 
 that of the attraction of gravity to the earth. 
 
 Father. Because when a body moved by a pro- 
 jectile force is turned away by a single impulse from 
 its original direction, it wfll continue to move in that 
 new line ; and a second application of the same im- 
 pulse again changes that new direction as far as the 
 first did, and so on. Thus the action of the earth's 
 attraction continually draws the moon from the new 
 direction in which she is every moment ready to fly 
 off; and this continual and uniform deflection from 
 a straight line forms a circular curve.
 
 68 MECHANICS. 
 
 The third law of motion, viz. that action and re- 
 action are equal and in contrary directions, may be 
 illustrated by the motion communicated by the per- 
 cussion of elastic and non-elastic bodies. 
 
 Emma. What are these, papa r 
 
 Father. Elastic bodies are those which have a 
 certain spring, by which their parts, upon being 
 pressed inwards, by percussion, return to their for- 
 mer state ; this property is evident in a ball of wool 
 or cotton, or in sponge compressed. JV on -elastic 
 bodies are those which, when one strikes another, 
 do not rebound, but move together, after the stroke. 
 
 Let two equal ivory balls a and b be suspended 
 by threads ; if a (Plate II, Fig. 15) be drawn a lit- 
 tle out of the perpendicular, and let fall upon b, it 
 will lose its motion by communicating it to b, which 
 will be driven to a distance c, equal to that through 
 which a fell ; and hence it appears that the re-ac- 
 tion of b was equal to the action of a upon it. 
 
 Emma. But do the parts of the ivory balls yield 
 by the stroke, or, as you call it, by percussion ? 
 
 Father, They do ; for if 1 lay a little paint on , 
 and let it touch b, it will make but a very small 
 speck upon it : but if it fall upon b, the speck will 
 be much larger ; which proves that the balls are 
 elastic, and that a little hollow, or dint, was made 
 in each by collision. If now two equal soft balls of 
 clay, or glazier's putty, which are non-elastic, meet 
 each other with equal velocities, they would stop
 
 LAWS OF MOTION. fo 
 
 and stick together at the place of their meeting, as 
 their mutual actions destroy each other. 
 
 Charles. I have sometimes shot my white alley 
 against another marble so plumply, that the marble 
 Jias gone off as swiftly as the alley approached it, 
 but the alley remained motionless in the place of 
 the marble. Are marbles, therefore, as well as ivo- 
 ry, elastic ? 
 
 Father. They are. If three elastic balls, a, b, c 
 (Plate ill, Fig. 16), be hung from adjoining centres, 
 and c be drawn a little out of the perpendicular, and 
 let fall upon 6, then will c and b become stationary, 
 and will be driven to o, the distance through which 
 c fell upon b. 
 
 If you hang any number of balls, as six, eight, Sec. 
 so as to touch each other, and if you draw the out- 
 side one away to a little distance, and then let it 
 fall upon the others, the ball on the opposite side 
 will be driven off while the rest remain stationary, 
 o equal is the action and re-action of the stationa- 
 ry balls divided among them. In the same manner, 
 if two are drawn aside and suffered to fall on the 
 rest, the opposite two will fly off, and the others 
 remain stationary. 
 
 There is one other circumstance depending upon 
 the action and re-action of bodies, and also upon 
 the vis inertia of matter, worth noticing : by some 
 authors you will find it largely treated upon. 
 
 If I strike a blacksmith's anvil with a hammer, 
 T
 
 70 F MECHANICS. 
 
 action and re-action being equal, the anvil strikes the 
 hammer as forcibly as the hammer strikes the anvil. 
 
 If the anvil be large enough, I might lay it on my 
 breast, and suffer you to strike it with a sledge ham- 
 mer with all your strength, without pain or risque, 
 for the vis inertia of the anvil resists the force of 
 the blow. But if the anvil were but a pound or 
 two in weight, your blow would probably kill me. 
 
 Emma. Is it owing to this principle, that when a 
 cannon on wheels is fired, it runs backward ? 
 
 Father. It is ; for the action of the powder is as 
 much exerted on the gun, as on the ball, but their 
 motions are contrary ; the ball moves forward and 
 the cannon backward. 
 
 \ ,
 
 MECHANICAL POWERS. 71 
 
 CONVERSATION XIV. 
 
 O fAe Mechanical Powers. 
 
 CHARLES. Will you now, papa, explain the 
 mechanical powers ? 
 
 Father. I will, and I hope you have not forgotten 
 what the momentum of a body is? 
 
 Charles. No ; it is the force of a moving body, 
 which force is estimated by the weight, multiplied 
 into its velocity. 
 
 Father. Then a small body may have an equal 
 momentum with one much larger? 
 
 Charles. Yes, provided the smaller body moves 
 as much swifter than the larger one, as the weight 
 of the latter is greater than that of the former. 
 
 Father. What do you mean when you say, that 
 one body moves swifter, or has a greater velocity 
 than another ? 
 
 Charles. That it passes over a greater space in 
 the same time. Your watch will explain my mean- 
 ing: the minute-hand travels round the dial-plate in 
 an hour, but the hour-hand takes twelve hours to 
 perform its course in, consequently the velocity of
 
 72 MECHANICS. 
 
 the minute-hand is twelve times greater than that of 
 the hour-hand ; because, in the same time, viz. twelve 
 hours, it travels twelve times the space that is gone 
 through by the hour-hand. 
 
 Father. But this can be only true on the supposi- 
 tion, that the two circles are equal. In my watch, 
 the minute hand is longer than the other, and, con- 
 sequently, the circle described by it is larger than 
 that described by the hour-hand. 
 
 Charles. I see at once, that my reasoning holds 
 good only in the case where the hands are equal. 
 
 Father. There is, however, a particular point of 
 the longer hand, of which it may be said, with the 
 strictest truth, that it has exactly twelve times the 
 velocity of the extremity of the shorter. 
 
 Charles. That is the point, at which, if the remain- 
 der were cut off, the two hands would be equal. 
 And, in fact, every different point of the hand de- 
 scribes different spaces in the same time. 
 
 Father. The little pivot on which the two hands 
 seem to move (for they are really moved by differ- 
 ent pivots, one within another) may be called the 
 centre of motion, which is a fixed point; and the 
 longer the hand is, the greater is the space de- 
 scribed. 
 
 Charles. The extremities of the vanes of a wind- 
 mill, when they are going very fast, are scarcely 
 distinguishable, though the separate parts, nearer 
 the mill, are easily discerned ; this is owing to the
 
 UZCHA-NICAL POWLES. 73 
 
 velocity of ihe extremities being so much greater 
 than that of the other parts. 
 
 Ewina,. Did not the swiftness of the round-ahouts 
 which we saw at the fair, depend on the same prin- 
 ciple, viz. the length of the poles upon which the 
 sen ts were fixed? 
 
 Father. Yes, the greater the distance at which 
 tljese seats were placed from the centre of motion, 
 the greater was the space which the little boys and 
 girls travelled for their half-penny. 
 
 Emma. Then those in the second row had a shorter 
 ride for their money, than those at the end of the poles? 
 
 Father. Yes, shorter as to space, but the same as 
 to time. In the same way, when you and Charles 
 go round the gravel-walk for half an hour's exer- 
 cise, if he run while you- walk, he will, perhaps, 
 have gone six or eight times round, in the same time 
 that you have been but three or four times ; now, as 
 to time, your exercise has- been equal, but he may 
 have passed over double the space in the same time. 
 
 Charles. How does this apply to the explanation 
 of the mechanical powers? 
 
 Father. You will find the application very easy: 
 without clear ideas of what is meant by time and 
 space, yeu cannot comprehend the principles of me* 
 chars ics. 
 
 There are six mechanical powers. The lever; 
 the wheel and axle; the pulley; the inclined plane; 
 the wedge ; and thtj .screw. 
 u
 
 74 MECHANICS. 
 
 JSmma. Why are they called mechanical powers ? 
 
 Father. Because, by their means, we are enabled 
 mecJianically to raise weights, move heavy bodies, 
 -and overcome resistances, which, without their as* 
 Distance, could not be done. 
 
 Cliarles. But is there no limit to the assistance 
 gained by these powers ? for I remember reading of 
 Archimedes, who said, that with a place for his ful^ 
 cruin he could move the earth itself. 
 
 JEimna. What is/a fulcrum ? 
 
 fat/ier. It is & fixed point, or prop, round which 
 the other parts- of a machine move. 
 ;<,; Charles. Is the pivot, upon which the hands of 
 your watch move, a fulcrum, then? 
 
 father. It is, and you remember we called it 
 alsa the centre of motion ; the rivet of these seissars 
 is also a fulcrum. 
 
 Emma. Is that a fixed point or prop? 
 
 Father. Certainly it is a / fixed point, as it re- 
 gards the two parts of the scissars ; for that always 
 remains in the same position, while the other parts 
 move about it. You will now understand that human 
 power, with all the assistance which art can give, is 
 Tery soon limited, and upon this principle, that what 
 \ we gain in power, we lose in velocity. That is, if by your 
 own unassisted strength, you are able to raise fifty 
 pounds to a certain height in one minute, and if by the 
 help of machinery, you wish to raise 50O pounds to the 
 same height, you will require ten minutes to perform
 
 MECHANICAL POWERS. 75 
 
 it in, or else you must move yourself ten times faster 
 than before; thus you increase your power tenfold, 
 but it is at the expense of velocity as measured by 
 time multiplied into space. Or, in other words, you 
 are enabled to do that with one effort in ten minutes, 
 which you could have done in ten separate efforts ia 
 the same time. 
 
 Emma. The importance of mechanics, then, is not 
 so very considerable as one, at first sight, would 
 imagine : since there is no real gain of force acquir- 
 ed by the mechanical powers. r ^ 
 
 Father. Though there be not any actual increase 
 of force gained by these powers, yet the advantages 
 which men derive from them are inestimable. If 
 there are several small weights, manageable by hu- 
 man strength, to be raised to a certain height, it may 
 be full as convenient to elevate them one by one, as 
 to take the advantage of the mechanical powers ia 
 raising them all at once. Because, as we have 
 shown, the same time will be necessary in both cases. 
 But suppose you have a large block of stone of a toa 
 weight to carry away, or a weight still greater, 
 what is to be done ? 
 
 Emma. I did not think of that. 
 * Father. Bodies of this kind cannot be separated 
 into parts proportionable to the human strength 
 without immense labour, nor, perhaps, without ren- 
 dering them unfit for those purposes to which they 
 are to be applied. Hence then you perceive the
 
 76 MECHANICS. 
 
 great importance of the mechanical powers, by the 
 use of which a man is able with ease to manage a 
 weight many times greater than himself. 
 
 Charles. I have, indeed, seen a few men, 
 by means of pulleys, and apparently with no very 
 great exertion, raise an enormous oak tree into a 
 timber-carriage, in order to convey it to the dock- 
 yard. 
 
 Father. A very excellent instance ; for, if the 
 tree had been cut into such pieces as could have 
 been managed by the natural strength of these men, 
 it would not have been worth carrying away for the 
 purpose of ship-building. 
 
 Emma. I acknowledge my error. 

 
 OF THE LEVEK. 77 
 
 CONVERSATION XV. 
 
 Of the Lever. 
 
 FATHER. We will now consider the Le~ 
 ver, which is generally called the first mechanical 
 power. 
 
 The lever is any inflexible bar of wood, iron, &c., 
 which serves to raise weights, while it is supported 
 at a point by a prop or fulcrum, on which, as the 
 centre of motion, all the other parts turn. AB (Plate 
 III, Fig. 17,) will represent a lever, and the point 
 c the fulcrum or centre of motion. Now, it is 
 evident, if the lever turn on its centre of motion 
 c, so that A comes into the position a ; B at the - 
 same time must come into the position b. If .both 
 the arms of the lever be equal, that is, if AC is equal 
 to BC, there is no advantage gained by it, for they 
 pass over equal spaces in the same time ; and, ac- 
 cording to the fundamental principle already laid 
 down (p. 127;, " as advantage or power is gained, 
 velocity must be lost,'* therefore, no velocity being 
 lost by a lever of this kind, there can be no power 
 gained.
 
 78 MECHANICS. 
 
 Cltarles. Why then is it called a mechanical 
 power? 
 
 Father. Strictly speaking perhaps it ought not to 
 be 'numbered as one. But it is usually reckoned 
 among them, having the fulcrum between the weight 
 and the power, which is the distinguishing property 
 of levels of the first kind. And, when the fulcrum 
 is exactly the middle point between the weight and 
 power, it is the common balance : to which, if scales 
 be suspended at AB, it is fitted for weighing all sorts 
 of commodities. 
 
 Emma. You say it is a lever of the first kind, 
 are there several sorts of levers ? 
 
 Father. There are three sorts; some persons 
 reckon four; the fourth, however, is but a bended 
 one of the first kind. A lever of tfle first kind (Plate 
 III, Fig. 18, 19) has the fulcrum between the weight 
 and power. 
 
 The second kind oflever (Plate III, Fig. 20) has 
 the fulcrum at one eud, the power at the other, and 
 the weight between them. 
 
 In the third kind (Plate III, Fig. 21) the power is 
 between the fulcrum and the weight. 
 
 Let us take the lever of the first kind (Fig. 18), 
 which, if it be moved into the position ab, by turn- 
 ing on its fulcrum c, it is evident that while A has tra- 
 velled over the *hort space A a, B has travelled over 
 the greater space B b, which spaces are to one an- 
 ther, exactly in proportion to the length of the arms
 
 OF THE LEVER. 79 
 
 AC and BC. Tf now you apply your hand first to the 
 point A, and afterwards to B, in order to move the le- 
 ver into the position a b, using the same velocity in 
 both cases, you will find, that the time spent in mov- 
 ing the lever when the hand is at B, will be as much 
 greater as that spent when the hand is at A, as the 
 arm iu: is longer than the arm AC, but then the ex- 
 ertion required will, in the same proportion, be less 
 at B than at A. 
 
 Charles. The arm BC appears to be four times the 
 length of AC. 
 
 Father. Then it is a lever which gains power in 
 the proportion of four to one. That is, a single pound 
 weight applied to the end of the arm BC, as at p, 
 will balance four pounds suspended at A, as w. 
 
 Charles. 1 have seen workmen move large pieces 
 of timber to very small distances, by means of a long 
 bar of wood or iron ; is that a lever? 
 
 Father. It is ; they force one end of the bar un- 
 der the timber, and then place a block of wood, 
 stone, &c., beneath, and as near the same end of the 
 lever as possible, for a fulcrum, applying their own 
 strength to the other : and power is gained in propor- 
 tion as the distance from the fulcrum to the part where 
 the men apply their strength, is greater than the dis- 
 tance from the fulcrum to that end under the timber. 
 
 Charles. It must be very considerable, for I have 
 seen two or three men move a tree, in this way, of 
 several tons weight I should think.
 
 CO MECHANICS. 
 
 Father. That is not difficult ; for supposing a le- 
 ver 10 gain the advantage of twenty to one, and a 
 man by his natural strength is able to move but a 
 Jiundred weight, he will find that by a lever of this 
 s<ort lie can move twenty hundred weight, or a ton ; 
 but for single exertions, a strong man can put forth 
 a much greater power, than that which is suffici- 
 ent to remove a hundred weight; and levers are 
 also frequently used, the ' advantage gained by 
 which is still more considerable than twenty to 
 one. 
 
 Charles. I think you said, the other day, that 
 the common steelyard made use of by the butcher, 
 is a lever? 
 
 Father. I did; the short arm AC (Plate III, Fig. 
 19) is, by an increase in size, made to balance the 
 longer one BC, and from c, the centre of motion, 
 the divisions must commence. Now if BC be divid- 
 ed into as many parts as it will contain, each equal 
 to AC, a single weight, as a pound p, will serve for 
 weighing any thing as heavy as itself, or as many 
 times heavier as there are divisions in the arm c. 
 If the weight p be placed at the division 1, in the 
 arm BC, it will balance one pound in the scale at 
 A ; if it be remaved to 3, 5, or 7, it will balance 3, 
 5, or 7 pounds in the scale; for these divisions be- 
 ing respectively 3, 5, or 7 times the distance from 
 He centre of motion c that A is, it becomes a lever, 
 which gains advantage at those points, in the
 
 OF THE LEVER. 61 
 
 proportion of 3, 5, and 7. If now the intervals 
 between the divisions on the longer arm be subdi- 
 vided into halves, quarters, &c., any weight may 
 be accurately ascertained to halves, quarters of 
 a pound, &c. 
 
 .-iil; 
 Mfed .7 
 
 '.
 
 82 
 
 MECHANICS, 
 
 . ib' 
 
 t .3&"3i0*J ;*fi 
 
 ntiii<p CONVERSATION XVI. 
 
 Of the Lever. 
 
 EMMA. What advantage has the steel-yard, 
 which you described in our last conversation, over 
 a pair of scales ? 
 
 Father. It may be much more readily removed 
 from place to place ; it requires no apparatus, and 
 only a single weight for all the purposes to which 
 it can be applied.' Sometimes the arms are not of 
 equal weight: in that case the weight P must be 
 moved along the arm uc, till it exactly balance the 
 other arm without a weight; and in that point a 
 notch must be made, marking over it a cipher 0, 
 from whence the divisions must commence. 
 
 Charles. Does there require great accuracy in the 
 manufacture of instruments of this kind ? 
 
 Father. Yes ; of such importance is it to the pub- 
 lic, that there should be no error or fraud by means 
 of false weights, or false balances, that it is the busi- 
 ness of certain public officers to examine at stated 
 seasons the weights, measures, &c. of every shop- 
 keeper in the land. Yet it is to be feared, that af-
 
 OF THE LEVER. 03 
 
 ter all precautions, much fraud is practised upon 
 the unsuspecting. 
 
 Emma. I one day last summer bought, as I sup- 
 posed, a pound of grapes at the door, but Charles 
 thinking there were not a pound we tried them in 
 your scales, and found but twelve ounces, or three 
 quarters, instead of a pound, and yet the scale went 
 down as if the man had given me full weight. How 
 was that managed ? 
 
 Father. It might be done many ways : by short 
 weights : or by the scale in which the fruit was 
 put being heavier than the other. But fraud 
 may be practised with honest weights and scales, 
 by making the arm of the balance on which the 
 weight hangs shorter than the other, for then a pound 
 weight will be balanced by as much less fruit than 
 a pound, as that arm is shorter than the other; this 
 was probably the method by which you were 
 cheated. 
 
 Emma. By what method could I have discover- 
 ed this cheat? 
 
 Father. The scales when empty are exactly ba- 
 lanced, but when loaded, though still in equilibrio, 
 the weights are unequal, and the deceit is instantly 
 discovered by changing the weights to the contrary 
 scales. I will give you a rule to find the true weight 
 of any body by such a false balance, the reason of 
 the rule you will understand hereafter: " Find the 
 weights of the body by both scales, multiply them to-
 
 84 MECHANICS. 
 
 get her, and then find the tquareroet of the product, 
 which is the true weight:' 
 
 ; Charles. Let me see if I understand the rule : 
 suppose a body weigh 16 ounces in one scale, and 
 in the other 12 ounces and a quarter, I multiply 16 
 by 12 and a quarter, and I get the product 196, the 
 square root of which is 14: for 14 multiplied into 
 itself gives 196; therefore the true weight of the 
 body is 14 ounces. 
 
 Father. That is just what I meant. To the lever 
 of the first kind maybe referred many common in- 
 struments, such as scissars, pincers, snuffers, &c., 
 which are made by two levers, acting contrary to 
 one another. \ .4,, > 
 
 Emma. The rivet is the fulcrum, or centre of mo- 
 tion, the hand the power used, and whatever is to 
 be cut is the resistance to be overcome. 
 
 Father. We now proceed to levers of the second 
 kind, in which the fulcrum c (Fig. 20) is at one end, 
 the power p applied at the other w, and the weight 
 to be raised w, somewhere between the fulcrum 
 and the power. 
 
 Charles. And how is the advantage gained to be 
 estimated in this lever? 
 
 /r/v ^'^':,Ti i -.- <. i* $ 
 
 father. By looking at the figure you will find that 
 power or advantage is gained in proportion as the 
 distance B, the point at which the power p acts, is 
 greater than the distance of the weight ,w from the 
 fulcrum.
 
 OF THE LBVEft. 55 
 
 Charles. Theft if tbe weight hang at one inch from 
 the fulcrum, and the power acts at five inches from 
 it, the power gained is five to one, or one pound at 
 p will balance five at w ? 
 
 Father. It will i for you perceive that the 
 power passes over five times as great a space as 
 the weight, or while the point A in the lever 
 moves over one inch, the point B will move over 
 five inched. 
 
 Emma. What things in common use are be refer- 
 red to the lever of the second kind ? 
 
 Father. The most common and useful of all 
 things ; every door, for instance, which turns on 
 hinges is a lever of this sort. The hinges may be 
 considered as the fulcrum or centre of motion, the 
 whole door is the weight to be moved, and the 
 power is applied to that side on which the lock is 
 usually fixed. 
 
 Emma. Now I see the reason why there is con- 
 siderable difficulty in pushing open a heavy door, if 
 the hand is applied to the part next the hinges, aU 
 though it may be opened with the greatest ease ia 
 the usual method. 
 
 Father. To the second kind of lever may be re- 
 duced nut-crackers; oars; rudders of ships; those 
 cutting-knives which have one end fixed in a block, 
 such as are used for cutting chaff, drugs, wood fov 
 patteps, &c.
 
 80 .MECHANICS 
 
 Emma. I do not see how oars and rudders are 
 levers ofthisrsort. * - 
 
 Father. The boat i the weight to be moved, the 
 water is the fulcrum, and the waterman at the han- 
 dle the power. The;inasts. of ships are also levers 
 of the second kind, for the bottom of the vessel is 
 the fulcrum, the ship the weight, and the wind acting 
 agajnst the sail is the movipg power. ., . ,,-0 a 
 
 The knowledge of this principle may be useful in 
 many situations and circumstances of life: If two 
 men unequal in strength have a heavy burden to 
 carry .on a pole between them, the ability of each 
 may be, consulted by placing the burden as much 
 nearer to the stronger man, as his strength is greater 
 than that of his partner. 
 
 Emma. Which would you call the prop in this 
 
 case - . '.;w m> ^':cdt*rl': 
 
 Father. The stronger man, for the weight is 
 nearest to him, and then the .weaker must , be consi- 
 dered as the power. Again, two horses may be so 
 yoked to a carriage that each shall draw a part pro- 
 portional to his strength, by dividing the beam in 
 such a manner, that the point of traction, or draw- 
 ing, may be as- much nearer to the stronger horse 
 than to the weaker, as the strength of the former ex- 
 ceeds that of the latter. 
 
 We will now describe the third kind of lever. In 
 this the prop or fulcrum c (Fig. 21) is at one end,
 
 OF THE LEVR. 87 
 
 the weight w at the other, and the power- P is 
 applied at B, somewhere between the prop and 
 
 weight.. x. A ' is es . 
 
 Charles. In this case, the weight being ifarther 
 from the centre of motion than the power, must pass 
 through more space than it. 
 
 Father. And what is the consequence of that? 
 Charles. That the power must be greater than 
 the weight, and as much greater as the distance of 
 the weight from the-^prop exceeds the distance 
 of the power from it, that is, to balance a weight 
 of three pounds at A^ .there will require the 
 exertion of a power P, acting at B, equal to five 
 pounds. _^___^ 
 
 Father. Since then' a lever of this kind is a dis- 
 advantage to the moving power, it is but seldom 
 used, and only in cases of necessity ; such as in 
 that of a ladder, which being fixed at one end against 
 a wall or other obstacle, is, by the strength of a 
 man's arm, raised into a perpendicular situation. 
 But the most important application of this third kind 
 of lever is manifest, in the structure of the limbs of 
 animals, particularly in those of man; to take the 
 arm as an instance ; when we lift a weight by the 
 hand, it is effected by means of muscles coming 
 from the shoulder blade, and terminating about 
 one-tenth as far below the elbow as the hand is : 
 pow the elbow being the centre of motion round
 
 Bit MECHANICS. '' 
 
 which the lower part of the arm turns, according 
 to the principle just laid down, the muscles must 
 exert a force ten times as great as the weight 
 that is raised. At first Tiew, this may appear a dis- 
 advantage, but -what is lost in power is gained in 
 velocity, and thus the human figure is better adapt-? 
 ed to the Yarious junctions it has to perform. 
 
 ! 01 
 
 T : -r-i/tit r.s*'. r 3 
 :? r it3^i >] ^jfii'/'>m ^i 
 
 ^r>^^.. 
 t ; .' Offl 
 
 . : ,ttiis ." 

 
 OF THE WHEEL AND AXIS, 89 
 
 CONVERSATION XVIL 
 
 Of t/ie Wheel and Axis. 
 
 FATHER. Well, Emma, do you understand 
 the principle of the lever, which we discussed so 
 much at large yesterday ? 
 
 Emma. The lever gains advantage, in proportion, 
 to space passed through by the acting power ; that is, 
 if the weight to be raised be at the distance of one 
 inch from the fulcrum, and the power is applied nine 
 inches distant from it, then it is a lever, which gains 
 advantage as 9 to J, because the space passed 
 through by the power is nine times greater than that 
 passed through by the weight ; and, therefore, what 
 is lost in time by passing through a greater space, 
 is gained in power. 
 
 Father. You recollect, also, what the different 
 kinds of levers are, I hope. 
 
 Epnma. I shall never see a balance without think- 
 ing of a simple lever of the first kind ; my scissars 
 will frequently remind me of a combination of two 
 levers of the same soil. The opening and shutting 
 of the door, will prevent me from forgetting the na- 
 
 A
 
 90 MECHANICS. 
 
 ture of the lever of the second kind : and I am sure, 
 that I shall never see a workman raise a ladder 
 against a house, without recollecting the third sort 
 of lever. 
 
 Father. Can you, Charles, tell us how the princi- 
 ple of momentum applies to the lever ? 
 
 Charles. The' momentum of a body is estimated 
 by its weight, multiplied into its velocity ; and the 
 velocity must be calculated by the space passed 
 through in a given time. Now, if 1 examine the le- . 
 ver (Fig. 18, 20), and consider it as an inflexible 
 bar, turning on a centre of motion, it is evident, that 
 the same time is used for the motion both of the 
 weight and the power, but the spaces passed over 
 are very different; that which the power passes 
 through being as much greater than that passed by 
 the weight, as the length of the distance of the 
 power from the prop is greater than the distance of 
 the weight from the prop; and the velocities, being 
 as the spaces passed in the same time, must be 
 greater in the same proportion. Consequently, the 
 velocity of p, the power, multiplied into its weight, 
 will be equal to the smaller velocity of w, multiplied 
 into its weight, and thus, their momenta being equal, 
 they will balance one another. 
 
 Father. This applies to the first and second kind 
 of lever; what do you say to the third? 
 
 Charles. In the third, the velocity of the power 
 p (Fig. 21), being less than that of the weight w, it
 
 OF THE WHEEL AND AXIS. 91 
 
 is evident, in order that their momenta may be equal, 
 that the weight acting at p must be as much greater 
 than that of w, as AC is less than BC. and then they 
 will be in equilibrio. 
 
 Father. The second mechanical power is the Wheel 
 and Axis, which gains power in proportion as the 
 circumference of the wheel is greater than that of 
 the axis ; this machine may be referred to the prin- 
 ciple of the lever. AB (Plate III. Fig. 22) is the 
 wheel, QD its axis, and, if the circumference, of the 
 wheel be eight times as great as that of the axis, then 
 a single pound p will balance a weight w of eight 
 pounds. 
 
 C/tarles. Is it by an instrument of this kind th^t 
 water is drawn from those deep wells so common in 
 many parts of the country ? 
 
 Father. It is; but as in most cases of this kind 
 only a single bucket is raised at once, there requires 
 but little power in the operation, and therefore, in- 
 stead of a large wheel as AB, an iron handle fixed 
 at Q is made use of, which, you know, by its circu- 
 lar motion, answers the purpose of a wheel. 
 
 Charles. I once raised some water by a machine 
 of this kind, and I found that as the bucket ascend- 
 ed nearer the top the difficulty increased. 
 
 Father. That must always be the case, where 
 the wells are so deep as to cause, in the ascent, the 
 rope to coil more than once the length of the axis, 
 because the advantage gained is in proportion as the
 
 2 MECHANICS. 
 
 circumference of .the wheel is greater than that of the 
 axis ; so that if the circumference of the wheel be 
 12 times greater than that of the axis, 1 pound ap- 
 plied at the former will balance 12 hanging at the 
 latter ; but by the coiling of the rope round the axis, 
 the difference between the circumference of the wheel 
 and that of the axis continually diminishes, conse- 
 quently the advantage gained is less every time a 
 new coil of rope is wound on the whole length of the 
 axis'; this explains why the difficulty of drawing the 
 wate^ or any other weight, increases as it ascends 
 nearer the top. 
 
 Charles. Then by diminishing the axis, or by in- 
 creasing the length of the handle, advantage is 
 gained? f arff',^3 
 
 Father, Yes, by either of those methods you 
 may gain power, but it is very evident that the axis 
 cannot be diminished beyond a certain limit, with- 
 out rendering it too weak to sustain the weight ; nor 
 can the handle be managed, if it be constructed on 
 a scale much larger than what is commonly used. 
 
 Charles. We must then have recourse to the wheel 
 with spikes standing out of it at certain distances 
 from each other to serve as levers. 
 
 '{ t* G> t 9 i~fr 1 *&* 
 
 Father. You may by this means increase your 
 power according to your wish, but it must be at the 
 expense of time, for you know that a simple handle 
 may be turned several times while you are pulling 
 the wheel round once. To the principle of the wheel
 
 OP THE WHEEL AHD AXIS. 03 
 
 and axis, may Ite referred the capstan; windlass, 
 and all those numerous kinds of cranes which are to 
 be seen at the different wharfs on the banks of the 
 Thames. 
 
 Charles. I have seen a crane," which consists of a 
 wheel large enough for a man to walk in. 
 
 Father. In this the weight of the man, or men 
 (for there are sometimes two or three), is the moving 
 power ; for, as the man steps forwards, the part upon 
 which he treads becomes the heaviest, and conse- 
 quently descends till it be the lowest. On the same 
 principle, you may see at the door of many bird -cage- 
 makers, a bird, by its weight, give a wicker cage a 
 circular motion ; now, if there were a small weight 
 suspended to the axis of the cage, the bird by its 
 motion would draw it up, for as it hops from the 
 bottom bar to the next, its mor,ientum causes that to 
 descend, and thus the operation is performed, both 
 with regard to the cage, and to those large cranes 
 which you have seen. 
 
 Emma. Is there no danger if the man happen 
 to slip? 
 
 Father. If the weight be very great, a slip with 
 the foot may be atiended.with.very; dangerous con- 
 sequences. To prevent which, there is generally 
 fixed at one end of the axis a little wheel G (Fig. 
 22), called a rachet- wheel ; with a catch H, to fall 
 into its teeth ; this will, at any time, support the 
 weight in case of an accident. Sometimes, instead 
 
 2B
 
 94 MECHANICS. 
 
 of men walking within the great wheel, cogs are set 
 round it on the outside, and a small trundle wheel 
 made to work in the cogs, and to be turned by a 
 winch. 
 
 Charles. You said that this mechanical power 
 might be considered as a lever of the first kind. 
 
 'Father. I did; and if you conceive the wheel and 
 axis (Fig. 22) to be cut through the middle in the 
 direction AB ; FGB (Plate III, Fig. 23) will represent 
 a section of it. AB is a lever, whose centre of mo- 
 tion is c ; the weight w, sustained by the rope AW, is 
 applied at the distance CA, the radius of the axis ; 
 and the power p acting in the direction BP, is appli- 
 ed at the distance CB, the radius of the wheel ; there- 
 fore, according to the principle of the lever, the 
 power will balance the weight when it is as much 
 less than the weight, as the distance cu is greater 
 than the distance of the weight AC. 
 
 m*:qn %&
 
 OF TSS .wiAn. 5 
 
 ftV 
 
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 -''** -A:Os2 . tj* *.- 
 
 uruir-j,;^ 9 |. -. '., 
 
 -'. -d-t>j.;i>h*i ^j*^ 
 
 CONVERSATION Xtll. 
 
 O/.rt. /W%. 
 
 *~ ' "V {.- -'^4- *i JP 4V rt J 
 
 FATHER. The third mechanical power, the 
 pulley t may be likewise explained on the principle of 
 the lever. The line AB (Plate IV, Fig. 24) may be 
 conceived to be a lever, whose arms AC and BC are 
 equal, and c the fulcrum, or centre of motion. If 
 now two equal weights, w and p, be hung on: the 
 cord passing over the pulley, they will balance one' 
 another, and the fulcrum will sustain both. 
 
 Charles. This pulley then, like j the common ba- 
 lance, gives no advantage? 
 
 Father. From the single fixed pulley no mecha- 
 nical advantage is derived; it is, nevertheless, of 
 great importance in changing the direction of a 
 power, and is very much used in buildings for draw- 
 ing up small weights, it being much easier for a 
 man to raise such burdens by means of a single pul- 
 ley, than to carry them up a long ladder. 
 
 Emma. Why is it called a mechanical power? 
 
 Father. Though a single fixed pulley gives no 
 advantage, yet when it is not fixed, or when two or
 
 g MECHANICS. ; 
 
 w. v^rrv v? 
 
 more are combined into what is called s, system of 
 pulleys, they then possess all the properties of the 
 other mechanical powers. Thus in CDB (Plate IV, 
 Fig. 25) c is the fulcrum, therefore a power p, act- 
 ing at B, -will sustain a double weight w, acting at 
 A, for BC is double ^the distance of AC from the 
 fulcrum. 
 
 Again, it is evident, in the present case, that the 
 whole weight is sustained by the cord EDP, and 
 whatever sustains half the cord, sustains also half 
 the weight; but one half is sustained by the fixed' 
 hook E, consequently the power at p has only the 
 other half to sustain, or, in other words, any given 
 power at p will keep in .equilibrio a double weight 
 at w. 
 
 Charles. Is the velocity of p double that of w ? 
 
 father. Undoubtedly ; if you compare the space* 
 passed through by the hand at p with that passed . 
 by w, you will- find that the former is just double of 
 the latter, and therefore the momenta of the power 
 and weight, as in the lever, are equal. 
 
 Charles. I think I see the reason of this, for if the 
 weight be raised an inch, or a foot, both sides of 
 the cord must also be raised an inch, or foot; but 
 this cannot happen without that part of the cord at p 
 passing through two inches, or two feet of space. 
 
 Father. You will now easily infer, from what has 
 been already shown of the single moveable pulley, 
 that, in a system of pulleys, the power gaine'd must'
 
 OF THE WHEEL ANU AXIS. 97 
 
 be estimated, by doubling the number- of pulleys in 
 the lower- or moveable block. So that' when the 
 fixed block 'a? (Plate IV, Fig. 26) contains two pul- 
 leys which only turn on their axes, and the lower 
 block y contains also two pulleys, which not only 
 turn on their axes, but also rise with the weight, the 
 advantage is as four \ that is, a single pound at p wilj 
 sustain four at w. 
 
 Charles. In the present instance also I perceive, 
 that by raising w an inch, there are four ropes short- 
 ened each an inch, and therefore the hand must have 
 passed through four inches of space in raising -the 
 weight a single inch; which establishes the maxim, 
 that what is gained in velocity is lost in space. But 
 you have only talked of the power of balancing or 
 sustaining the weight, something more must, I sup- 
 pose, be added to raise it. 
 
 ^.'father. There must ; considerable allowance must 
 likewise be made for the friction of the cords, and 
 of the pivots, or axes, on which the pulleys turn. lu 
 the mechanical powers, in general, one-third of the;o 
 power must be added for the loss sustained .by 'fric- 
 tion, and for the imperfect manner in which ma- 
 chines are commonly constructed. Thus, if by theory 
 you gain a power of 600 ; in practice^ you must 
 reckon only upon 400. In those pulleys which we 
 have been describing, writers have taken notice of 
 three things, which take muchjrom the general ad- 
 vantage and convenience of pulleys as a mechanical 
 power. The fast is, that the diameters of the axes 
 2c
 
 og MECHANICS. 
 
 *?r -MIX A ~ ^" T 
 
 bear a great proportion to their own diameters. 
 second is, thai in working they are apt to rub against 
 one another, or against the side of the block. And 
 the third disadvantage is the stiffness of the rope that 
 goes over and under them. Oi ^ ; ^ s - 
 
 The first two objections have been, in a great de- 
 gree, removed by the concentric .pulley, invented by 
 Mr. James White : B (frate ' IV, Fig. 27) is a solid 
 block of brass, in which grooves are cut, in the pro- 
 portion of 1, 3, 5, 7, 9, &c., and A is anothe* 
 block of the same kind, whose grooves are in the 
 proportion of 2, 4, 6, 8, 10, &c., and round these, 
 grooves a cord is passed, by. which means they an- 
 swer the purpose of so many distinct pulleys, every 
 point of which moving with the velocity of the string 
 in contact with it, the whole friction is removed to 
 the two centres of motion of the blocks A and B: 
 besides it is of no small advantage, that the pulleys, 
 being all of one piece, tUere.is.no rubbing one 
 against the others. . - :A **, 
 
 Emma. Do you calculate the power gained by 
 this pulley, in the same method as with the com- 
 mon pulleys? 
 
 . * . 'R I"T 
 
 Father. Yes, for pulleys of every kind the rule is 
 general, the advantage gained is found by doubling 
 the number of the pulleys in the lower block : in 
 that before you there are six grooves, which answer 
 to as many distinct pulleys, and consequently the 
 power gained is twelve, or one pound at p will ba- 
 lance twelve pounds at w. ..... . .
 
 O? TH -WHEBX. ANB AXWL 
 
 ' 
 
 iasjt:! : 'io licq bl 
 
 ... 
 
 CONVERSATION XIX. 
 
 ftp" 1 : - 
 
 j^ilj o^woe^ *>cli pa(#^*i$J 
 
 _ 
 
 
 
 Of *As Inclined Plane, 
 
 FATHER. We may now describe the inclined 
 plane, which is the fourth mechanical power. 
 
 Charles. You will not be able, I think, to reduce 
 {bis also to the principle of the lever. 
 
 Father. No, it is a distinct principle, and some 
 writers on these subjects reduce at once the six 
 mechanical powers to two, viz* the lever and inclin- 
 ed plane. 
 
 Emma. How do you estimate the advantage 
 gained by this mechanical power? 
 
 Father. The method is very easy, for just as 
 much as the length of the plane exceeds its per- 
 pendicular height, so much is the advantage gained. 
 Suppose AB (Plate TV, Fig. 28) is a plane standing 
 on the table, and cp another plane inclined to it ; if 
 the length CD be three times greater than the per- 
 pendicular tieight; then the cylinder E will be sup- 
 ported upon the plane CD, by a weight equal to the 
 third part of its own weight.
 
 100 ' MECHANICS. 
 
 Emma. Could I then draw up a weight on such 
 a plane with a third part of the strength that I must 
 exert in lifting it up at the end ? 
 
 Father. Certainly you might; allowance, how- 
 ever, must be made for overcoming the friction ; but 
 then you perceive, as in other mechanical powers, 
 that you will have three times the space to pass 
 over, or that as you gain J?OM;/; you will lose time. 
 
 Charles. Now I understand the reason why some- 
 times there are two or three strong planks laid from 
 the street to the ground-floor warehouses, making 
 therewith an inclined plane, on which heavy pack- 
 ages are raised or lowered. ^ 
 
 father. The inclined plane is chiefly used for 
 raising heavy weights to small heights, for in ware- 
 houses situated in the upper part of buildings, cranes 
 and pulleys are better adapted for the purpose. 
 
 Charles. I have sometimes amused myself by ob- 
 serving the difference of time which one marble has 
 taken to roll down a smooth board, and another 
 which has fallen by its own gravity without any. 
 support. 
 
 Father. And if it were a long plank, and you 
 took care to let both marbles drop from the hand 
 at the same instant, I dare say you found the differ- 
 ence very evident. 
 
 Charles. I did, and now you have enabled me to 
 account for it very satisfactorily, by showing me 
 that as much more time is spent in raising a body, 
 along an inclined plane', than in lifting k up at the 
 
 -
 
 OF THE INCLINED PLANE. 101 
 
 end, as that plane is longer than its perpendicular 
 height. For I take it for granted that the rule holds 
 in the descent as well as in the ascent. 
 
 '*IJ iji ' .C'.; 
 
 Father. If you have any doubt remaining, a 
 few words will make every thing clear. Suppose 
 your marbles placed on a plane perfectly horizon- 
 ta3, as on this table, they will remain at rest wher- 
 ever they are placed : now if you elevated the plane 
 in such a manner that its height should be equal to 
 half the length of the plane, it is evident from what 
 has been shown before, that the marbles would 
 require a force equal to half their weight to sus- 
 tain them in any particular position : suppose then 
 the plane perpendicular to the table, the marbles 
 will descend with their whole weight, for now the 
 plane contributes in no respect to support them, 
 consequently they would require a power equal 
 to their whole weight to keep therp from descend- 
 ing. 
 
 Charles. And the swiftness with which a body 
 falls is to be estimated by the force \yith which it 
 was acted upon? 
 
 Father. Certainly, for you are now sufficiently 
 acquainted with philosophy to know that the effect 
 must be estimated from the cause. Suppose an in- 
 clined plane is thirty-two feet long, and its perpen- 
 dicular height is sixteen feet, what time will a mar- 
 ble take in falling down the plane, and also in de- 
 
 2D
 
 MECHANICS. 
 
 scending from the top to the earth by the force of 
 gravity? 
 
 Charles. By the attraction of gravitation, a body 
 falls sixteen feet in a second (see p. 40), therefore the 
 marble will be one second in falling perpendicularly 
 to the ground ; and as the length of the plane is 
 double its height, the marble must take two seconds 
 to roll down it. 
 
 Father. I will try you with another example. If 
 there be a plane 64 feet perpendicular height, and 
 3 times 64, or 192 feet long, tell me what time a 
 marble will take in falling to the earth by the attrac^ 
 tion of gravity, and how long it will be in descend- 
 ing down the plari'e.~ i! 
 
 Charles. By the attraction of gravity it will fall 
 in two seconds ; because, by multiplying the sixteen 
 feet which it falls in the first second, by the square of 
 two seconds (the time) or four, I get sixty-four, the 
 height of the plane. But the plane being three times 
 as long as it is perpendicularly high, it must be three 
 times as many seconds in rolling down the plane as 
 it was in descending freely by the force of gravity, 
 that is, six seconds. 
 
 Emma. Pray, papa, what common instruments 
 are to be referred to tins mechanical power, in ther 
 same way as scissars, pincers, &c., are referred to 
 the lever ? J &* 
 
 Father. Chisels, hatchets, and whatever other
 
 OF THE INCLINED PLANE. 103 
 
 sharp instruments are chamfered, or sloped down 
 to an edge on one side only, may be referred to 
 the principle of the inclined plane. 
 
 The principle of the inclined plane is applied in 
 the construction of carriage-ways, for the convey- 
 aance of heavy loads up steep elevations : also in 
 railways, &c. 
 
 iioj. ,.(fl 2 .$iH f V i -:-?*;i f I) o 
 en1 1? 39ii^3ui] olodw titit si :*a : oias. airl 'i
 
 7 ^"V ' f^ 
 
 )64 >is4u, MECHANICS. 
 
 
 .... ... .l,,w 
 
 CONVERSATION XX. 
 
 o) & )W/i;'t>? 
 oy bi.Q .n?siij U'u /.^ 
 
 j '' 
 
 FATHER. The next mechanical power is the 
 wedge, which is made up of the two inclined planes 
 BEFG and CEFG (Plate IV, Fig. 2Q), joined together 
 at their bases CEFG : DC is the whole thickness of the 
 wedge at its back ABCD, where the power is applied, 
 and DF and CF are the length of its sides; now there 
 will be an equilibrium between the power impelling 
 the wedge downward, and the resistance of the 
 wood, or other substance acting against its sides, 
 when the thickness DC Of the wedge is to the length 
 of the two sides, or, which is the same thing, when 
 half the thickness DE of the wedge at its back is to 
 the length of DF one of its sides, as the power 
 is to the resistance. 
 
 Charles. This is the principle of the inclined 
 plane ? 
 
 Father. It is, and notwithstanding all the dis- 
 putes which the methods of calculating the advan- 
 tage gained by the wedge have occasioned, I see no
 
 OF THE WEDGE. 105 
 
 reason to depart from the opinion of those who con- 
 sider the wedge as a double inclined plane. 
 
 Emma. I have seen people cleaving wood with 
 wedges, but they seem to have no effect, unless great 
 force and great velocity are also used. 
 
 Father. No, the power of the attraction of cohe- 
 sion, by which the parts of wood stick together, is 
 so great, as to require a considerable momentum to 
 separate them. Did you observe nothing else in the 
 operation worthy of your attention ? 
 
 Charles. Yes, I also took notice that the wood 
 generally split a little below the place to which the 
 wedge reached. 
 
 Father. This happens in cleaving most kinds of 
 wood, and then the advantage gained by this me- 
 chanical power, must be in proportion as the length 
 of the sides of the cleft in the wood is greater than 
 the length of the whole back of the wedge. There 
 are other varieties in the action of the wedge; but, 
 at present, it is not necessary to refer to them. 
 
 Emma. Since you said that all instruments, which 
 sloped off to an edge on one side only, were to be 
 explained by the principle of the inclined plane ; so, 
 I suppose, that those which decline to an edge onboth 
 sides, must be referred to the principle of the wedge. 
 
 Father. They must, which is the case with many 
 chisels, and almost all sorts of axes, &c. 
 
 Charles. Is the wedge much used as a mecha- 
 nical power? ^ 
 2 E
 
 106 ' HECHAN1CS. 
 
 Father. It is of great importance in a vast va- 
 riety of cases in which the other mechanical powers 
 are of no avail ; and this arises from, the momen- 
 tum of the blow, which is greater, beyond compa- 
 rison, than the application of any dead weight or 
 pressure, such as is employed in the other mecha- 
 nical powers. Hence it is used in splitting wood, 
 rocks &c., and even the largest ship may be raised 
 to a small height by driving a wedge below it. 
 
 Emma. Has it been applied to any other pur-- 
 poses ? 
 
 Father. It is used for raising the beams of a 
 house, when the floor gives way, by- reason of too 
 great a burden having been laid upon them. 
 
 It is usual also in separating large mill-stones 
 from siliceous sand-rocks, to bore horizontal holes 
 under them in a circle, and fill these with pegs or 
 Avedges made of dry wood, which gradually swell 
 by the moisture of the earth, and in a day or two 
 lift up the mill stone without breaking it. 
 
 The principle of the wedge is called into action 
 by almost every mechanic, and in a thousand in- 
 stances, in which the reason of the thing is not even 
 thought of. To mention a single instance, builders, 
 in raising their scaffolds, always tighten the ropes 
 round their scaffolding poles by means of wedges 
 driven between the cords and the poles.
 
 OF THE SCREW. JQ 
 
 .... -j, T 
 
 " '' ' ? '/'-'': -if n* -^o r 
 
 CONVERSATION XXI. 
 
 Of the Screw. 
 
 FATHER. Let us now examine the properties 
 of the sixth and last mechanical power, the screw; 
 which, however, cannot be called a simple mecha- 
 nical power, since it is never used without the assist- 
 ance of a lever or winch ; by which it becomes 
 a compound engine, of great power in pressing- 
 bodies together, or in raising great weights. AB 
 (Plate IV, Fig. 30) is the representation, of one, to- 
 gether with, the lever DF, 
 
 Emma. You said just now, papa, that all the 
 mechanical powers were reducible either to the 
 lever or inclined plane : how can the screw be 
 referred to either ? 
 
 Father. The screw is composed of two parts, 
 one of which, A B, is called the screw, and consists 
 of a spiral protuberance, called the thread, which 
 may be supposed to be wrapt round a cylinder ; the 
 other part CD, called the nut, is perforated to the 
 dimensions of the cylinder; and in the internal ca- 
 vity is also a spiral groove adapted to receive the
 
 108 MECHANICS. 
 
 thread. Now, if you cut a slip of writing-paper in 
 the form of an inclined plane a b c (Fig. 30), and 
 then wrap it round a cylinder of wood, you will 
 find that it makes a spiral answering to the spiral 
 part of the screw ; moreover, if you consider the 
 ascent of the screw, it will be evident that it is pre- 
 cisely the ascent of an inclined plane. 
 
 Charles. By what means do you calculate the 
 advantage gained by the screw? 
 
 Father. There are, at first sight, evidently two 
 things to be taken into consideration ; the first is 
 the distance between the threads of the screw ;-~ /: 
 aad the second is the length of the lever. 
 
 Charles. Now I comprehend pretty clearly how 
 it is an inclined plane, and that its ascent is more or' 
 less easy as the threads of the spiral are nearer of ,. 
 farther distant from each other. 
 
 Father. Well then, let me examine, by a ques- 
 tion, whether your conceptions be accurate : sup- 
 pose two screws, the circumferences of whose cy- 
 linders are equal to one another ; but in one, the 
 distance of the threads to be an inch apart; and 
 that of the threads of the other only one-third of 
 an inch; what will be the difference f the ad- ^ 
 vantage, gained by one of the screws over the 
 other? 
 
 Charles. The one, whose threads are three times 
 nearer than those of the other, must, I should think, 
 give three times the most advantage.
 
 OF THE SCREW. 109 
 
 Father. Give me the reason for what you as- 
 sert. 
 
 Charles, Because, from the principle of the in- 
 clined plane, I learnt that if the height of two planes 
 were the same, but the length of one, twice, thrice, 
 or four times greater than that of. the other, the 
 mechanical advantage gained by the longer plane 
 would be two, three, or four times more than that 
 gained by the shorter. Now, in the present case, the 
 height gained in both screws is the same, one inch, 
 but the space passed in that, three of whose threads 
 gp to an inch, must be three times as great as the- 
 space passed in the other; therefore, as space is pas- 
 sed, or time lost, just in proportion to the advan- 
 tage gained, I infer that three times more advan- 
 tage is gained by the screw the threads of which 
 are one-third of an inch apart, than by that whose 
 threads are an inch apart. 
 
 Father. Your in/erence is just, and naturally 
 follows from an accurate knowledge of the prin- 
 ciple of the inclined plane. But we have said no- 
 thing about the lever. 
 
 Charles. This seemed hardly necessary, it being 
 so obvious to any one, who will think a moment, 
 that power is gained by that, as in levers of the 
 first kind, according to the length FD from the 
 nuL 
 
 Father. Let us now calculate the advantage gain- 
 ed by a screw, the threads of which are half an 
 . 2F
 
 HO MECHANICS. 
 
 inch distance from one another, and the lever 7 feet 
 long. 
 
 Charles, I think you once told me that, if the 
 radius of a circle was given, in order to find the 
 circumference, I must multiply that radius by 6. 
 
 Father. I did ; for though that is not quite 
 enough, yet it trill answer all common purposes, till 
 you are a little more expert in the use of decimals. 
 
 Charles. Well, then, the circumference of the cir- 
 cle made by the revolution of the lever \vill be 7 
 feet, multiplied by 6, which is 42 feet, or 504 inches ; 
 but, during this revolution, the screw is raised only 
 half an inch, therefore the space passed by the mov- 
 ing power will be 1008 times greater than that gone 
 through by the weight, consequently the advantage 
 gained is 1008, or one pound applied to the lever 
 will balance 1008 pounds acting against the screw. 
 
 Father. You perceive that it follows as a corol- 
 lary from what you have been saying, that there are 
 two methods by which you may increase the mecha- 
 nical advantage of the screw. 
 
 Cltarles. I do ; it may be done either by taking 
 a longer lever, or by diminishing the distance of the 
 threads of the screw. 
 
 Father. Tell me the result then, supposing the 
 threads ef tfce screw so fine as to stand at the dis- 
 tance of but one quarter of an inch asunder; and 
 that the length of the lever were 8 feet instead of 7. 
 
 Charles. The circumference of the circle made
 
 OF THE SCREW, 111 
 
 by the lever will be 8 multiplied by 6, equal to 48 
 feet or 57$ inches, or 2304 quarter inches, and as 
 the elevation of the screw is but one quarter of an 
 inch, the space passed by the power will, there- 
 fore, be 2304 times greater than that passed by the 
 weight, which is the advantage gained in this in- 
 stance. 
 
 Father. A child, then, capable of moving the le- 
 ver sufficiently to overcome the friction, with the 
 addition of a power equal to one pound, will be able 
 to raise 2304 pounds, or something more than 20 
 hundred weight and a half. The strength of a pow- 
 erful man would be able to do 20 qr 30 times as 
 much more. 
 
 Charles. But I have seen, at a paper-mill, to which 
 I once went, six or eight men use all their strength 
 in turning a screw, in order to press out the water 
 of the newly made paper. The power applied in 
 that case must have been very great indeed. 
 
 Father. It was; but 1 dare say that you are 
 aware that it cannot be estimated by multiplying the 
 power of one man by the number of men employed, 
 
 Charles. That is, because the men standing by 
 the side of one another, the lever is shorter to every 
 man the nearer he stands to the screw, consequent- 
 ly though he may exert the same strength, yet it is 
 not so effectual in moving the machine, as the exer- 
 tion of him who stands nearer to the extremity of 
 the lever.
 
 112 MECHANICS. 
 
 Father. The tnie method, therefore, of calculat- 
 ing the power of this machine, aided by the strength 
 of these men, would be to estimate accurately the 
 power of each man according to 'his position, and 
 then adding all these separate advantages together 
 for the total power gained. 
 
 Emma. A machine of this kind, is, I believe, used 
 by bookbinders, to press the leaves of the books to- 
 gether before they are stitched ? 
 
 Father. Yes, it is found in every bookbinder's 
 workshop, and is particularly useful where persons 
 are desirous of having small books reduced to a still 
 smaller size far the pocket. It is also the princi- 
 pal machine used for coining money, for taking off 
 copper-plate prints, and for printing in general. 
 
 It would, my dear, be an almost endless task, 
 were we to attempt to enumerate all the purposes 
 to which the screw is applied in the mechanical arts 
 of life : it will, perhaps, be sufficient to tell you, 
 that wherever great pressure is required, there the 
 power of the screw is uniformly employed.
 
 SCIENTIFIC DIALOGUES. 
 
 PART II. ASTRONOMY,
 
 CONTENTS OF PART II. 
 
 ON ASTRONOMY. 
 
 Conversation Page 
 
 I. Of the Fixed Stars I 
 
 II. Of the Fixed Stars 7 
 
 III. Of the Fixed Stars, and Ecliptic 13 
 
 IV. Of the Ecliptic 20 
 
 V. Of the Solar System .. 23 
 
 VI. Of the Figure of the Earth 30 
 
 VII. Of the Diurnal Motion of the Earth 35 
 
 VIII. OfDay and Night 42 
 
 IX. Of the Annual Motion of the Earth 48 
 
 X. Of the Season* 52 
 
 XL OftheSeasons 57 
 
 XII. Of the Equation of Time 65 
 
 XIII. Of Leap-Year 78 
 
 XIV. OftheMoon 76 
 
 XV. OfEclipses 83 
 
 XVI. OftheTides 89 
 
 XVII. Of the Harvest Moon , 96 
 
 XVIII. Of Mercury 102 
 
 XIX. OfVenus 106 
 
 XX. OfMars -. Up 
 
 XXI. OfJupiter 114 
 
 XXII. OfSaturn 117 
 
 XXIII. Of the Herschel Planet 120 
 
 XXIV. Of the Smaller Planets 123 
 
 XXV. OfComets ^ 125 
 
 XXVI. Of the Sun 133 
 
 XXVII. Of the Fixed Stars ..130
 
 . 
 . ili'i;.
 
 SCIENTIFIC DIALOGUES. 
 
 CONVERSATION I. 
 
 <tei .<<$<? rafc HtjJ ^eiWtv ai . tuj 
 
 Of the Fixed Stars. 
 
 f . , . ! ' t J n 
 
 TUTOR CHARLES JAMES. 
 
 CHARLES. The delay occasioned by our un- 
 usual long walk, has afforded us one of the most 
 brilliant views of the heavens that I ever saw. 
 
 James. It is uncommonly clear ; and the longer I 
 keep my eyes fixed upwards, the more stars seem 
 to appear. How is it possible to number these stars? 
 and yet I have heard that they are numbered, and 
 even arranged in catalogues according to their ap- 
 parent magnitudes. Pray, sir, explain to us how 
 this business was performed. 
 
 Tutor. This I will do, with great pleasure, some 
 time hence, but at present, I must tell you that in 
 Viewing the heavens with the naked eye, we are 
 very much deceived as to the supposed number of 
 stars that are at any time visible. It is generally 
 admitted, and on good authority too, that there 
 are never more than one thousand stars visible to 
 B
 
 2 ASTRONOMY. 
 
 the sight, unassisted by glasses, at any one time, 
 and in one place. 
 
 James. What! can I see no more than a thou- 
 sand stars if I look ail around the heavens ? I 
 should suppose there were millions. 
 
 Tutor. This number is certainly the limit of what 
 yon can at present behold ; and that which leads 
 you, and persons in general, to conjecture that the 
 number is so much larger, is owing to an optical 
 deception. 
 
 James. Are we frequently liable to be deceived 
 by our senses? 
 
 Tutor. We are, if we depend on them singly ; 
 but where we have an opportunity of calling in the 
 assistance of one sense to the aid of another, we 
 are seldom subject to this inconvenience. 
 
 Ckarles. Bo you not know that if you place a 
 small marble in the palm of the left hand, and then 
 cross the second finger of the right hand over the 
 first, and in that position, with your eyes shut, 
 move the marble with those parts of the two fingers 
 at once, which are not accustomed to come into 
 contact with any object at the same time, that the 
 one marble will appear to the touch as two ? Iq. 
 this instance, without the assistance of our eyes, 
 we should be deceived by the sense of feeling. 
 
 Tutor. This is to the point, and shows that the 
 judgement formed by means of a single sense is no^ 
 always to be depended upon.
 
 OF THE FIXED STARS. 3 
 
 James. I recollect the experiment very well. But 
 that has nothing to do with the false judgement 
 which we are said to form about the number of 
 stars. vi||MM 
 
 Tutor. You are right ; it does not immediately 
 concern the subject before us; but it may be useful 
 as affording a lesson of modesty, by instructing us 
 that we ought not to close our minds against new 
 evidence that may be offered upon any topic, not- 
 withstanding the opinions we may have already 
 formed. You say you see millions of stars, where- 
 as the ablest astronomers assert, that with the 
 naked eye you cannot at one time see so many as 
 a thousand. 
 
 Charles. I should indeed have thought with my 
 brother, had you not asserted the contrary; and I 
 am anxious to know how the deception happens, 
 for I am sure there must be a great deception some- 
 where, if I do not at this time behold very many 
 thousands of stars in the heavens. 
 
 Tutor. You know that we see objects only by 
 means of the rays of light which proceed from 
 them in every direction. And you must for the 
 present give me credit when I tell you, that the 
 distance of the fixed stars from us is immensely 
 great, consequently the rays of light have to travel 
 this distance, in the course of which, especially in 
 their passage through our atmosphere, they are 
 subject to numberless reflections and refractions.
 
 4 ASTRONOMY. 
 
 By means of these, other rays of light come to the 
 eye, every one of which, perhaps, impresses upon 
 the mind the idea of so many separate stars. Hence 
 arises that optical fallacy by which ure are led to 
 believe the stars which we behold are innumerable. 
 
 James. I should like to see an experiment to 
 confirm this. 
 
 Tutor. I have no objection : in every case you 
 ought to. require the best evidence that the subject 
 will admit of: 
 
 To ask or search I blame thee not, for heaven '>* 
 
 v Is as the book of God before thee set, 
 
 "Wherein to read his woudrous works, and learn 
 His seasons, hours, or days, ov months, or years. 
 MILTON. 
 
 I will show you two experiments which will go a 
 good way to remove the difficulty. But, for this 
 purpose, we must step into the house. 
 
 Here are two common looking-glasses, which phi- 
 losophically speaking, are plane mirrors. I place 
 them in such a manner on the table that they sup- 
 port one another from falling by meeting at the tops. 
 I now place this half-crown between them, on a 
 book, to raise it a little above the table. Tell, me 
 how many pieces of money you would suppose there 
 were, if you did not know that I had used but one. 
 
 James. There are several in the glasses. 
 
 Tutor. I will alter the position of ;the glasses a 
 little, by making them almost parallel to one an- 
 other; now look iuto them., and say what you see.
 
 OF THE FIXED STARS. 5 
 
 James. There are more half-crowns now than 
 there were before. 
 
 Tutor. It is evident, then, that by reflection only, 
 a single object, for J have made use of but one 
 half-crown, will give you the idea of a vast number. 
 
 Charles. If a little contrivance had been used to 
 conceal the method of making the experiment, I 
 should not have believed but that there had been 
 several half-crowns instead of one. 
 H Tutor. Bring me your multiplying glass ; look 
 through it at the candle : how many do you seer 
 or rather how many candles should you suppose 
 there were, did you not know that there was but 
 one on the table? 
 
 James. A great many, and a pretty sight it is. 
 
 Charles. Let me see ; yes, there are : but I can 
 easily count them ; there are sixteen. \ Tt r 
 
 Tutor. There \yill be just as many images of the 
 candle, or any other object at which you look, as 
 there are different surfaces on your glass. For by 
 the principle of refraction, the image of the candle 
 is seen in as many different places as the glass has 
 surfaces; consequently, if instead of 16 there had 
 been 60, or, if they could have been cut and po- 
 lished s.o small, 600, then the single candle would 
 have given you the idea of 60, or 600. What think 
 you now about the stars? 
 
 James. Since I have seen that reflection and re^ 
 fraction will each, singly, afford such optical cje- 
 C
 
 ASTRONOMY. 
 
 ceptions, 1 can no longer doubt, but that, if both 
 these causes are combined, as you say they are 
 with respect to the rays of light coming from the 
 fixed stars, a thousand real luminaries may have 
 the power of exciting in my mind the idea of 
 millions. 
 
 Tutor. I will mention another experiment, for 
 which you may be prepared against the next clear 
 star-light night. Get a long narrow tube, the longer 
 and narrower the better, provided its weight does 
 not render it unmanageable: examine through it 
 any one of the largest fixed stars, which are called 
 stars of i\ie first magnitude, and you will find, that 
 though the tube takes in as much sky as would con- 
 tain many such stars, yet that the single one at 
 which you are looking, is scarcely visible, by the 
 few rays which come directly from it : this is an- 
 other proof that the brilliancy of the heavens is 
 much more owing to reflected and refracted light, 
 
 than to the direct rays flowing from the stars. 
 
 v V *ffj(-vfli- #} 
 

 
 OF THE FIXED ATARS. 
 
 CONVERSATION II. 
 
 . 
 
 'fa ii 
 
 O/" the Fixed Stars. 
 
 CHARLES. Another beautiful evening 1 presents 
 itself; shall we take the advantage which it offers 
 of going on with our astronomical lectures ? 
 
 Tutor. I have no objection, for we do not always 
 enjoy such opportunities as the brightness of the 
 present evening affords. 
 
 James. I wish very much to know how to distin- 
 guish the stars, and to be able to call them by their 
 proper names. 
 
 Tutor. This you may very soon learn ; a few 
 evenings, well improved, will enable you to distin- 
 guish all the stars of the first magnitude which are 
 visible, and all the relative positions of the different 
 constellations. 
 
 James. What are constellations, sir? 
 
 Tutor. The ancients, that they might the bet- 
 ter distinguish and describe the stars, with regard 
 to their situation in the heavens, divided them into 
 constellations, that is, groups of stars, each group 
 consisting of such stars as were near to each other, 
 giving them the names of such men or things, as
 
 8 ASTRONOMV. 
 
 they fancied the space which they occupied in the 
 heavens represented. 
 
 Charles. Is it then perfectly arbitrary, that" one 
 collection is called the great bear ; another the dra- 
 gon; a third Hercules, and so on? 
 
 Tutor. It is ; and though there have been addi- 
 tions to the number of stars in each constellation, 
 and various new constellations invented by modern 
 astronomers, yet the original division of the stars 
 into these collections was one of those few arbitra- 
 ry inventions which have descended without altera- 
 tion, otherwise than by addition, from the days of 
 Ptolemy down to the present time. 
 
 Charles. How do astronomers express the re- 
 spective distances of the stars from each other? 
 
 Tutor. If you look around you at the line that 
 seems to separate the sky from the earth, called 
 the horizon, you will observe that it appears per- 
 fectly circular. All such circles in {he heavens are 
 called great circles, and are uniformly divided into 
 360 equal parts, called degrees. These are sub r 
 divided into minutes and seconds, each decree 
 containing 60 minutes, and each minute 60 seconds. 
 These divisions are for shortness sake, generally 
 expressed by marks placed over figures. Thus 25 
 4' 8" means twenty-five degrees, four minutes, an4 
 eight seconds. 
 
 If you observe one star on tjie horizon due East 
 of you, another due South, can you now tell me
 
 OF THE FIXED STARS. 9 
 
 how far the one is distant from the other? 
 
 James. As the whole circle of the horizon con- 
 tains 360, and the space from East to South is one 
 fourth of that circle, I suppose the distance of the 
 two stars from each other must be 90. 
 
 Tutor. You are right; and any smaller distance 
 is estimated proportionally. Do you know how to 
 find the four cardinal points, as they are usually 
 called, the North, South, West, and East? 
 
 James. O yes. I know that if I look at the sun 
 at twelve o'clock at noon, I am also looking to the 
 south, where he then is ; my back is towards the north; 
 the west is on my right hand, and the east on my left. 
 
 Tutor. But you must learn to find these points 
 without the assistance of the sun, if you wish to be 
 a young astronomer. 
 
 Charles. I have often heard of the north pole star; 
 that \vill perhaps answer the purpose of the sun, 
 when he has left us. 
 
 Tutor. You are right; it is so called, be- 
 cause all the other stars in their apparent motion 
 from East to West, seem to move round it in circles 
 or portions of circles ; as if the sky were an actual 
 hollow sphere studded with all those luminaries, 
 and the polar star one extremity of the axis or pole on 
 which it revolved ; while the spectator on the earth 
 occupied the centre of the sphere. 
 
 James. How can we find the place of the Polar 
 
 Star? 
 
 ft
 
 & ASTRONOMY. 
 
 Tutor. Do you see those seven stars which are 
 in the constellation of the Great Bear; some people 
 have supposed their position will aptly represent 
 SL plough; others say, that they are more like a wag- 
 gon and horses; the four stars representing the 
 body of the waggon, and the other three the horses : 
 and hence they are called by some the plough, and 
 by others they are called Charles's wain or waggon. 
 Here is a drawing of it, (Plate I, Fig. I ;) a b dg re- 
 present the four stars, and ez B the other three. 
 
 Charles. What is the star p ? 
 
 Tutor. That represents the polar star to which 
 you just now alluded ; and you observe, that if a 
 line were drawn through the stars b and a, and pro- 
 duced far enough, it would nearly touch it. 
 
 James. Let me look in the heavens for it by this 
 guide. There it is, I suppose ; it shines with a steady 
 and rather dead kind of light, and it appears to me 
 that it would be a little to the right of the line pass- 
 ing through the stars b and a. 
 
 Tutor. It would, And these stars are generally 
 known by the name of the pointers, because they 
 point to .p the north pole, which is situated a little 
 more than two degrees from the star p. 
 
 Charles. Is that star always in the same part of 
 the heavens ? 
 
 Tutor. It is. But we shall have occasion to refer to 
 it again ; at present I have directed your attention to 
 it, as a proper method of finding the Cardinal points 
 by star-light.
 
 OF TJHE FIXED STARS. 11 
 
 James. Yes, I understand now, that if I look to 
 the north, by standing with my face to that star, the 
 south is at my back, on my right hand is the east, 
 and the west on my left. 
 
 Tutor. This is one important step in our astrono- 
 mical studies ; but we can make use of these stars 
 as a kind of standard, in order to discover the names 
 and positions of others in the heavens. 
 
 Charles. In what way must we proceed in this 
 business ? 
 
 Tutor. I will give you an example or two : con- 
 ceive a line drawn from the star z, leaving* B a little 
 to the left, and it will pass through that very brilli- 
 ant star A near the horizon towards the west. -\t\ 
 
 James. I see the star, but how am. I to know its 
 name? 
 
 Tutor. Look on the celestial globe for the star 
 z, and suppose the line drawn on the globe, as we 
 conceived it done in the heavens, and you will find 
 the star, and its name. 
 
 Charles. Here it is ; its name is Arcturus. 
 
 Tutor. Take the figure, (Fig. 1,) and place Arc- 
 turns at A, which is its relative position, in respect 
 to the constellation of the Great Bear. Now, if 
 you conceive a line drawn through the stars g and b> 
 and extended a good way to the right, it will pass 
 just above another very brilliant star. Examine the 
 globe as before, and find its name. 
 
 Charles. It is Capella, the goat. 
 
 Tutor, Now, whenever you see any of these
 
 12 ASTRONOMY. 
 
 stars, you will know where to look for the others 
 without hesitation. 
 
 James. But do they never move from their 
 places? 
 
 Tutor. With respect to us, they seem to move 
 together with the whole heavens. But they always 
 remain in the same relative position, with respect to 
 each other. Hence they are called fixed stars, in 
 opposition to the planets, which, like our. earth, are 
 continually changing their places both with regard 
 to the fixed stars, and to themselves also. 
 
 Charles. I now understand pretty well the me- 
 thod of acquiring a knowledge of the names and 
 places of the stars. 
 
 Tutor. And with this we will put an end to our 
 present conversation. 
 
 . - .. j. *A ^ V- T *" *> fc r * ' *r ** 
 
 r*J* ddtoQfefertoil ;;!:. .-c'YV 
 
 
 i
 
 OF THE ECLIPTIC. 13 
 
 . 
 CONVERSATION III. 
 
 i&fotlJ-J cii' iteirigiHteih -vliacs !'-'.r' i^V &mti$tf&'ft 
 
 Of the Fixed Stars, and Ecliptic. 
 
 TUTOR. I dare say that you will have no dif- 
 ficulty in finding the north polar star, as soon as we 
 go into the open air. 
 
 James. 1 shall at once know where to look for 
 that and the other stars which you pointed out last 
 night, if they have not changed their places. 
 
 Tutor. They always keep the same position with 
 respect to each other, though their situation, with 
 regard to the heavens, will be different at different 
 seasons of the year, and in different hours of the 
 night. Let us go into the garden. 
 
 Charles. The stars are all in the same place as 
 we left them last evening. Now, sir, if we conceive 
 a straight line drawn through the two stars in the 
 plough, which, in ypur figure, (Fig. 1,) are marked 
 d and g, and to extend a good way down, it will pass 
 or nearly pass through a very bright star, though 
 not so bright as Arcturus or CapeUa. What is that 
 called? 
 
 Tutor. It is a star of the second magnitude, and 
 
 E
 
 14 ASTRONOMY. 
 
 if you refer to the celestial globe, in the same way 
 as you were instructed last night, you will find it 
 is called Regulus, or Cor Leonis, the Lion's heart. 
 By this method you may quickly discover the names 
 of all the principal stars, and afterwards, with a 
 little patience, you will easily distinguish the others, 
 which are less conspicuous. 
 
 Charles. But they have not all names ; how are 
 
 i 'r j ^ 
 
 they specified ? 
 
 Tutor. If you look upon the globe, you will ob- 
 serve that they are distinguished by the different 
 letters of the Greek alphabet; and in those constel- 
 lations, in which there are stars of different appa- 
 rent magnitudes, the largest is alpha, the next in 
 size beta, the third y gamma, the fourth $ delta, 
 and so on. 
 
 James. Is there any particular reason for this ? 
 
 Tutor. The adoption of the characters of the 
 Greek alphabet, rather than any other, was perfect- 
 ly arbitrary; it is however, of great importance, 
 that the same characters should be used in general 
 by astronomers of all countries, for by this means 
 the science is in possession of a sort of universal 
 language. 
 
 Charles. Will you explain how this is? 
 
 Tutor. Suppose an astronomer in North America, 
 Asia, or any other part of the earth, observe a 
 comet in that part of the heavens where the con- 
 stellation of the plough is situated, and he wishes 

 
 OP THE ECLIPTIC. 1$ 
 
 to describe it to his friend in Great Britain, in order 
 that he may know, whether it was seen by the in- 
 habitants of this island. For this purpose he has 
 only to mention the time when he discovered it; its 
 position, as nearest to some one of the stars, calling 
 it by the Greek letter by which it is designated ; 
 and the course which it took from one star towards 
 another. Thus he might say, that on such a time 
 he saw a comet near 5 in the Great Bear, and that 
 its course was directed from 5 to , or any other, as 
 it happens. 
 
 Charles. Then, if his friend here had seen a comet 
 at the same time, he would, by this means, know 
 whether it was the same or a different comet ? 
 
 Tutor. Certainly, and hence you perceive of what 
 importance it is, that astronomers in different coun- 
 tries should agree to mark the same stars and sy- 
 stems of stars by the same character. But to return 
 to that star, to which you just called my attention, '. 
 the cor leonis, it is not only a remarkable star, but 
 its position is also remarkable, it is situated in the 
 ecliptic. 
 
 James. What is that, sir ? 
 
 Tutor. The ecliptic is an imaginary great circle 
 in the heavens, which the sun appears to describe in 
 the course of a year. If you look on the celestial 
 globe, you will see it marked with a reel line. 
 
 James. But the sun seems to have a circular mo- 
 tion in the heavens every day.
 
 1(3 ASTRONOMY. 
 
 Tutor. It does ; and this is called its apparent 
 diurnal, or daily motioti, which is very different 
 from the path it appears to traverse in the course 
 of a year. The former is observed by the most in- 
 attentive spectator, who cannot but know, that the 
 sun is seen every morning in the East, at noon 
 in the South, and in the evening in the West; but 
 the knowledge of the latter must be the result of 
 patient observation. 
 
 James. How is the sun's annual motion ascer- 
 
 tained ? 
 
 Tutor. This phenomenon may be distinctly 
 observed by remarking on any clear evening, any 
 bright fixed star visible after sun-set near the place 
 where the sun sunk below the horizon. On the fol- 
 io wing evening the star will cease to become visible 
 on account of its approach to the sun. In the same 
 way the stars to the eastward of it will in succes- 
 sion appear to approach the sun, until there is a 
 complete revolution of the heavens. Or the Sua 
 may be considered as approaching successively a 
 complete ring of stars, moving in them from West 
 to East, and it is that ring which is called the 
 Ecliptic. 
 
 Charles. And what is the green line which cros- 
 ses it? 
 
 Tutor. It is called the Equator-, this is an ima- 
 ginary circle belonging to the earth, which you 
 must take for granted, a little longer, is of a globuv
 
 OF THE ECLIPTIC. 17 
 
 lar fbrm e If yoa can conceive the plane of the ter- 
 restrial equator to be produced to the sphere of the 
 fixed stars, it would mark out a circle in the heavens, 
 called the celestial equator or equinoctial, which 
 would cut the ecliptic in two parts. The two rings 
 cross each other at an angle of 23. 28". And the 
 distance of the sun, in any point of the Ecliptic, from 
 the Equator is called his declination. Of course 
 when he is in either of those points of the Ecliptic 
 at which it cuts the Equator he has no decima- 
 tion. 
 
 James. Can we trace the circle of the ecliptic in 
 the heavens? 
 
 Tutor. It may be done with tolerable accuracy 
 by two methods \first, by observing several remark- 
 able fixed stars, to which the moon in its course 
 seems to approach. The second method is by ob 
 serving the places of the planets. 
 
 Charles. Is the moon then always in the ecliptic ? 
 
 Tutor. Not exactly so; but it is always either 
 in the ecliptic, or within five degrees and a third of 
 it on one side or the other, The greater planets also, 
 by which I mean Mercury, Venus, Mars, Jupiter, 
 Saturn, and Herschel, are never more than eight de- 
 grees distant from the line of the ecliptic. 
 
 James. How can we trace this line, by help of the 
 fixed stars ? 
 
 Tutor. By comparing the stars in the heavens, 
 with their representatives on the artificial globe, a
 
 18 ASTRONOMY. 
 
 practice which may be easily acquired, as you have- 
 seen. I will mention to you the names of those stars? 
 and you may first find them on the globe, and then 
 refer to as many of them as are now visible in the 
 heavens. The first is in the Ram's horn, called a 
 Arietis, about .ten degrees to the north of the edip- 
 tic ; the second is the star Aldebaran in the Bull's 
 eye, six degrees south of the ecliptic. 
 
 Charles. Then if at any time I see these two stars, 
 I know- that the ecliptic runs between them, and 
 nearer to Aldebaran, than to that in the Rani's horn. 
 
 Tutor. Yes : now carry your eye eastward to a 
 distance somewhat greater from Aldebaran, than 
 that is east of Arietis, and you will perceive two 
 bright stars at a small distance from one another, 
 called Castor and Pollux ; the lower one, and that 
 which is least brilliant, is Pollux, seven degrees on 
 the north side of the ecliptic. Following the same 
 track, you will come to Regulus, or the cor leonis, 
 which, i have already observed, is exactly in the 
 line of the ecliptic. Beyond this, and only two de- 
 grees south of that line, you will find the beautiful 
 star in the.virgiu's, hand, called Spica Virginis. Yon 
 then arrive at Antares, of the Scorpions hearty five 
 degrees on the same side of the ecliptic. Afterwards 
 you will find aAquila, which is situated nearly thir- 
 ty degrees north of the ecliptic : and farther on is 
 the star Fomalhaut in the Fish's mouth, about as 
 many degrees south of that line. The ninth and
 
 OF THE ECLIPTIC. 19 
 
 last of these stars is Pegasus, in the wing of the Fly- 
 ing-horse, which is north of the ecliptic nearly twenty 
 degrees. 
 
 James. Upon what account are these nine stars 
 particularly noticed ? 
 
 Tutor. They are selected as the most conspicu- 
 ous stars near the moon's orbit, and are considered 
 as proper stations, from which the moon's distance 
 is calculated for every three hours of time; and 
 hence are constructed those tables in the Nautical 
 Almanac, by means of which Navigators, in their 
 most distant voyages, are enabled to estimate, on the 
 trackless ocean, the particular part of the globe on 
 which they are. 
 
 Charles. What do you mean by the Nautical Al- 
 manac ? 
 
 Tutor. It is a kind of National almanac, intended 
 chiefly for the us*e of persons traversing the mighty 
 ocean. It was begun in the year 1767, by Dr. 
 Maskelyne, the Astronomer Royal ; and is published 
 by anticipation for ^several years before-hand for the 
 convenience of ships going out upon long voyages. 
 This work has been: found eminently important in 
 the course of voyages round the world for making 
 discoveries. 

 
 20 ASTRONOMY. 
 
 . 
 
 CONVERSATION IV. 
 
 , 
 
 Of the Ecliptic. 
 
 j 
 
 Charles. Will you explain the use of those cha- 
 racters I see used in Almanacs and*books of Astro- 
 nomy. 
 
 Tutor. If you look at the circle of the Ecliptic 
 on the globe, you will find twelve of those charac- 
 ters marked, which represent the 12 divisions, call- 
 ed the signs of the Zodiac, They are as follows : 
 
 <T> Aries. Leo. f Sagittarius. 
 
 # Taurus. tlji Virgo. \^> Capricornus. 
 
 n Gemini. Libra. 3 Aquarius. 
 
 05 Cancer. ^ Scorpio. X Pisces. 
 
 James. What do you mean by the Zodiac ? 
 
 Tutor. It is an imaginary broad circle or belt sur- 
 rounding the heavens, about sixteen degrees wide ; 
 along the middle of which runs the ecliptic, The 
 term Zodiac is derived from a Greek word signi- 
 fying an animal, because each of the twelve signs 
 formerly represented some animal; and as the whole 
 circle of the Zodiac contains 360, each sign of course 
 extends 30. 
 
 James. Why are the signs of the Zodiac called 
 by the several names of Aries, Taurus, Leo, &c.
 
 OF THE ECLIPTIC. 21 
 
 I see no likeness in the heavens to Rams, or Bulls, 
 or Lions,- which are the English words for those 
 Latin ones. 
 
 Tutor. Nor do I ; nevertheless, the ancients saw, 
 by the help of a strong imagination, a similarity 
 between those animals, and the places which cer- 
 tain groups of stars took up in the heavens, and 
 gave them the names which have continued to this 
 day. 
 
 Charles. Perhaps these were originally invented, 
 in the same way as we. sometimes figure to our ima- 
 gination the appearances of men, beasts, ships* trees, 
 &c. in the flying clouds or in the fire. 
 \ Tutor. They might possibly have no better au- 
 thority for their origin. At any rate it will be use- 
 ful for you to have the names of the twelve signs in 
 your memory, as well as the order in which they 
 stand : I will therefore repeat some lines written by 
 Dr. Watts, in which they are expressed in English, 
 and will be easily remembered : 
 
 The Rum, the Bull, the heavenly Twins, 
 , And next the Crab, the Lion shines, 
 
 The FiYginandthe Scales; 
 The Scorpion, Archer, and Sea-Goat, 
 The Man that holds the watering-pot, 
 And Fish with glittering tails. 
 
 Charles. We come now to the characl 
 denote the planets. 
 
 Tutor. These, like the former, are but a kind 
 of short-hand characters, which it is esteemed ea-
 
 22 ASTRONOMY. 
 
 sier to write, than the names of the planets at length. 
 They are as follow : 
 
 y The Herschel. The Sun. 
 
 ^ Satirn. 9 Venni. 
 
 ^ Jupiter. g Mercury, 
 
 Mars. C The Moon. 
 (D The Earth. 
 
 James. What is meant by the latitude of a star, 
 sir? 
 
 Tutor. The latitude of any heavenly body is its 
 distance from the ecliptic north or south. The la- 
 titude of Venus, on ner; year's day, 1803, was 4 
 north. 
 
 Charles. Then the latitude of heavenly bodies^ 
 has the same reference to the ecliptic, that declina- 
 tion has to the equator ; and since the sun is always 
 in the ecliptic, therefore he can have no latitude. 
 
 Tutor. Right, the longitude of the sun and pla- 
 nets is the only thing that remains to be explained. 
 The longitude of a heavenly body is its distance 
 from the first point of the sign Aries, and it is mea- 
 sured on the ecliptic. It is usual, however, to ex- 
 press the longitude of a heavenly body by the degree 
 of the sign in which it is. In this way the sun's 
 longitude on the first of January, 1809, was in Ca- 
 pricorn 10. 45' 14"; that of the moon in Cancer, 
 0. 4""; that of Jupiter in Pisces, 13. 35'.
 
 OF THE SOLAR SYSTEM. 23 
 
 CONVERSATION V. 
 
 Of the Solar System. 
 
 TUTOR. We will now proceed to the descrip- 
 tion of the Solar System. 
 
 James. Of what does that consist, sir r 
 
 Tutor. It consists of the sun, and planets, with 
 their satellites or moons. It is called the Solar Sys- 
 tem, from Sol the sun, because the sun is supposed 
 to be fixed in the centre, while the planets, and our 
 earth among them, revolve round him at different 
 distances. 
 
 Charles. But are there not some people who be- 
 lieve that the sun goes round the earth ? 
 
 Tutor. Yes, it is an opinion emb^ced by the 
 generality of persons, not accustomed to reason on 
 these subjects. It was adopted by Ptolemy, who 
 supposed the earth perfectly at rest, and the sun, 
 planets, and fixed stars to revolve about it every 
 twenty-four hours. 
 
 James. And is not that the most natural supposi- 
 tion r
 
 $4 ASTRONOMY 
 
 Tutor. If the sun and stars were small bodies in 
 comparison of the earth, and weVe s^ua^tej^^^) 
 very great distance from it, then the system main- 
 tained by Ptolemy and his followers might appear 
 the most probable. 
 
 James. Are the snu and stars very lar^bod^ 
 
 then? ^ftittvfli iv***9*vQ^la& wtett 
 Tutor. The sun is more than a million of times 
 
 larger than the earth which we inhabit, and many of 
 the fixed stars are probably much larger than he is* 
 
 Charhs. What is the reason, then, that they ,ap^ 
 pear so small? & ^ ^t^aiAc .''/tOiiJzadrnijn 
 
 Tutor. This appearance is caused by. the im- 
 mense distance there is between us and these jbo- 
 dies. It is known with certainty, that the sun is 
 more than 95 millions of miles distant from the earth., 
 and the nearest fixed star is probably more than 
 two hundred thousand times farther from us than 
 even the sun himself *. 
 
 Charles. But we can form no conception of such 
 distances. 
 
 Tutor. We talk of millions with as much ease as 
 
 of hundreds or tens, but it is not, perhaps, possible 
 
 for the mind to form any adequate conceptions of 
 
 such high numbers. Several methods have been 
 
 $*fi& VtS'fa .'$ i f ;~:~":i " 
 
 The yonng reader will, when he is able to nrnnage the subject, see this 
 learly demonstrated by a series of propositions in the 5th book of Dr. En- 
 field's Institutes of Natural Philosophy. Second Edition. See p. 340 to 
 the end of book V.
 
 OP THE SOLAR SYSTEM. 25 
 
 adopted to assist the mind in comprehending the 
 vastness of these distances. You have some idea 
 of the swiftness with which a cannon-ball proceeds 
 from the mouth of the gun r 
 
 James. I have heard that it moves at the ave- 
 rage rate of eight miles in a minute. 
 
 Tutor. And you know how many minutes there 
 are in a year r 
 
 James. I can easily find that out by multi- 
 plying 365 days by 24 for the number of hours, 
 and that product by 60, and I shall have the 
 number of minutes in a year, which number 
 is 525,600. 
 
 Tutor. Now if you divide the distance of the 
 sun from the earth by the number of minutes in a 
 year multiplied by 8, because the cannon-ball tra- 
 vels at the rate of 8 miles in one minute, you will 
 know how long any body issuing from the sun, with 
 the velocity of a cannon-ball, would employ in 
 reaching the earth. 
 
 Charles. If 1 divide 95,000,000 by 525,600, mul- 
 tiplied by 8, or 4,204,800, the answer will be more 
 than 22, the number of years taken for the journey. 
 
 Tutor. Is it then probable that bodies so large, 
 and at such distances from the earth, should re- 
 volve round it every day ? 
 
 Charles. I do not think it is. Will you, sir, go 
 on with the description of the solar system? 
 
 H
 
 2& ASTRONOMY. 
 
 Tutor. According to this system, the sun is in 
 the centre, about which the planets revolve froin 
 west to east, according to the order of the signs 
 in the ecliptic ; that is, if a planet is seen in Aries^ 
 it advances to Taurus, then to Gemini, and so on. 
 James. How many planets are there belonging 
 to the sun ? 
 
 Tutor. There are seven, besides some snaaller bo- 
 dies of the same kind discovered within these nine 
 years. C (Plate 1, Fig. 2) represents the sun, thq 
 nearest to which Mercury revolves in the circle a ; 
 next to him is the beautiful planet Venus, \\hQ per T 
 forms her revolution in the circle b ; then comejf 
 the Earth in t ; next to which is Max*, in e ; then 
 Jupiter in the circle./*; afterwards Saturn in g; and 
 far beyond him the planet Hersckcl performs his- 
 revolution in the circle h. 
 
 James. For what are the smaller circles 
 which -ore attached to several of the larger ones in- 
 tended ? 
 
 Tutor. They are intended to represent the orbits 
 of the several satellites or moons belonging to some* 
 of the planets. 
 
 James. "What do you mean by tne word orbit? 
 
 Tutor. The path described by a planet in its* 
 
 course round the sun, or by a moon round its piv 
 
 mary planet, is called its 'orbit. 'Look to the orbit 
 
 of the earth in t (Fig. 2), and you will see a little
 
 or TH S^A* OTSTEM. 27 
 
 circle which Represents the pr&jfc ha which Qurnaoon 
 
 J3as .-ngjttor M&WW 39* 
 
 ing either to ]$ercury, Yf^us, pr 
 you observe by the figure, has four moons: Saturn 
 has seven ; and Herschel (which also goes by the 
 name of the Georgium Sid us) has six ; these for 
 want of room are not drawn. in the plate. 
 
 Charles. The solar system then consists of the 
 sun as a centre, round which revolve seven planets, 
 and eighteen satellites or moons. Are there no 
 other bodies belonging to it ? 
 
 Tutor. Yes, as I just observed, four other pla- 
 netary bodies have been very lately discovered as 
 belonging to the solar system. These are very small. 
 They are called Ceres, Pallas, Juno, and Vesta. 
 There are comets also which make their appear- 
 ance occasionally; and it would be wrong posi- 
 tively to affirm, that there can be no other planet 
 belonging to the Solar System; since, besides 
 the four bodies just mentioned, it is only within 
 these thirty years that the seventh or the Herschel 
 has been known to exist as a planet connected 
 with this system. 
 
 Charles. Who first adopted the system of the 
 world which you have been describing?
 
 28 ASTRONOMY. 
 
 Tutor. It was conceived and taught by Pytha- 
 goras to his disciples, 500 years before the time of 
 Christ. But it seems soon to have been disregard- 
 ed, or perhaps totally rejected, till about 300 year* 
 ago, when it was revived by Copernicus, and is at 
 length generally adopted by men of science. 
 
 IvflR 
 -oioo 
 
 a 
 
 
 
 : ' 
 ^3>a 
 
 olofK 
 
 T! OH gflifKT W"V- -.>;?) "U; yKn<j gjifj ^J.^^fj 
 
 ; r
 
 0? THE FIQURE OF THE EARTH. V3 
 
 ;'-:Ur * ".c * ; -'.;- -.- , -;' ,;; .: 
 
 * e . 
 
 Ms- .ji-:jrr.. 
 
 -^j- 
 
 -.- 
 
 O/* the Figure of the Earth. 
 
 TUTOR. Having, in our last conversation, given 
 yon a description of the Solar System in general, 
 we will now proceed to consider each of its parts 
 separately: and since we are most of all concerned 
 with the earth, we will begin with that body. 
 
 James. You promised to give us some reasons 
 why this earth must be in the form of a globe and 
 not a mere extended plane, as it appears to com- 
 mon observation. 
 
 Tutor. Suppose you were standing by the sea- 
 shore, on a level with the water, and at a very con- 
 siderable distance, as far as the eye can reach, you 
 observe a ship approaching, what ought to be the 
 appearance, supposing the surface of the sea to be 
 a flat plane? 
 
 Charles. We should, I think, see the whole ship 
 at once, that is, the hull would be visible as soon 
 as the top-mast. 
 
 Tutor. It certainly must, or indeed rather sooner, 
 because the body of the vessel being so much larger 
 i
 
 30 ASTRONOMY. 
 
 than a slender mast, it must necessarily be visible 
 at a greater distance. 
 
 James. Yes, I can see the steeple of a church 
 at a much greater distance than I can discern the 
 iron conductor which is upon it, and that I can 
 perfectly see long before the little piece of gold wire, 
 which is fixed at its extremity, is visible. 
 
 Tutor. Well, but the top-mast of a vessel at sea 
 is always in view some little time before the hull of 
 the .vessel x:an be discerned. Now, if the surface of 
 the sea be .globular, this ought to be the appearance, 
 because the protuberance or swelling of the water 
 between the vessel and the eye of the spectator* 
 will hide the body, of the ship some time after the 
 pendant is seen above. 
 
 Charles, In the same way as if a high building-, 
 a church for instance,, were situated on one side of 
 a hill, and 1 was walking up on the opposite side, 
 the. steeple, would come first in sight, and as I ad- 
 vanced towards the summit, the other parts would 
 come successively in view.., fc? ^. ^.,,' 
 
 Tutor. Your illustration is quite to the purpose : 
 in the same way two persons, walking up a hill on 
 the opposite sides, will- perceive each other's lieads 
 first; and as they advance to the top, the other 
 parts of their bodies will become visible. With re- 
 spect to the ship, the following figure will conveythe 
 idea very completely^ (Plate I; Fig. 3.) Suppose 
 CAB represent a small part of the curved surface
 
 OF THE FIGURE OP THE EARTH. ^ 
 
 sof the sea; if a spectator stand at B, while- a ship 
 is at c, only a small part of the mast is visible to 
 him, but as it advances, more of the ship is seen, 
 till it arrive at e, when the whole will be ia' sight. 
 
 Charles. When I stood by the sea-side the wa- 
 ter did not appear to>me to be curved. 
 
 Tutor. Perhaps not ; but its convexity may be 
 discovered upon any still water ; as upon a river, 
 which is extended a mile or tVo in length, for you 
 might see a very small boat at' that distance while 
 standing upright; if then you stoop down so as to 
 bring your eye near' the water, you will fintf the 
 surface of it rising in such a manner as to cover the 
 boat, and intercept its view completely. Another 
 proof of the globular figure of the' earth is, that it is 
 necessary for those who are employed in cutting 
 canals, to make a certain allowance fof the con- 
 vexity, since the true level is not a straight line, but a 
 curve which falls below it eight inched in every mile. 
 
 Charles. I 'have heard of people sailing round 
 the world, which is another proof, I imagine, of 
 the globular figure of the earth. 
 
 Tutor. It is a well known fact that navigators 
 have set out from a particular port, and by steer- 
 ing their course continually westward, have at 
 length arrived at the same place from whence they 
 first departed. Now had the earth been an extend- 
 ed plane, the longer they had travelled, the farther 
 must they have been from home.-- fe^e
 
 32 ASTRONOMY. 
 
 Charles. How is it known that they continued 
 the same course ? Might they not have been driven 
 round at open sea ? 
 
 Tutor. By means of the mariner's compass, 
 the history, properties, and uses of which, I will 
 explain very particularly in a future part of our 
 lectures, the method of sailing on the ocean by one 
 certain tract, is as sure as travelling on the high 
 road from ^iilcutta to Benares. By this method, 
 Jwdinand ^lagellan sailed in the year 15 19 from 
 the western coast of Spain, and continued his voy- 
 age in a westward course till his ship arrived after 
 1124 days in the same port from whence it set 
 out. The same with respect to Great Britain, was 
 done by our own countrymen Sir Francis Drake, 
 Lord Anson, Captain Cook, and many others. 
 
 C/tarles. Is then the common terrestrial globe a 
 just representation of the earth? 
 
 Tutor. It is, with this small difference*, that 
 the artificial globe is a perfect sphere, whereas the 
 
 What tlie earth loses of its sphericity, by mountains and vallies, is 
 very inconsiderable: the highest mountain bearing so little proportion to its 
 bulk, as scarcely to be equivalent to the minutest protuberance on the 
 surface of an orange; 
 
 These inequalities to us seem great; 
 
 But to an eye that comprehends the whole, 
 
 The tumour, which to us so monstrous seems, 
 
 Is as a grain of sparkling saud that clings 
 
 To the smooth surface of a sphere of glass ; 
 
 Or as a fly upon the convex dome 
 
 Of a sublime, stupendous edifice. LOFFT.
 
 OF THE FIGURE OF THE EARTH. 53 
 
 earth is a spheroid, that is, in the shape of an 
 orange, the diameter from pole to pole being about 
 25 miles shorter than that at the equator. 
 ,. James* What are the poles, sir ? 
 
 Tutor. In the artificial globe (Plate I, Fig. 4>) 
 there is an axis N s about which it turns; .now the 
 two extremities or ends of this axis N and s are 
 called the poles^ : ,v.^. 
 
 c Charles Isi there any , axis helongw^tQ $)$ 
 .earth? adl 'nrifttiiia niie$62 fw&nifvB^ 
 
 ^ Tutor, i No ;. but, >#s_. we shall to-morrow, show's 
 the earth turns round once in every 24 hours, so as- 
 tronomers imagine an axis upon which it revolves as 
 upon a centre, the extremities of which imaginary 
 .axis are- the poles of the earth ; of these N the north 
 pole points at all times exactly to .p, (Fig, 1,) the 
 north pole of the heavens which we have already 
 described, and which is, as you recollect, withia 
 two degrees of the polar star, f t <-I 
 
 James. And how do you define the equator ?^^ 
 
 Tutor. The equator AB (Fig 4) is the circumfe- 
 rence of an imaginary circle drawn round the earth 
 at an equal distance from each pole. 
 
 Charges, And I think you told us, that if we 
 conceived this circle extended every way to the 
 fixed stars, it would form the celestial equator. 
 
 Tutor. I did ; it is also called the equinoctial, 
 and you must not forget, that in this case it would 
 cut the circle of the ecliptic CD in two points. 
 K
 
 34 ASTRONOMY. 
 
 James. Why is the ecliptic marked on the ter^ 
 restrial globe, since it is a circle peculiar to the 
 heavens. 
 
 Tutor. Though the ecliptic be peculiar to the 
 heavens, and the equator to the earth, yet they are 
 both drawn on the terrestrial and celestial globes, 
 in order, among other things, to show the position 
 which these imaginary circles have to one another. 
 
 I shall now conclude our present conversation, 
 with observing, that besides the proofs already ad- 
 duced for the globular form of the earth, there 
 are others equally conclusive, which will be better 
 understood a few days hence.
 
 OF THE DIURNAL MOTION OF THE EARTH. 35 
 
 CONVERSATION VII. 
 
 Of the Diurnal Motion of the Earth. 
 
 TUTOR. Well, gentlemen, are you satisfied 
 that the earth on which you tread is a globular body, 
 and not a mere extended plane ? 
 
 Charles. Admitting the facts which you men- 
 tioned yesterday, viz. that the top-mast of a ship 
 at sea is always visible before the body of the ves- 
 sel comes into sight ; that navigators have repeat* 
 edly, by keeping the same direction, sailed round 
 the world ; and that persons employed in digging 
 canals, can only execute their work with effect, by 
 allowing for the supposed globular shape of the 
 earth, it is evident the earth cannot be a mere ex- 
 tended plane. 
 
 James. But all these facts can be accounted for, 
 upon the supposition that the earth is a globe, and 
 therefore you conclude it is a globe : this was, I 
 believe, the nature of the proof? 
 
 Tutor. It was ; let us now advance one step far- 
 ther, and show you that this globe turns on an ima-
 
 36 ASTRONOMY. 
 
 ginary axis every twenty-four hours ; and thereby 
 causes the succession of day and night. 
 
 James. I shall wonder if you are able to afford 
 such satisfactory evidence of the daily motion of 
 the earth, as of its globular form. 
 
 Tutor. I trust, nevertheless, that the arguments 
 On this subject will be sufficiently convincing, and 
 that before we part you will admit, that the appa- 
 rent motion of the sun and stars is occasioned by 
 the diurnal motion of the earth. 
 
 Charles. I shall be glad to hear how this can be 
 proved ; for if, in the morning, I look at the sun 
 when rising, it appears in the east, at noon it has 
 travelled to 'the south, and in the evening I see it 
 set in the western part of the heavens. 
 
 James. Yes, and we observed the same last night 
 (March the first) with respect to Arcturus, for about 
 eight o'clock it had just risen in the north-west part 
 of the heavens, and when we went to bed two hours 
 after, it had ascended a good height in the heavens, 
 evidently travelling towards the west. 
 
 Tutor. It cannot be denied that the heavenly 
 bodies appear to rise in the east and set in the 
 west ; but the appearance will be the same to us, 
 whether those bodies revolve about the earth while 
 that stands still, or they stand still while the earth 
 turns on its axis the contrary way. 
 
 Charles. Will you explain this, sir ? 
 
 Tutor. Suppose OR c B (Plate, I Fig. 5), to
 
 OF THE DIURNAL MOTION OP THE EARTH. 37 
 
 represent the earth, T the centre on which it 
 turns from west to east, according to the order of 
 the letters G R c B. If a spectator on the surface 
 of the earth at R, see a star H, it will appear to him 
 to. have just risen ; if now the earth be supposed to 
 turn on its axis a fourth part of a revolution, the 
 spectator will be carried from R to c, and the star 
 will be just over his head; when another fourth part 
 of the revolution is completed, the spectator will 
 be at B, and to him the star at H will be setting, and 
 will not be visible again till he arrive, by the rota- 
 tion of the earth, at the station R. 
 
 Charles. To the spectator, then, at R, the ap- 
 pearance would be the same whether he turned 
 with the earth into the situation B, or the star at 
 H had described, in a contrary direction, the space 
 H z o in the same time. 
 
 Tutor. It certainly would. 
 
 James. But if the earth really turned on its axis, 
 should we not perceive the motion? 
 
 Tutor. The earth in its diurnal rotation being 
 subject to no impediments by resisting obstacles, 
 its motion cannot affect the senses. In the same 
 way ships on a smooth sea are frequently turned 
 entirely round by the tide, without the knowledge of 
 those persons who happen to be busy in the cabin 
 or between the decks. 
 
 Charles. That, is, because they pay no attention
 
 38 ASTRONOMY. 
 
 to any oilier object but the vessel in which they are. 
 Every part of the ship moves with themselves. 
 
 James. Bat if while the ship is turning, without 
 their knowledge, they happen to be looking at fixed 
 objects, what will be the appearance r 
 
 Tutor. To them, the objects which are at rest 
 will appear to be turning round the contrary way. 
 In the same manner we are deceived in the motion 
 of the earth round its axis ; for if we attend to no- 
 thing but what is connected with the earth, we can- 
 not perceive a motion of which we partake ourselves ; 
 and if we fix our eyes on the heavenly bodies, the 
 motion of the earth being so easy, they will appear 
 to be turning in a direction contrary to the real 
 motion of the earth. 
 
 Charles. I have sometimes seen a sky-lark ho- 
 vering and singing over a particular field for seve- 
 ral minutes together ; now if the earth is continu- 
 ally in motion while the bird remains in the same 
 part of the air, why do we not see the field, over 
 which he first ascended, pass from under him? 
 
 Tutor. Because the atmosphere, in which the 
 lark is suspended, is connected with the earth, par- 
 takes of its motion, and carries the lark along with 
 it ; and therefore, independently of the motion given 
 to the bird by the exertion of ita wings, it has an* 
 other in common with the earth,, yourself, and all 
 things on it, and, being common to us all, we have
 
 OF THE DIURNAL MOTION OF THE EARTH. 9 
 
 no methods of ascertaining the fact by means qf 
 the senses. 
 
 James. Though the motion of a ship cannot be 
 observed without objects at rest to compare with it, 
 yet I cannot help thinking that if the earth moved, 
 we should be able to discover it by means of the 
 stars, as they are fixed. 
 
 Tutor. Do you not remember once sailing very 
 swiftly on the river, when you told me that you 
 thought that all the trees, houses, &c., on its banks 
 were in motion ? 
 
 James. I now recollect.it well, and I had some 
 difficulty in persuading myself that it was not 30.^ -^ 
 
 Cliarles. This brings to my mind a still stronger 
 deception of this sort : when travelling with great 
 speed in a post-chaise, I suddenly waked .from a 
 sleep in a smooth but narrow road, and I could 
 scarcely help thinking for several minutes, but that 
 the trees and hedges were running away from us, 
 and not we from them. 
 
 Tutor. I will mention another curious instance 
 of this kind ; if you ever happen to travel pretty 
 swiftly in a carriage by the side of a field ploughed 
 into long narrow ridges, and perpendicular to the 
 road, you will think that all the ridges are turning 
 round in a direction contrary to that of the carnage. 
 These facts may satisfy you that. the appearances 
 will be precisely the same to us, whether the earth
 
 . 
 
 40 ASTRONOMY. 
 
 turn on its axis from west to east, or the sun and 
 stars move from east to west. 
 
 James. They will: btit which is the more natu- 
 ral conclusion? 
 
 Tutor. This you shall determine for yourself. 
 If the earth (Fig. 4), turns on its axis in 24 hours, 
 at what rate will any part of the equator AB mover 
 
 Charles. To determine this we must find the 
 measure of its circumference, and then dividing this 
 by 24, we shall get the number of miles passed 
 through in an hour. 
 
 Tutor. Just so: now call the semi-diameter 
 of the earth 4,000 miles, which is rather more than 
 the true measure. 
 
 James. Multiplying this by six* will give 24,000 
 miles for the circumference of the earth at the 
 equatoi, and this divided by 24, gives 1,000 miles 
 for the space passed through in an hour. 
 
 Tutor. You are right. The sun, I have already 
 told you, is 95 millions of miles distant from the 
 earth; tell me therefore, Charles, at what rate that 
 
 * If the reader would be accurate in his calculations, he mnst take the 
 mean radius of the earth at 3963 miles, and this multiplied by 0,28318 will 
 give 24,012 miles for the circumference. Through the remainder of this 
 work the decimals in multiplication are omitted, in order that the mind may 
 not be burdened with odd numbers. It seemed necessary, however, in this 
 place, to give the true semi-diameter of the earth, and the number (accu- 
 rate to five places of decimals), by which if the radius of any circle be mul- 
 tiplied, the circumference is obtained.
 
 OF THE FIGURE OF THE EARTH. 41 
 
 body must travel to go 'round the earth in 24 
 hours? 
 
 Charles. I will ; 95 millions multiplied by six 
 will give 570 millions of miles for the length of his 
 circuit, this divided by 24 gives nearly 24 millions 
 of miles for the space he must travel in an hour, to 
 go round the earth in a day. 
 
 Tutor. Which now is the more probable con- 
 clusion, either that the earth should have a diurnal 
 motion on its axis of 1000 miles in an hour, or that 
 the sun-, which is a million of times larger than the 
 earth, should travel 24, millions of miles in the same 
 time ? 
 
 James, It is certainly more rational to conclude 
 that the earth turns on its axis, the effect of which 
 you told ; , us wa* the alternate succession of day, 
 and night. 
 
 Tutor, I did ; and on this and some other topics 
 we will enlarge to-morrow. 
 
 * Jv*. -.'l^*-U'd 
 
 t-f ,-^v/^ 
 : -. . r
 
 42 - ASTRONOMY, 
 
 CONVERSATION VIII. 
 
 Of Day and Night. 
 
 JAMES. You are now, sir, to apply the rota- 
 tion of the earth about its axis to the succession of 
 day and night. 
 
 Tutor. I will; and for this purpose, suppose 
 G R c B (Plate VI, Fig 5.), to be the earth, revolving 
 on its axis, according to the order of the letters, 
 that is, from G to R, R to c, &c. If the sun be fixed 
 in the heavens at z, and a line H o be drawn 
 through the centre of the earth T, it will represent 
 that circle, which when extended to the heavens is 
 called the rational horizon. 
 
 Charles. In what does this differ from the sensi- 
 ble horizon ? 
 
 Tutor. The sensible horizon is that circle in the 
 heavens which bounds the spectator's view, and 
 which is greater or less, according as he stands 
 higher or lower. For example ; an eye placed at 
 five feet above the surface of the earth or sea, sees 
 2| miles every way : but if it be at ''20 feet high,
 
 OF DAY AND NIGHT. 43 
 
 that is 4 times the height, it will see 5 miles, or 
 twice the distance*. 
 
 Charles. Then the sensible differs from the ra- 
 tional horizon in this, that the former is seen from 
 the surface of the earth, and the latter is supposed 
 to be viewed from its centre. 
 
 Tutor. You are right ; and the rising and setting 
 of the sun and stars are always referred to the ra- 
 tional horizon. 
 
 James. Why so ? they appear to rise and set as 
 soon as they get above, or sink below that bounda- 
 ry which separates the visible from the invisible part 
 of the heavens. 
 
 Tutor. The reason is this, that the distance of 
 the sun and fixed stars is so great in comparison of 
 4000 miles (the difference between the surface and 
 centre of the earth), that it can scarcely be taken 
 into account. 
 
 Charles. But 4000 miles seem to me an im- 
 mense space. 
 
 Tutor. Considered separately, they are so, but 
 when compared with p5 millions of miles, the dis- 
 tance of the sun from the earth, they almost vanish 
 as nothing. 
 
 James. But do the rising and setting of the moon, 
 which is at the distance of 240 thousand miles only, 
 respect also the rational horizon ? 
 
 Tutor. Certainly ; for 4000 compared with 240 
 
 * See Dr. Ashvrorth'j Trigonometry, Prop. S4. 2d Edition, 1803.
 
 44 ASTRONOMY. 
 
 thousand, bear only the proportion of 1 to 60. Now 
 if two spaces were marked out on the earth in dif- 
 ferent directions, the one 60 and the other 61 yards, 
 should you at once be able to distinguish the great- 
 er from the less? 
 
 Charles. I think not. 
 
 Tutor. Just in the same manner does the dis- 
 tance of the centre from the surface of the earth 
 vanish in comparison of its distance from the 
 moon. 
 
 James. We must not, however, forget the suc- 
 cession of day and night. 
 
 Tutor. Well then ; if the sun be supposed at z, 
 it will illuminate, by its rays, all that part of the 
 earth that is above the horizon H o : to the inhabi- 
 tants of G, its western boundary, it will appear just 
 rising ; to those situated at n, it will be noon ; and 
 to those in the eastern part of the horizon c, it will 
 be setting. 
 
 Cliarles. I see clearly why it should be noon to 
 those who live at R, because the sun is just over 
 their heads, but it is not so evident, why the sun must 
 appear rising and setting to those who are at o 
 and c. 
 
 Tutor. You are satisfied that a spectator can- 
 not, from any place, observe more than a semi- 
 circle of the heavens at any one time ; now what 
 part of the heavens will the spectator at G ob- 
 serve ?
 
 OF DAY AND NIGHT. 45 
 
 James. He will see the concave hemisphere 
 z o N. 
 
 Tutor. The boundary to his view will be N and 
 z, will it not ? 
 
 Ckarles. Yes; and consequently the sun at z, 
 will to him be just coming into sight. 
 
 Tutor. Then by the rotation of the earth, the 
 spectator at G will in a few hours come to R, when, 
 to him, it will be noon ; and those who live at R, 
 will have descended to c ; now what part of the 
 heavens will they see in this situation? 
 
 James. The concave hemisphere N H z, and z 
 being the boundary of their view one way, the sun 
 will to them be setting. 
 
 Tutor. Just so. After which they will be turned 
 away from the sun, and consequently it will be night 
 to them till they come again to G. Thus, by this 
 simple motion of the earth on its axis, every part 
 of it is, by turns, enlightened and warmed by the 
 cheering beams of the sun. 
 
 Charles. Does this motion of the earth account 
 also for the apparent motion of the fixed stars ? 
 
 Tutor. It is owing to the revolution of the earth 
 round its axis, that we imagine the whole starry fir- 
 mament revolves about the earth in 24 hours, ap- 
 pearing to turn on an axis, near one extremity of 
 which, as I said before, is placed the polar star. 
 
 James. Is not the fact you now mentioned an 
 additional argument also in support of the spheri- 
 
 N
 
 46 ASTRONOMY. 
 
 cal form of the earth? If it were an extended plane, 
 the sun and stars mast appear to rise at the same 
 moment to the inhabitants of all parts of the earth. 
 
 Tutor. It certainly must. But the contrary is 
 so well ascertained, that the distance a ship has 
 sailed east or west from a place is most easily and 
 commonly determined on this very principle by 
 means of accurate time-keepers called chronometers. 
 Can you calculate what allowance of easting or 
 westing should be made for the difference of one 
 hour of time ? 
 
 Charles. As it is midnight on the other side of 
 the globe while it is mid-day with us, the 12th part 
 of that distance, or 15 should be allowed for every 
 hour's difference of time. 
 
 Tutor. You are quite right. And in the same 
 way you can calculate proportionally for any 
 smaller difference of time. Supposing therefore 
 you set your watch at 12 o'clock when it is mid-day 
 at Saugor, and after sailing some days to the east- 
 wards observe, that it is mid-day, when by your 
 watch it is only 11 o'clock, you conclude that you 
 have made 15 of easting. 
 
 James. Why do we not see the stars by day as 
 well as by night ? 
 
 Tutor. Because in the day time, the sun's rays 
 are so powerful, as to render those coming from the 
 fixed stars invisible. But if you ever happen to go 
 down into any very deep mine, or coal-pit, where
 
 OF DAY AND NIGHT. 47 
 
 the rays of the sun cannot reach the eye, and it be 
 a clear day, you may, by looking up to the heavens, 
 see the stars at noon as well as by night. 
 
 Charles. If the earth always revolve on its axis 
 in 24 hours, why does the length of the days and 
 nights differ in different seasons of the year ? 
 
 Tutor. This depends on other causes connected 
 with the earth's annual journey round the sun, upon 
 which we will converse the next time we meet.
 
 48 ASTRONOMY. 
 
 c^ 3fih&*9g * uo v 
 
 fHlu vet ?c iteW tJs&QQf!^.* ^<' siii,$ea 
 
 CONVERSATION IX. 
 
 
 TUTOR. Besides the di'wwaJ motion of the 
 earth, by which the succession of day and night is 
 produced ; it has another, called its annual motion, 
 \vhichisthejourneyitperforins round the sun in 
 365 days, 5 hours, 48 minutes, and 49 seconds; 
 and this is the cause of the sun's apparent annual 
 motion in the ecliptic. 
 
 Charles. Are the different seasons to be ac- 
 counted for by this motion of the earth ? 
 
 Tutor. Yes, it is the cause of the different lengths 
 of the days and nights, and consequently of the 
 different seasons, viz. Spring, Summer, Autumn, 
 and Winter. 
 
 James. How is it known that the earth makes 
 this annual journey round the sun ? 
 
 Tutor. I have already told you, that if the sun 
 be seen near a fixed star to-day at sun-set, it will, 
 in a few weeks, be found near another consider- 
 ably to the east of that one : and if the observations 
 be continued through the year, we shall be able to
 
 OF THE ANNUAL MOTION Of THE EARTH. 49 
 
 trace him round the heavens to the same fixed star 
 from which we set out ; consequently, the sun must 
 have made a journey round the earth in that time, 
 or the earth round him. 
 
 James. And the sun being a million times larger 
 than the earth, you will say that it is more natural, 
 that the smaller body should go round the larger, 
 than the reverse. 
 
 Tutor. That is a proper argument : but it may be 
 stated in a much stronger manner. The sun and 
 earth mutually attract one another, and since they 
 are in equilibrio by this attraction, you know their 
 momenta must be equal,* therefore the earth being 
 the smaller body, must make out by its motion 
 what it wants in the quantity of its matter, and, 
 of course, it must be that which performs the 
 journey. 
 
 James. But if you refer to the principle of the 
 lever, to explain the mutual attraction of the sun and 
 earth, it is evident, that both bodies must turn 
 round some point as a common centre. 
 
 Tutor. They do ; and that is the common cen- 
 tre of gravity of the two bodies. Now this point 
 between the earth and sun is within the surface of 
 the latter bocty. 
 
 Charles. I understand how this is ; because the 
 centre of gravity between any two bodies, must be 
 
 * See Part I. Conversation XIV. p. 71. 
 
 I JJJu-
 
 50 ASTRON'OMY. 
 
 as ranch nearer to the centre of the larger body than 
 the smaller, as the former contains a greater quan- 
 tity of matter than the latter. 
 
 Tutor. You are right : but you will not conclude 
 that, because the sun is a million of times larger 
 than the earth, therefore, it contains a quantity of 
 matter, a million of times greater than that con- 
 tained in the earth. 
 
 James. Is it then known, that the earth is com- 
 posed of matter more dense than that which com- 
 poses the bo^y of the sun? 
 
 Tutor. The earth is composed of matter four 
 times denser than that of the sun ; and hence the 
 quantity of matter in the sun is only between two 
 and three hundred thousand times greater than that 
 which is contained in the earth. 
 
 Charles. Then for the momenta of these two 
 bodies to be equal, the velocity of the earth must 
 be between two and three hundred thousand times 
 greater than that of the sun. 
 
 Tutor. It must ; and to effect this, the centre of 
 gravity between the sun and earth, must be as much 
 nearer to the centre of the sun, than it is to the 
 centre of the earth, as the former body contains a 
 greater quantity of matter than the latter:. and hence 
 it is found to be several thousand miles within the 
 surface of the sun. 
 
 James. I now clearly perceive, that since one of 
 these bodies revolves about the other in the space
 
 OF THE ANNUAL MOTION OF THE EARTH. 51 
 
 of a year, and that they both move round their 
 common centre of gravity, that it must of necessity 
 be the earth which revolves about the sun, and not 
 the sun round the earth. 
 
 Tutor. Your inference is just. To suppose that 
 the sun moves round the earth, is as absurd as to 
 maintain, that a mill-stoue could be made to move 
 round a pebble.
 
 52 ASTRONOMY. 
 
 CONVERSATION X, 
 
 TUTOR. I will now show you how the differ- 
 ent seasons are produced by the annual motion of 
 the earth. 
 
 James. Upon what do they depend, sir. 
 
 Tutor. The variety of the seasons depends (1), 
 upon the length of the days and nights; aud (2), 
 upon the position of the earth with respect to the 
 sun. 
 
 Charles. But if the earth turn round its imagin- 
 ary axis every 24 hours, ought it not to enjoy equal 
 days and nights all the year? 
 
 Tutor. This would be the case if the axis of the 
 earth N s (Plate VI, Fig. 6), were perpendicular to 
 a line c E drawn through the centres of the sun and 
 earth; for then as the sun always enlightens one 
 half of the earth by its rays, and as it is day at 
 any given place on the globe, so long as that place 
 continues in the enlightened hemisphere, every part, 
 except the two poles, must, during its rotation on 
 its axis, be one half of its time in the light and the
 
 OF THE SEASONS. 53 
 
 other half in darkness : or, in other words, the days 
 and nights would be equal to all the inhabitants of 
 the earth, excepting to those, if any, who live at 
 the poles. 
 
 James. Why do you except the people at the 
 poles? 
 
 Tutor. Because the view pf the spectator situ- 
 ated at the poles N and s, must be bounded by the 
 line c E, consequently to him the sun would never 
 appear to rise, or set, but would always be in the 
 horizon. 
 
 Charles. If the earth were thus situated, would 
 the rays of the sun always fall vertically to the 
 same part of it ? 
 
 Tutor. They would : and that part would be 
 Q the equator; and, as we shall presently show, the 
 heat excited by the sun being greater or less in pro- 
 portion as his rays fall more or less perpendicularly 
 upon any body, the parts of the earth about the equa- 
 tor would be scorched up, while those beyond 40 or 
 50 degrees on each side of that line and the poles, 
 would be desolated by an unceasing winter. 
 James. In what manner is this prevented r 
 Tutor. By the axis of the earth N s (Plate VJ, 
 Fig. 7), being inclined or bent about 23 degrees and 
 a half out of the perpendicular. In this case you 
 observe, that all the parallel circles, except the 
 equator, are divided into two unequal parts, having 
 a greater or le portion of their circumferences in 
 p
 
 the 
 
 'res^^t fc> # the 
 
 
 Charles. At what season of the year is the earth 7 
 represented in this figure? 
 
 Tutor. At our summer season : for you observe 
 that the parallel circles in the northern -hemisphere 
 hiive their greater v parts enlightened and their 
 smaller parts in the'dark. If DL represent that cir- 
 cle of latitude on the globe in which Great Britain 
 is situated, it is evident that about two-thirds of it is 
 in the light, and only one-third in dark ness:: V.iw\O 
 
 You nill also remember that parallels of latitude 
 are supposed circles on the surface of the earth, and 
 are shown by rea| drcles on its representative the 
 terrestrial globe, drawn parallel to the equator.'' f r : 
 
 James. Is that the reason why our days towards 
 the middle of June are 13 hours 24 minutes long, 
 and the nights but 10 hours, 36 minutes? 
 
 Tutor. It is: and if you look to the parallel next 
 beyond that marked D L, you will see a still greater 
 disproportion between the day and nights and the 
 parallel more north than this is entirely in the light. 
 1 Charles. Is it then all clay there ? 
 
 Tutor. To the whole space between that and 
 the pole it is continual day for sometime, the dura- 
 tion of which is in proportion to its vicinity to the 
 pole; and at the pole there is apermmient day-light 
 for six months' tog'ethd*.
 
 OF -THE SEASONS. 55 
 
 A Aiui durhig 't^airYiftie it triust, i "Sip- 
 pose, be night to the people who lire' tit the 'smitfi 
 pole? 1 a a ^ 
 
 ' Tutor! Yes, the figure shows that the south pole 
 is in darkness; and you may observe, that to the. 
 inhabitants living in equal i>arallels of latitude, the 
 one north, and the other south, the length of the 
 days to the one will be always equal to the length 
 of the nights to (he other. 
 
 Charles. What then shall we say to those who 
 live at the equator, and consequently who have no 
 latitude ? 
 
 Tutor. To them the days and nights are alivays 
 equal, and of course twelve hours each in length; 
 and this is also evident from the figure, for in every 
 position of the globe one-half of the equator is in 
 the light, and the other half in darkness. 
 
 James. If, then, the length of the days is the 
 cause of the different seasons, there can be no va- 
 riety, iii this respect, to those who live at the 
 equator. 
 
 Tutor. You seem to forget that the change in 
 the seasons depends upon the pgsition of the earth 
 with respect to the sun, that is, upon the perpendi- 
 cularity with which the rays of light fall upon any 
 particular part of. the earth ; as well as upon the 
 length of days. 
 
 Charles. Does this make any material difference 
 with regard to the heat of the sun?
 
 56 ASTRONOMY. 
 
 Tutor. It does: let A B (Plate VI. Fig. 8), re- 
 present a portion of the earth's surface, on which 
 the sun's rays fall perpendicularly; let B c repre- 
 sent an equal portion on which they fall obliquely 
 or aslant. It is manifest that B c, though it be equal 
 to A B, receives but half the light and heat that 
 A B does. 
 
 O) '*7f ?j 
 
 -li/ Oil SO C0 S'lSlf) t 
 
 $iij ic evil orf.v 
 
 ; *r
 
 OP THE SEASONS. 57 
 
 CONVERSATION XL 
 
 Of the Seasons. 
 
 TUTOR. Let us now take a view of the earth 
 in its annual course round the sun, considering its 
 axis as inclined 23 degrees to a line perpendicular 
 to its orbit, and keeping, through its whole journey, 
 a direction parallel to itself; and you will find, that, 
 according as the earth is in different parts of its 
 orbit, the rays of the sun are presented perpendi- 
 cularly to the equator, and to every point of the 
 globe, within 23J degrees of it both north and 
 south. 
 
 This figure (Plate VI, Fig. 9), represents the earth 
 in four different parts of its orbit, or as it is situated 
 with respect to the sun in the months of March, 
 June, September, and December. 
 
 Charles. The earth's orbit is not made circular 
 in the figure. 
 
 Tutor. No. The orbit itself is nearly circular, 
 but we are supposed to view it from the sides 
 D, and therefore, though almost a circle, it ap- 
 Q
 
 58 ASTRONOMY. 
 
 pears to be a long ellipse. All circles appear el- 
 liptical in an oblique view, as is evident by looking 
 obliquely at the rim of a bason, at some distance 
 from you. For the true figure of a circle can only 
 be seen when the eye is directly over its centre. 
 You observe that the sun is not in the centre. 
 
 James. I do ; and it appears nearer to the earth 
 in the winter, than in the summer. 
 
 Tutor. We are indeed more than three millions 
 of miles nearer to the sun in December than we 
 are in June. <>> 
 
 Charles. Is this possible, and yet qur winter , i? 
 much colder than the summer ? 
 
 Tutor. . Notwithstanding this, it is a well-known 
 fact. For it is ascertained, that our. summer, that 
 is, the time that passes between the vernal and au- 
 tumnal equinoxes, is nearly eight days longer than 
 our winter, or the time between the autumnal and 
 vernal equinoxes. Consequently the motion of the 
 earth is slower in the former case than in the latter, 
 and therefore, as we shall see, it must be at a greater 
 distance from the sun. Again, the sun's apparent 
 diameter is greater in our winter than in summer, but 
 the apparent diameter of any object increases in 
 proportion as our distance from the object is dimi- 
 nished, and therefore we conclude, that we are nearer 
 the sun in winter than in summer. The sun's apparent 
 diameter in winter is 32 75 "; in summer 31'. .40 . 
 James. But if the earth is farther from the sun
 
 OF THE SEASONS. 69 
 
 ill summer than in winter, why are our winters so 
 much colder than our summers? 
 
 Tutor. Because first, in the summer, the sun 
 rises to a much greater height above our horizon, 
 and therefore its rays coming more perpendicularly, 
 more of them, as we showed you yesterday, must 
 fall upon the surface of the earth, which is the prin- 
 cipal cause of our summer's heat. Secondly, in 
 the summer, the days are very long, and the nights 
 short; therefore the earth and air are heated by the 
 
 sun in the day, more than they are cooled in the 
 j 
 
 James. Why have we not, then, the greatest heat 
 at the time when the days are longest? 
 
 Tutor. The hottest season of the year is certainly 
 a month or two after this, which may be thus ac^ 
 counted for. A body once heated does not grow 
 cold instantaneously, but gradually ; now, as long 
 as more heat comes from the sun in the day, than 
 is lost in the night, the heat of the earth and air will 
 be daily increasing, and this must evidently be the 
 case for some weeks after the longest day, both on 
 account of the number of rays which fall on a given 
 space, and also from the perpendicular direction of 
 those rays. 
 
 James. Will you explain to us in what manner 
 the seasons are .produced ? 
 
 Tutor. By referring to the figure (Plate VI, 
 Fig. 9,) you will observe, that in the month of June,
 
 60 ASTRONOMY. 
 
 the north pole of the earth inclines towards the sun, 
 and consequently brings all the northern parts of the 
 globe more into light, than at any other time in the 
 year. 
 
 Charles. Then to the people in those parts it is 
 summer. 
 
 Tufor. It is : but in December, when, the earth is 
 in the opposite part of its orbit, the north pole de^ 
 clines from the sun, which occasions the northern 
 places to be more in the dark than in the light; and 
 the reverse at the southern places, 
 
 James. Is it then summer to the inhabitants of 
 the southern hemisphere? 
 
 * ? *HV A ''/""' 
 
 Tutor. Yes, it is ; and winter to us. In the 
 months of March and September, the axis of the 
 earth does not incline to, nor decline from, the sun, 
 but is perpendicular to a line drawn from its centre ; 
 and then the poles are in the boundary of light and 
 darkness, and the sun being directly vertical to, or 
 over the equator, makes equal day and night at all 
 places. Now trace the annual motion of the earth 
 in its orbit for yourself, as it is represented in the 
 figure. 
 
 Charles. I will, sir : about the 20th of March 
 the earth is in Libra, and consequently to its inha- 
 bitants the sun will appear in Aries, and be vertical 
 to the equator. 
 
 Tutor. And then the equator, and all its parallels, 
 are equally divided between the light and dark, 
 .*- ; >
 
 OF THE SEASONS. 61 
 
 Charles. Consequently the days and nights are 
 equal all over the world. As the earth pursues its 
 journey from March to June, its northern hemis- 
 phere comes more into light, and on the 21st of that 
 month, the sun is vertical to the tropic of Cancer. 
 
 Tutor. And you then observe that all the circles 
 parallel to the equator are unequally divided ; those 
 in the northern half have their greater parts in the 
 light, and those in the southern half have their 
 larger parts in darkness. 
 
 Charles. Yes ; and of course it is summer to the 
 inhabitants of the northern hemisphere, and winter 
 to the southern* qj f 
 
 I now trace it to September, when I find the sun 
 vertical again to the equator, and, of course, the 
 days and nights are again equal. And folio wing 
 the earth in its journey to December, or when it has 
 arrived at Cancer, the sun appears in Capricorn, 
 and is vertical to that part of the earth called the 
 tropic of Capricorn ; and now the southern pole is 
 enlightened, and all the circles on that hemisphere 
 have their larger parts in light, and, of course, it is 
 summer to those parts, and winter to us in the north- 
 ern hemisphere. 
 
 Tutor. Can you, James, now tell me why the 
 days lengthen and shorten from the equator to the 
 polar circles every year ? 
 
 James. I will try to explain myself on the sub- 
 ject. Because the sun in March is vertical to the
 
 62 ASTKOKOMY. 
 
 equator, and from that time to the 2 1st of June 
 it becomes vertical successively to all other parts of 
 the earth, between the equator and the tropic of Can- 
 cer; and in proportion as it becomes vertical to the 
 more northern parts of the earth, it declines from 
 the southern, and, consequently, to the former the 
 days lengthen, and to the latter they shorten* From 
 June to September the sun is again vertical succes- 
 sively to all the same parts of the earth, but in a 
 reverse order. 
 
 Charles. Since it is summer to all those parts of 
 the earth, where the sun is vertical, and we find 
 that the sun is vertical twice in the year to the 
 equator, and every part of the globe between the 
 equator and tropics, there must be also two summers 
 in a year to all those places. 
 
 Tutor. There are ; and in those parts near the 
 equator, they have two harvests every year.^But 
 let your brother finish his description. 
 
 James. From September to December, it is suc- 
 cessively vertical to all the parts of the earth situ- 
 ated between the equator and the tropic of Capri- 
 corn, which is also the cause of the lengthening of 
 the days in the southern hemisphere, and of their 
 becoming shorter in the northern. 
 
 Tutor. Can you, Charles, tell me why there is 
 sometimes no day, at others no night for some lit- 
 tle time together within the polar circles ? 
 
 Charles. The sun always shines upon the earth.
 
 OP ?HE SEASONS. 93 
 
 90 degrees eVefy Way, and when lie is Vertical td 
 the tropic of Cancer, which is 23 degrees north of 
 the equator*, he must shine the same number of de- 
 grees beyond the pdle, or ta the polar circle, and 
 while he thus shines, there can be no night to the 
 people within that polar circle ; and, of course, to the 
 inhabitants at the southern polar circle, there cinbd 
 no days at the same time, for as the sun's rays 
 reach but 90 degree! every way, they cannot shine 
 far enough to reach them. 
 
 Tutor. Tell me, now, why there is but one day 
 and night in the whole year at the poles ? 
 
 Charles. For the reason which 1 have just given, 
 the sun must shine beyond the north-pole all the 
 time he is vertical to those parts of the earth, situ- 
 ated between the equator and the tropic of Cancer, 
 that is, from March the 21st to September the 20th, 
 during which time there can be no night at the north- 
 pole, nor any day at the south pole. The reverse 
 of this may be applied to the southern pole. 
 
 James. I understand now, that the lengthening 
 and shortening of the days, and different seasons, 
 are produced by the annual motion of the earth 
 round the sun ; the axis of the earth, in all parts 
 of its orbit, being kept always pointing in the same 
 direction, or parallel to itself. But if thus parallel 
 to itself, how can it in all positions point to the 
 pole-star in the heavens? 
 
 Tutor. Because the diameter of the earth's or-
 
 64 ASTRONOMY. 
 
 bit AC is nothing in comparison of the distance of 
 the earth from the fixed stars. Suppose you draw 
 two parallel lines at the distance of three or four 
 yards from one another, will they not both point 
 alike to the moon when she is in the horizon ? 
 
 James. Three or four yards cannot be account- 
 ed as any thing, in comparison of 240 thousand miles, 
 the distance of the moon from us. 
 
 Tutor. Perhaps three yards bear a much greater 
 proportion to 240 thousand miles, than 190 millions 
 of miles bear to our distance from the polar star. 
 
 *W
 
 OF THE EQUATION OF TIME, 
 
 CONVERSATION XII. 
 
 Of the Equation of Time. 
 
 TUTOR. You are now, I presume, acquainted 
 with the motions peculiar to this globe on which 
 we live ? 
 
 Charles. Yes : it has a rotation on its axis from 
 west to east every 24 hours, by which day and night 
 are produced, and also the apparent diurnal motion 
 of^he heavens from east to west. 
 
 James. The other is its annual revolution in an 
 orbit round the sun, likewise from West to east, at 
 the distance of about 95 millions of miles from 
 the sun. 
 
 Tutor. You understand also, in what manner 
 this annual motion of the earth, combined with the 
 inclination of its axis, is the cause of the variety of 
 seasons. 
 
 We will therefore proceed to investigate another 
 curious subject, viz. the equation of time, and to 
 explain to you the difference between equal and 
 apparent time.
 
 66 ASTRONOMY; 
 
 Charles. Will you tell us what you mean by the 
 words equal and apparent, as applied to time ? 
 
 Tutor. Equal time is measured by a clock, that 
 is supposed to go without any variation, and to 
 measure exactly 24 hours from noon to noon. And 
 apparent time is measured by the apparent motion 
 of the sun in the heavens, or by a good sun-dial. 
 
 Charles. And what do you mean, sir, by the 
 equation oj time ? 
 
 Tutor. It is the adjustment of the difference of 
 time, as shown by a well-regulated clock and a true 
 sun-dial. 
 
 James. TJpon what does this difference depend r 
 
 Tutor. It depends first upon the inclination of 
 the earth's axis. And secondly upon the elliptic 
 form of the earth's orbit : for, as we have already 
 seen, the earth's orbit being an ellipse, its motion is 
 quicker when it is in peri/ielion, or nearest to the 
 sun ; and slower when it is in aphelion, or farthest 
 from the sun, 
 
 Charles. But I do not yet comprehend what the 
 rotation of the earth has to do with the going of a 
 clock or watch. 
 
 Tutor. The rotation of the earth is the most 
 equable and uniform motion in nature, and is com- 
 pleted in 23 hours, 56 minutes, and 4 seconds; this 
 space of time is called a sidereal day, because any 
 fixed star observed to rise or set at a certain time 
 one day, will rise or set again in this time. But a
 
 OF THE EQUATION OF TIME. (57 
 
 solar or natural day, which our clocks are intended 
 to measure, is the time from one mid-day to the next, 
 when the sun returns to the meridian, or that line in 
 the heavens which passes due north and south over 
 the place of observation. 
 
 James. What occasions this difference between 
 the solar and sidereal day? 
 
 Tutor. The distance of the fixed stars is so great, 
 that the diameter of the earth's orbit, though 190 
 millions of miles, when compared with it, is but a 
 point, and therefore any meridian on the earth will 
 revolve from a fixed star to that star again in exact- 
 ly the same time, as if the earth had only a diurnal 
 motion, and remained always in the same part of 
 its orbit. But with respect to the sun, as the 
 earth advances almost a degree eastward in its 
 orbit, in the same time that it turns eastward 
 round its axis, it must make more than a complete 
 rotation before it can come into the same position 
 with the sun that it had the day before. In the same 
 way, as when both the hands of a watch or clock 
 set off together at twelve o'clock, the minute-hand 
 must travel more than a whole circle before it will 
 overtake the hour-hand, that is, before they will be 
 in the same relative position again. Thus the side- 
 real days are shorter than the solar ones by about 
 four minutes, as is evident from observation. 
 
 Charles. Still I do not understand the reason why 
 the clocks and dials do not asrree.
 
 68 ASTRONOMY. 
 
 Tutor. A good clock is intended to measure 
 that equable and uniform time which the rotation 
 of the earth on its axis exhibits ; whereas the dial 
 measures time by the apparent motion of the sun, 
 which, as we have explained, is subject to varia- 
 tion. Or thus ; though the earth's motion on its 
 axis be perfectly uniform, and consequently the ro- 
 tation of the equator, the plane of which is perpen- 
 dicular to the axis, or of any other circle parallel 
 to it, be likewise equable, yet we measure the length 
 of the natural day by means of the sun, whose appa- 
 rent annual motion is not in the equator, or any of its 
 parallels, but in the ecliptic, which is oblique to it. 
 
 James. Do you mean by this, that the equator 
 of the earth, in its annual journey, is not always 
 directed towards the centre of the sun? 
 
 Tutor. I do : twice only in the year, aline drawn 
 from the centre of the sun to that of the earth 
 passes through those points where the equator and 
 ecliptic cross one another; at all other times,, it 
 passes through some other part of that oblique cir- 
 cle, which is represented on the globe by the eclip- 
 tic line. Now when it passes through the equator 
 or the tropics, which are circles parallel to the 
 equator, the sun and clocks go together as far as 
 regards this cause ; but at other times they differ, 
 because equal portions of the ecliptic pass over the 
 mericl ian in unequal parts of time on account of its 
 obliquity.
 
 OF THE EQUATION OF TIME. 69 
 
 Charles. Can you explain this by a figure? 
 
 Tutor. It is easily shown by the globe which 
 this figure nr N =* s (Plate VI, Fig. 10), may repre- 
 sent; v =2; will be the equator, <r 23 =2= the northern 
 half of the ecliptic, and r yp A the southern half. 
 Make chalk or pencil marks , 6, c, d, *>, /,.g, A t all 
 round the equator and ecliptic, at equal distances 
 (suppose 20 degrees) from each other, beginning at 
 Aries. Now by turning the globe on its axis, you 
 will perceive that all the marks in the first quadrant 
 of the ecliptic, that is, from Aries to Cancer, come 
 sooner to the brazen meridian than their corre- 
 sponding marks on the equator: those from the 
 beginning of Cancer to Libra come later : those 
 from Libra to Capricorn sooner : and those from 
 Capricorn to Aries later. 
 
 Now time as measured by the sun-dial is repre- 
 sented by the marks on the ecliptic ; that measured 
 by a good clock, by those on the equator. 
 
 Charles. Then while the sun is in the first and 
 third quarters, or, what is the same thing, while 
 the earth is travelling through the second and fourth 
 quarter, that is, from Cancer to Libra, and from 
 Capricorn to Aries, the sun is faster than the 
 clocks, and while it is travelling the other two 
 quarters it is slower. 
 
 Tutor. Just so : because while the earth is tra- 
 velling through the second and fourth quadrants, 
 equal portions of the ecliptic come sooner to the me-
 
 70 ASTRONOMY. 
 
 ridian than their corresponding parts of the equa- 
 tor: and during its journey through the first and 
 third quadrants, the equal parts of the ecliptic 
 arrive later at the meridian than their corresponding 
 parts of the equator. 
 
 James. If I understand what you have been say- 
 ing, the dial and clocks ought to agree at the equi- 
 noxes, that is, on the 20th of March, and the 23d 
 of September ;*but if I refer to the Ephemeris, I find 
 that on the former day (1809) the clock is 8 minutes 
 before the sun ; and on the latter day the clock is 
 almost 8 minutes behind the sun. 
 
 Tutor. If this difference between time measured 
 by the dial and clock depended only on the inclina- 
 tion of the earth's axis to the plane of its orbit, the 
 clocks and dial ought to be together at the equi- 
 noxes, and also on the 21st of June and the 21st of 
 December, that is, at the summer and winter sol- 
 stices; because, on those days, the apparent revolu- 
 tion of the sun is parallel to the equator. But I told 
 you there was another cause why this difference 
 subsisted. 
 
 Charles. You did : and that was the elliptic 
 form of the earth's orbit. 
 
 Tutor. If the earth's motion in its orbit were uni- 
 form, which it would be if the orbit were circular, 
 then the whole difference between equal time as 
 shown by the clock, and apparent time as shown 
 by the sun, would arise from the inclination of the
 
 OF THE EQUATION OF TIME. 71 
 
 earth's axis. But this is not the case, for the earth 
 travels, when it is nearest the sun, that is, in the 
 winter, more than a degree in 24 hours, and when 
 it is farthest from the sun, that is, in summer, less 
 than a degree in the same time : consequently from 
 this cause the natural day would be of the greatest 
 length when the earth was nearest the sun, for it 
 must continue turning the longest time after an entire 
 rotation in order to bring the meridian of any place 
 to the sun again: and the shortest day would be 
 when the earth moves the slowest in her orbit. Now 
 these inequalities, combined with those arising from 
 the inclination of the earth's axis, make up that dif- 
 ference which is shown by the equation table, found 
 in the Ephemeris, between good clocks and true 
 sun-dials.
 
 72 ,2V ASTRONOMY. 
 
 - 
 
 : 
 
 CONVERSATION XIII. 
 
 ;je. ' :r-:*i ' u;f?".; Si.'i m 
 
 O/ Leap-Year. 
 
 JAMES. Before M'e quit the subject of time, 
 will you give us some account of what is called in 
 our almanacs Leap- Year. 
 
 Tutor. I will. The length of our year is, as you 
 know, measured by the time which the earth takes 
 in performing her journey round the sun, jn the 
 same manner as the length of the day is measured 
 by its rotation on its axis. Now, to compute the 
 exact time taken by the earth in its annual journey, 
 was a work of considerable difficulty. Julius Cae- 
 sar was the first person who seems to have attained 
 to any accuracy on this subject. 
 
 Charles. Do you mean the Roman General, who 
 landed in Great Britain ? 
 
 Tutor. I do. He was not less celebrated as a man 
 of science, than he was renowned as a general. 
 Julius Caesar, who was well acquainted with the 
 learning of the Egyptians, fixed the length of the 
 year to be 365 days and 6 hours, which made it six 
 hours longer than the Egyptian year. Now, in
 
 OF LEAP-YEAR. 73 
 
 order to allow for the odd 6 hours in each year, he 
 introduced an additional day every fourth year, 
 which accordingly consists of 366 days-, and is call* 
 ed ieopYear, while the other three have only 365 
 days each. From him it is denominated the Julian 
 year* 
 
 James. It is also Called the Bissextile in the 
 almanacs, what does that mean? 
 
 Tutor. The Romans inserted the intercalary day 
 between the 23d and 24th of February : and be- 
 cause the 23d of February, in their calendar, was cal- 
 led sexto calendas Martii, the 6th of the calends of 
 March ; the intercalated day was called bis sexto 
 calendas Martii, the second sixth of the calends of 
 March, and hence the year of intercalation had the 
 appellation of Bissextile. This day was chosen at 
 Rome, on account of the expulsion of Tarquin from 
 the throne, which happened on the 23d of February. 
 We introduce, in Leap-Yeai^ a new day in the same 
 month, namely; the 29th. 
 
 Charles. Is there any rule for knowing what year 
 is Leap- Year ? 
 
 Tutor. It is known by dividing the date of the 
 year by 4 if there be no remainder, it is Leap- Year ; 
 thus 1799 divided by 4, leaves a remainder of 3, 
 showing, that it is the third year after Leap-Year. 
 These two lines contain the rule : 
 
 Divide by 4 ; what's left, shall be 
 Foi Leap-Year ; for past 1, 2, 3. 
 U
 
 74 ASTRONOMY. 
 
 James. The year, however, does not consist of 
 365 days and 6 hours, but of 365 days, 5 hours, 48 
 minutes, and 49 seconds*. Will not this occasion 
 some error? 
 
 Tutor. It will: and by substracting the latter 
 number from the former, you will find that the er- 
 ror amounts to 11 minutes and 11 seconds every 
 year, or to a whole day in about 130 years : not- 
 withstanding this, the Julian year continued to be 
 in general use till the year 1582, when Pope Grego- 
 ry XIII. undertook to rectify the error, which, at 
 that time, amounted to ten days. He according- 
 ly commanded the ten days between the 4th 
 and 15th of October in that year to be suppressed, 
 so that the 5th day of that month was called the 
 15th. This alteration took place through the greater 
 part of Europe, and the year was afterwards called 
 the Gregorian year, or New Style. In this country, 
 the method of reckoning, according to the New 
 Style, was not admitted into our calendars until the 
 year 1752, when the error amounted to nearly 11 
 days, which were taken from the month of Septem- 
 ber, by calling the 3d of that month the 14th. 
 
 Charles. By what means will this accuracy be 
 maintained ? 
 
 Tutor. The error amounting to one whole day 
 in about 130 years, it is settled by an act of parlia- 
 ment, that the year 1800 and the year 1900, which 
 
 See Conversation IX, p. 4$,
 
 or I,EAP-YEAK. 5 
 
 are, according to the rule just given, Leap- Years, 
 shall be computed as common years, having only 
 365 days in each: and that every four hundredth 
 year afterwards should be common years also. If 
 this method be adhered to, the present mode of 
 reckoning will not v#ry a single day from true time, 
 in less than 5000 years. 
 
 By the same act of parliament, the legal beginning 
 of the year was changed from the 25th of March to 
 the Jst of January. So that the succeeding months 
 of January, February, and March, up to the 24th 
 day, which would, by the Old Style, have been 
 reckoned part of the year 1753, were accounted as 
 the first three months of the year 1753. Hence we 
 sometimes see such a date as this, Feb. 10, 1774-5, 
 that is, according to the Old Style it was 1774, but 
 according to the New it is 1775, because now the 
 year begins in January instead of March, 
 
 - .r 
 
 il 

 
 76 
 
 srft ot -^ 
 201* fid .^isyjr* 4K>oi laoa, o.AM^qaoc id Usija 
 
 'lo 'tfbofa ^n'.^i b&ioi&c. J fcodtem ?&i 
 
 ^ 
 
 
 5TUTOR. You are now, geudemen, acquainted 
 with the reasons for the division of time into days 
 and years. 
 
 Charles. These divisions have their foundation! 
 in nature, the former depending upon the rotation 
 of the earth on its axis; the latter upon its revolu- 
 tion in an elliptic orbit about the sun as a centre : tif 
 motion. 
 
 James. Is there any natural reason for the divi- 
 sion of years into weeks, or of days into hours, mi- 
 nutes, and seconds? 
 
 Tutor. These divisions were invented entirely 
 for the convenience of mankind, and are according- 
 ly different in different countries. Tiiere is, however, 
 another division of time marked out by nature. 
 
 Charles. What is that, sir? 
 
 Tutor. The length of the month : not indeed that 
 month which consists of four weeks, nor that by 
 which the year is divided into 12 parts. These are 
 both arbitrary. But by a mouth is meant the time
 
 OF THE MOON. 77 
 
 which the moon takes in performing her journey 
 round the earth. 
 
 James. How many days does the moon take for 
 this purpose? 
 
 Tutor. If you refer to the time in which the moon 
 revolves from one point of the heavens to the same 
 point again, it consists of 27 days, 7 hours, and 43 
 minutes, this is called the periodical month : but if 
 you refer to the time passed from new moon to new 
 moon again, the month consists of 29 days, 12 hours, 
 and 44 minutes, this is called the synodical month. 
 
 Cliarles. Pray explain the reason of this dif- 
 ference. 
 
 Tutor. It is occasioned by the earth's annual 
 motion in its orbit. Let us refer to our watch as an 
 example. The two hands are together at 12 o'clock ; 
 now when the minute-hand has made a complete 
 revolution, are they together again? 
 
 James. IS o ; for the hour-hand is advanced the 
 twelfth part of its revolution, which, in order that 
 the other may overtake, it must travel five minutes 
 more than the hour. 
 
 Tutor. And something more, for the hour hand 
 does not wait at the figure I, till the other comes 
 tip : and therefore they will not be together till be- 
 tween 5 and 6 minutes after one. 
 
 Now apply this to the earth and moon, suppose 
 (Plate VI I, Fig. 11), s to be the sun; T the earth, 
 in a part of its orbit Q L ; and E to be the position 
 x
 
 .X i 
 
 78 ASTRONOMY. 
 
 ;.-fei 
 
 ;.-feijii/> *$ seaiiuii^j 4*1 u/iw cooi a^i^K 
 of the moon : if the earth had 110 motion, the moon 
 
 would move round its orbit E H c into the position 
 E again, in 27 days, 7 hours, 43 minutes ; but while 
 the moon is describing her journey, the earth has 
 passed through nearly a twelfth part of its orbit, 
 which the moon must also describe before the two 
 bodies come again into the same position that they 
 before held with respect to the sun: this takes up 
 so much wore time as to make hersynodical mOntfi 
 equal to 29 days, 12 hours, and 44 minutes : hence 
 the foundation of the division of time into months. 
 
 We will now proceed to describe some other par- 
 ticulars relating to the moon, as a body depending, 
 like the earth, on the sun for her light and heat. 
 
 Charles. Does the moon shine with a borrowed 
 light only? 
 
 Tutor. This is certain; for otherwise, if like the 
 sun, she were a luminous body, she would always 
 shine with a full orb as the sun does. Her diame* 
 ter is nearly 2200 miles in length 
 
 James. And I remember she is at the distance 
 of 240,000 miles from the earth. 
 
 Tutor. The sun s (Phte VII, Fi. 11), always en- 
 lightens one half of the moon E, and its whole en- 
 lightened hemisphere, or a part of it, or none at all, 
 is seen by us according to her different positions in 
 the orbit with respect to the earth, for only those 
 parts of the moon are visible at T which are cut off 
 by, and an /ii. the orik :
 
 OF THE MOON. 79 
 
 James* Then when the moon is at E, no part of 
 its enlightened side is visible to the earth. 
 
 Tutor. Yon are right : it is then new moon, or 
 change, for it is usual to call it new moon the first 
 day it is visible to the earth, which is not till the 
 second day after the change. And the moon being 
 in a line between the sun and earth, they are said 
 to be in conjunction. 
 
 Charles. And at A all the illuminated hemisphere 
 is turned to the earth. 
 
 Tutor. This is called full moon ; and the earth 
 being between the sun and moon, they are said to 
 ; be in opposition. The enlightened parts of the lit- 
 tle figures on the outside of the orbit, represent the 
 appearance of the moon as seen by a spectator on 
 (he earth. 
 
 James. Is the little figure then opposite E wholly 
 dark to show that the moon is invisible at change * 
 
 Tutor. It is : and when it is at F, a small part 
 of the illuminated hemisphere is wit/tin the moon's 
 orbit, and therefore to a spectator on the earth jt 
 appears horned; at o one half of .the enlightened 
 hemisphere is visible, and it is said to be in quadra- 
 ture: at H three-fourths of the enlightened part is 
 visible to the earth, and it is then said, to be gib- 
 bous: and at A the whole enlightened face of the 
 moon is turned to the earth, and it is said to be 
 full. The same may be said of the rest. 
 
 The horns of the moon before conjunction or new
 
 80 ASTRONOMY. 
 
 moon, are turned to the east ; after conj auction they 
 are turned to the west. 
 
 Charles. I see the figure is intended to show 
 that the moon's orbit is elliptical: does she also 
 turn upon her axis ? 
 
 Tutor. She does; and she requires the same 
 time for her diurnal rotation, as she takes in com- 
 pleting her revolution about the earth ; and conse- 
 quently, though every part of the moon is succes- 
 sively presented to the sun, yet the same heuii- 
 sphere is always turned to the earth. This is known 
 by observation with good telescopes. 
 
 James. Then the length of a day and night in 
 the muuii is equal to more than 29 days and a half 
 of ours. -..i it 
 
 Tutor. It is so : and therefore, as the length of 
 her year, which is measured by her journey round 
 the sun, is equal to that of ours, she can have but 
 about twelve days and one-third, in a year. An- 
 other remarkable circumstance relating to the moon, 
 is, that the hemisphere next the earth is never in 
 darkness, for in the position E, when it is turned 
 from the sun, it is illuminated by light reflected from 
 the earth, in the same manner as we are enlightened 
 by a full moon. But the other hemisphere of the 
 moon has a fortnight's light and darkness by turns. 
 Charles. Can the earth, then, be considered as a 
 satellite to the moon ? 
 
 Tutor. It would, perhaps, be inaccurate to de-
 
 OF THE MOON. 81 
 
 nominate the larger bpdy a satellite to tlie smaller, 
 but, with regard to affording reflected light, the 
 earth is to the moon what the moon is to the earth, 
 and subject to the same changes of horned, gib- 
 bous, full, &c. 
 
 Charles. But it must appear much larger than 
 the moon. 
 
 Tutor. The earth will appear to the inhabitants 
 of the moon, about 13 times as large as the moon 
 appears to us. When it is new moon to us, it is 
 full earth to them, and the reverse. 
 
 James. Is the moon then inhabited as well as the 
 earth ? 
 
 Tutor. Though we cannot demonstrate this fact, 
 yet there are many reasons to induce us to believe 
 it: for the moon is a secondary planet of consider- 
 able size; its surface is diversified like that of the 
 earth with mountains and valleys ; the former have 
 been measured by Dr. Herschel, and some of them 
 found to be about a mile in height. The situation 
 of the moon, with respect to the sun, is much like 
 that of the earth, and by a rotation on her axis, and 
 a small inclination on that axis to the plane of her 
 orbit, she enjoys, though not a considerable, yet an 
 agreeable variety of night and of seasons. To the 
 moon, our globe appears a capital satellite, under- 
 going the same changes of illumination as the moon 
 does to the earth. The sun and stars rise and set 
 there as they do here, and heavy bodies will fall on
 
 82 ASTRONOMY. 
 
 the moon as they do on the e^rth. Hence we are 
 led to conclude that, like the earth, the moon also 
 is inhabited. Dr. Herschel -discovered some years 
 ago three volcanoes, all burning in the moon ; but 
 no large seas or tracts of water have been observed 
 there, nor is the existence of a lunar atmosphere 
 certain. Therefore her inhabitants must materially 
 differ from those who live upon the earth. 
 
 tt.si^ ','vsi*. nl^ii 
 
 !il 'Kwif .-.;-,. 
 

 
 OF ECLIPSES. 83 
 
 CONVERSATION XV. 
 
 Of Eclipses. 
 
 CHARLES. Will you, sir, explain to us the 
 nature and causes of eclipses ? 
 
 Tutor. I will, with great pleasure. You must 
 observe, then, that eclipses depend upon this simple 
 principle, that all opaque or dark bodies, when ex- 
 posed to any light of the sun, cast a shadow behind 
 them in an opposite direction. 
 
 James. The earth, being a body of this kind, 
 must cast a very large shadow on its side which is 
 opposite to the sun. 
 
 Tutor. It dt>es : and an eclipse of the moon hap- 
 pens when the earth T (Plate VII, Fig. 12), passes 
 between the sun s and the moon M, and it is occasi- 
 oned by the earth's shadow being cast on the moon. 
 
 Charles. When does this happen? 
 
 Tutor. It is only when the moon is full, or in 
 opposition, that it comes within the shadow of the 
 earth. 
 
 James. Eclipses of the moon, however, do not
 
 84 ASTRONOMY. 
 
 happen every time it is full : what is the reason of 
 this? 
 
 Tutor. Because the orbit of the moon does not 
 coincide with the plane of the earth's orbit, but one 
 half of it is elevated about five degrees and a third 
 above it, and the other half is as much below it: 
 and therefore, unless the fall moon happen in or near 
 one of the nodes, that is, in or near the points in 
 which the two orbits intersect each other, she will 
 pass above or below the shadow of the earth, in 
 which case there can be no eclipse. 
 
 Charles. What is the greatest distance from the 
 node, at which an eclipse of the moon can happen ? 
 Tutor. There can be no eclipse, if the moon, at 
 the time when she is full, be more than 12 degrees 
 from the node ; when she is within that distance, 
 there will be a partial or total eclipse, according as 
 a part, or the whole disk or face of the moon falls 
 within the earth's shadow. If the eclipse happen 
 exactly when the moon is full in the node, it is call- 
 ed a central eclipse. 
 
 James. I suppose the duration of the eclipse lasts 
 all the time that the moon is passing through the 
 shadow. 
 
 Tutor. It does : and you observe that the sha- 
 dow is considerably wider than the moon's diameter, 
 and therefore an eclipse of the moon lasts some- 
 times three or four hours. The shadow also you 
 perceive is of a conical shape, and consequently, as
 
 OF ECLIPSES. 85 
 
 the moon's orbit is an ellipse and not a circle, the 
 moon will, at different times, be eclipsed when she 
 is at different distances from the earth. 
 
 Charles. And according as the moon Is nearer 
 to, or farther from the earth, the eclipse will be of a 
 greater or less duration : for the shadow being coni- 
 cal becomes less and less, as the distance from the 
 body by which it is cast is greater. 
 
 Tutor. It is by knowing exactly att what distance 
 the moon is from the earth, and of course the width 
 of the earth's shadow at that distance, that all 
 eclipses are calculated with the greatest accuracy, 
 for many years before they happen. Now it is found, 
 that, in all eclipses, the shadow of the earth is circu- 
 lar, which is a demonstration, that the body by which 
 it is projected is of a spherical form, for no other sort 
 of figure would, in all positions ', cast a circular sha- 
 dow. This is mentioned as another proof, that the 
 earth is a spherical body, 
 
 James. It seems to me to prdve another thing, 
 viz. that the snn must be a larger body than the 
 earth. 
 
 Tutor. Youf conclusion is just, for if the two 
 bodies were equal to one another (Plate VII, Fig. 13), 
 the shadow would be cylindrical: and the moon 
 would always pass through it in the same time, whe- 
 ther near the earth or at her greatest distance, which 
 is not the case ; and if the earth were the larger body, 
 (Plate VII, Fig. 14), its shadow would be of the
 
 86 ASTRONOMY. 
 
 figure of a cone, the sun at its vertex, and the far- 
 ther it were extended, the larger would it become. 
 In either case the shadow would run out to an infi- 
 nite space, and accordingly must sometimes involve 
 in it the other planets, and eclipse them, which is 
 contrary to fact. Therefore, since the earth is neither 
 larger than, nor equal to the sun, it must be the 
 lesser body. We will now proceed to the eclipses 
 of the sun. 
 
 Charles. How are these occasioned ? 
 Tutor. An eclipse of the sun happens when the 
 moon M, passing between the sun s and the earth T, 
 (Plate VII, Fig. 15), intercepts the snn's light. 
 
 James. The sun then can be eclipsed only at the 
 new moon. 
 
 Tutor. Certainly ; for it is only when the moon is 
 in conjunction that it can pass directly between the 
 snn and earth. 
 
 Charles. Is it only when the moon at her con- 
 junction is near one of its nodes, that there can be 
 an eclipse of the sun ? 
 
 Tutor. An eclipse of the sun depends upon this 
 circumstance : for unless the moon is in, or near one 
 of its nodes, she cannot appear in the same plane 
 with the sun, or seem to pass over his disk. In every 
 other part of the orbit she will appear above or be- 
 low the sun. If the moon be in one of the nodes, 
 she will, in most cases, cover the whole disk of the 
 sun, and produce a total eclipse ; if she be any where
 
 OF ECLIPSES. 87 
 
 within about 16 degrees of a node, a partial eclipse 
 will be produced. 
 
 The sun's diameter is supposed to be divided into 
 12 equal parts, called digits, and in every partial 
 eclipse, as many of these parts of the sun's diameter 
 as the moon covers, so many digits are said to be 
 eclipsed. 
 
 James. 1 have heard of annular eclipses, what 
 are they, sir ? 
 
 Tutor. When a ring of light appears round tbe edge 
 of the moon during an eclipse of the sun, it is said 
 to be annular, from the Latin word annulus, a ring : 
 these kind of eclipses are occasioned by the moon 
 being at her greatest distance from the earth at the 
 time of an eclipse, because in that situation the ver- 
 tex, or tip of the cone of the moon's shadow, does 
 not reach the surface of the earth. 
 
 Charles. How long can an eclipse of the sun last ? 
 
 Tutor. A total eclipse of the sun is a very curi- 
 ous and uncommon spectacle; and total darkness 
 cannot last more than three or four minutes. Of 
 one that was observed in Portugal, 150 years ago, 
 it is said that the darkness was greater than that of 
 the night ; that stars of the first magnitude made 
 their appearance ; and that the birds were so ter- 
 rified that they fell to the ground. 
 
 James. Was this \isible only at Portugal ? 
 
 Tutor. It must have been seen at other places, 
 though we have no account of it. The moon, how-
 
 88 ASTRONOMY. 
 
 ever, being a body much smaller than the earth, and 
 having also a conical shadow, can with that shadow 
 only cover a smaller part of the earth; whereas an 
 eclipse of the moon may be seen by all those that 
 are on that hemisphere which is turned towards it. 
 (See Plate VII, Fig. 15 and 12.) 
 
 You will also observe, that an eclipse of the sun 
 may.be total to the inhabitants near the middle of 
 the earth's disk, and annular to those places near 
 the edges of the disk; for in the former case the 
 moon's shadow will reach the earth, and in the lat^ 
 ter, on account of the earth's sphericity, it will not. 
 
 Charles. Have not eclipses been esteemed aa 
 omens presaging some direful calamity ? isti i 
 
 Tutor. Till the causes of these appearances were 
 discovered, they were generally beheld with terror 
 by the inhabitants of the world. 
 
 ZR[ Tua srh \o ?j?qifo3 u& fir,:i prtol // 
 -i;u.> TVYT r, ?.\ f.uA 3rii Vj a^jifob tbJc I 
 
 ob J.5&V . hU ^fDSJOT(3 llp4n.'n<XttW 
 
 
 .
 
 Or THE TIDES. 89 
 
 CONVERSATION XVI, 
 
 TUTOR. We will proceed to the consideration 
 of the Tides, or the flowing and ebbing of the 
 ocean. 
 
 James. Is this subject connected with astronomy? 
 
 Tutor. It is, inasmuch as the tides are occasion- 
 ed by the attraction of the suii and moon iipou the 
 water, but more particularly by that of the latter. 
 You will readily conceive that the tides are depen- 
 dent upon some known and determinate laws, be- 
 cause, if you turn to the Ephemeris, or indeed to 
 any almanac, you will see that the exact time of 
 high water at London-bridge for every day in the 
 year is set down. 
 
 Charles. I have frequently wondered hour this 
 could be known with such a degree of accuracy : 
 indeed there is not a waterman that plies at the 
 stairs, but can readily tell when it will be high water. 
 
 Tutor. The generality of the watermen are pro- 
 bably as ignorant as yourself of the cause by which 
 the waters flow and ebb, but by experience they 
 
 2A
 
 $0 ASTRONOMY, 
 
 know that the time of high water differs on each 
 day about three quarters of an hour, or a little more 
 or less, and therefore, if it be high water to-day at 
 six o'clock, they will, at a guess, tell you, that to- 
 morrow the tide will not be up till a quarter be- 
 fore seven. 
 
 James. Will you explain the causes? 
 Tutor. 1 will endeavour to do this in an easy 
 and coucise manner, without fatiguing your memory 
 with a great variety of particulars. 
 
 You must bear in mind then, that the tides are 
 occasioned by the attraction of the sun and moon 
 upon the waters of the earth : perhaps a figure may 
 be of some assistance to you. Let Ap LW (Plate VII, 
 Fig. 16), be supposed the earth, c its centre ; let the 
 dotted circle represent a mass of water covering the 
 earth : let M be the moon in its orbit, and s the sun. 
 When discussing the force of gravity as causing 
 the moon to move in a circle round the earth, I 
 jnentioned that were this action to cease for an in- 
 stant the moon would fly off from its circular course, 
 like a stone from a sling when you let go the string. 
 Now the moon by its attraction also causes the earth 
 to deflect from its circular course round the sun, 
 which we may consider as its projectile or tangen- 
 tial course with regard to the moon. You know 
 too that the force of attraction* is as the square of the 
 distance, and therefore the parts of the earth's cir- 
 
 * See Part I. page 35.
 
 OF TH-E TIDES. 91 
 
 cumference next the moon are more strongly attract* 
 ed by it than the rest of the earth. 
 
 The fluid parts at A are thus raised in the direc* 
 tion of the moon, or in other words they are more 
 deflected from the projectile course than the rest of 
 the earth. For the same reason the side of the 
 earth furthest from the moon being less attracted 
 than the rest pf the earth, will have a greater ten- 
 dency to go off in the projectile course, and the 
 waters at i, will consequently rise from the earth. 
 
 Charles. The waters then rise at A because they 
 have less, and at B because they have more centri- 
 fugal force than the rest of the earth, 
 
 Tutor, That is the explanation, It is evident, 
 that, the quantity of the water being the same, a rise 
 cannot take place at a and 6, without the parts at 
 p and N being at the same time depressed. 
 
 James. In this situation the water may be consi- 
 dered as partaking of an oval form. 
 
 Tutor. If the earth and moon were without mo- 
 tion, and the earth covered all over with water, the 
 attraction of the moon would raise it up in a heap in 
 that part of the ocean to which the moon is vertical, 
 and there it would always continue; but, by the 
 rotation of the earth on its axis, each part of its sur- 
 face is presented every day to the action of the 
 moon in the 2 nodes already described, and thus are 
 produced two floods and two ebbs. 
 
 James. You have told us that the tides are pro-
 
 )2 ASTRONOMY. 
 
 cluced in those parts of the earth to which the moon 
 is nearest or most distant, but this effect is not cou- 
 iined to those parts. 
 
 Tutor. It U not, but there the attraction of the 
 moon has the greatest effect ; in all oilier parts the 
 projectile force approaches more nearly to that of 
 the average of the whole earth, and therefore in these 
 places there is less deflection from the regular cir- 
 cular course round the sun. 
 
 Charles. Are there two tides exactly iu every 
 24 hours? 
 
 Tutor. If the moon were stationary, or rather 
 always iu the same relative position with regard to 
 the sun and earth, this would be the case; but 
 because that body is also proceeding every day 
 about 13 degrees from west to east in her orbit, the 
 earth must make more than one revolution on its 
 axis before the sam3 meridian is in conjunction with 
 the moon, and hence two tides take place ia about 
 24 hours and 50 minutes. 
 
 James. But the tides rise higher at some seasons 
 than at others : how do you account for this ? 
 
 Tutor. The moon goes round the earth in an el- 
 liptic or oval orbit, and therefore she approaches 
 nearer to the earth in some parts of her orbit, than 
 in others. When she is nearest, the attraction is the 
 strongest, and consequently it raises the tides most: 
 and when she is farthest from the earth, her attrac- 
 tion is the least, and the tides the lowest.
 
 OP THE TIDES. 93 
 
 James. Do they rise to different heights in differ- 
 ent places ? 
 
 Tutor. They do : in the Black Sea and the Medi- 
 terranean the tides are scarcely perceptible. At 
 the mouth of the Indus the water rises and falls full 
 30 feet. The tides are remarkably high in the Straits 
 of Sunda, in the Red-Sea, along the Coasts of China, 
 Japan, &c. In general, the tides rise highest and 
 strongest in those places that are narrowest. 
 
 Charles. \ have read of seas where there are no 
 tides. How is this accounted for ? 
 
 Tutor. The waters that are raised in one place 
 must be supplied from those places that are not 
 subjected to the same action. It requires therefore 
 3- very great extent of ocean to admit of the produc- 
 tion of a full tide; so that even in so large a body 
 of water as the Caspian Sea it is calculated that the 
 highest tide cannot exceed 6 inches ; a quantity sd 
 small, that a slight breeze of wind from the shore 
 will be sufficient to prevent the accumulation of the 
 water, and IB ay even produce a depression* 
 
 Charles. YOU said the sun's attraction occasjon- 
 jed tides as well as that of the moon^ ji j$r J 
 
 Tutor. }t does : but, owing to the immense dis- 
 tance of the sun from the earth, the difference 
 pf its attraction for the nearest and most {distant 
 sides of the earth is much less in proportion to the 
 whole force of its attraction, than in the case pf the 
 pjoonj or in other words the difference of the 
 2 B
 
 94 ASTRONOMY. 
 
 squares Si A and of s L is much less iri proportion 
 to the squares^ of s L than the difference of the 
 squares of M A and of M L to the square of the dis- 
 tance M L. It is computed, that the force of thef 
 moon raises the waters in the Great Ocean 5 feet, 
 whereas that of the sun raises it only 2 feet. When 
 both the attraction 1 Of the sun and moon act in the 
 samef direction, that is, at new and full moon, the 
 combined forces of both raise the tide 7 feet. But 
 when the moon is in her quarters, the attraction of 
 one of these bodies raises the water, while that of 
 the other depresses it ; and therefore the smaller 
 force of the sun must be* substracted from that of 
 the moon, consequently the tides will be no more 
 than 3 feet. The highest tides are called spring- tides, 
 and the lowest are denominated neap-tides. 
 
 James. I understand, that, in the former case, 
 the height to which the tides are raised must be 
 calculated by adding together the attractions of the 
 snn and moon ; and in the latter, it must be estimat- 
 ed by the difference of these attractions. 
 
 Tutor. Yon are right* When the sun and moon 
 are both vertical to the equator of the earth, and the 
 moon at her least distance from the earth, then the 
 tides are highest. 
 
 Charles. l>o the highest tides happen at the 
 Equinoxes ? 
 
 Tutor. It is found by experience that the tides, 
 as in every other instance where matter b put irf
 
 OP THE TIDES. 93 
 
 motion, advance after the force that has caused 
 them has passed over. 
 
 The waters of the ocean being once put in motion 
 by the moon, and brought to that elevation which 
 its disturbing force simply is calculated to produce, 
 will continue to rise for some time after ; and would 
 do so even if the moon's attraction were to cease. It 
 is not therefore just at the Equinoxes that the high- 
 est tides occur ; nor on the days of the new and 
 full moon that we have the highest springs ; nor yet 
 have we high water at the very time when the moon 
 passes our meridian or that on the side of the earth 
 opposite to us ; but some time often 
 
 *:,.: ,:.i/i ' e wii.> rut r,r $n 
 3;J--ff; hum ;H?#s & .# no u 
 
 '.3ti .ftut-t roir 
 
 f i Iftitt 
 
 'ih w t.^ttOWfcO! 
 
 44 ; .^>swlL 
 
 no -*t*?o* !*>*iflttfl*c
 
 CONVERSATION XVII, 
 
 } oi e 
 
 "*/- ^ 
 
 il .r ol 'iiow ;ioiJ3Ji-.;J * HOOCH saili iw* oo. r j 
 >^Ofthe Harvest Moon. 
 
 TUTOR. From : what we said yesterday, you 
 will easily understand the reason why the moon rises 
 about three quarters of an hour later every day than 
 on the one preceding. 
 
 Charles. It is owing to the daily progress which 
 the moon is making in her orbit, on which ac- 
 count any meridian on the earth must make more 
 than one complete rotation on its axis, before it 
 comes again into the situation with respect to the 
 moon that it had before. And you told us that this. 
 occasioned a difference of about 50 minutes. 
 
 Tutor. At the equator this is generally the dif- 
 ference of time between the rising of the moon on. 
 one day and the preceding. But in places of con- 
 siderable latitude, as Great Britain, there is a re- 
 markable difference about the time of harvest, when 
 at the season of full moon she rises for several nights 
 together only about 20 minutes later on the one day 
 than on that immediately preceding. By thus sue- 
 peediug the suu before the twilight is ended, the
 
 OF THE HAHVES'f MOON. 07 
 
 n*> '* 
 
 moon prolongs the light to the great benefit of those 
 who are engaged in gathering in the fruits of the 
 earth ; and hence the full moon at this season is 
 called the harvest moon. 
 
 James. But the people at the equator do not en- 
 joy this benefit. 
 
 Tutor. Nor is it necessary that they should, for 
 in those parts of the earth, the seasons vary but lit- 
 tle, and the weather changes but seldom, and at 
 stated times; to them, then, moon-light is not want- 
 ing for gathering the fruits of the earth. 
 
 Charles. Can you explain how it happens, that 
 in high latitudes the moon at this season of the year 
 rises one day after another with so small a differ- 
 ence of time? 
 
 Tutor. With the assistance of a globe I could at 
 once clear the matter up. But I will endeavour to 
 give you a general idea of the subject without that 
 instrument. That the moon loses more time in her 
 risings when she is in one part of her orbit, and less 
 in another, is occasioned by the moon's orbit lying 
 some times more oblique to the horizon than at others. 
 
 James. But the moon's path is not marked on 
 the globe. 
 
 Tutor. It is not ; you may, however, consider it, 
 without much error, as coinciding with the ecliptic. 
 And in the latitude of London, as much of the eclip- 
 tic rises about Pisces and Aries in two hours as the 
 moon goes through io six days ; therefore while the 
 2c
 
 98 ASTitcrNc: Y. 
 
 moon is iu these signs she differs but two hours in 
 rising for six days together ; that is, one day with 
 another, about 20 minutes later every day than t on 
 the preceding. 
 
 Charles. Is the moon in those signs at the time 
 of harvest ? 
 
 Tutor. In August and September you know that 
 the sun appears in Virgo and Libra, and of course 
 when the moon is full, she must be in the opposite 
 signs, viz. Pisces and Aries. 
 
 James. Are there then two full moons that afford 
 us this advantage? 
 
 Tutor. There are, the one when the sun is in 
 Virgo, which is called the harvest moon ; the other 
 when the sun is in Libra, and which, being less ad- 
 Tantageous, is called the hunters moon. You ought 
 to be told that when the moon is in Virgo and Libra, 
 then she rises with the greatest difference of time, 
 viz. an hour and a quarter later every day than the 
 former. 
 
 Charles. Will you explain, sir, how it is that the 
 people at the equator have no harvest moon ? 
 
 Tutor. At the equator, the north and south poles 
 lie in the horizon, and therefore the ecliptic makes 
 the same angle southward with the horizon when 
 Aries rises, as it does northward when Libra rises ; 
 but as the harvest moon depends upon the different 
 angles, at which different parts of the ecliptic rise, it 
 is evident there can be no harvest moon at the equator.
 
 OF HARVEST MOON. 89 
 
 The farther any place is from the equator, if it be 
 not beyond the polar circles, the angle which the 
 ecliptic makes with the horizon, when Pisces and 
 Aries rise, gradually diminishes, and therefore when 
 the moon is in these signs she rises with a nearly 
 proportionable difference later every day than on 
 the former, and this is more remarkable about the 
 time of full moon. 
 
 James. Why have you excepted the space on the 
 globe beyond the polar circles? 
 
 Tutor. At the polar circles, when the sun touches 
 the summer tropic, he continues 24 hours above the 
 horizon ; and 24 hours below it when he touches 
 the winter tropic. For the same reason the full moon 
 neither rises in the summer, when she is not wanted ; 
 nor sets in the winter, when her presence is so neces- 
 sary. These are the only two full moons which hap- 
 pen about the tropics ; for all the others rise and 
 set. In summer the full moons are low, and their 
 stay above the horizon short: in winter they are 
 high, and stay long above the horizon. A wonder- 
 ful display this of the divine wisdom and goodness, 
 in apportioning the quantity of light suitable to the 
 various necessities of the inhabitants of the earth, 
 according to their different situations. 
 
 Charles. At the poles, the matter is, I suppose, 
 still different. 
 
 Tutor. There one-half of the ecliptic never sets, 
 and the other half never rises ; consequently the suo
 
 100 ASTRONOMY. 
 
 continues one-half year above the horizon, and the 
 other half below it. The full moon being always 
 opposite to the sun can never be seen to the inhabi- 
 tants of the poles, while the sun is above the horizon. 
 But all the time that the sun is below the horizon, 
 the full moon never sets. Consequently to them the 
 moon is never visible in their summer; and in their 
 winter they have Her always before and after the full, 
 shining for 14 of our days and nights without inter- 
 mission. And when the sun is depressed the lowest 
 Tinder the horizon, then the moon ascends with her 
 highest altitude. 
 
 James. This indeed exhibits in a high degree the 
 attention of Providence to all his creatures. But if 
 1 understand you, the inhabitants of the poles have 
 in their winter a fortnight's light and darkness 
 by turns. 
 
 Tutor. This would be the case for the whole 
 six months that the sun is below the horizon, if there 
 were no refraction* ; and no substitute for the light 
 of the moon. But by the atmosphere's refracting 
 the sun's rays, he becomes visible a fortnight sooner, 
 and continues a fortnight longer in sight, than he 
 would otherwise do were there no such property be- 
 longing to the atmosphere. And in those parts of 
 the winter, when it would be absolutely dark in the 
 absence of the moon, the brilliancy of the Aurora 
 
 * The subject of refraction will be very particularly explained when we 
 come to Optics.
 
 OF THE HARVEST MOON. 101 
 
 Borealis, is probably so great as to afford a very 
 comfortable degree of light. Mr. Hearne hi his tra- 
 vels near the polar circle, has this remark in his jour- 
 nal ; " December 24. The days were so short, that 
 the sun only took a circuit of a few points of the 
 compass above the horizon, and did not at its great- 
 est altitude rise half way up the trees. The brilli- 
 ancy of the Aurora Borealis, however, and of the 
 stars, even without the assistance of the moon, made 
 amends for this deficiency ; for it was frequently so 
 light all night, that I could see to read a small 
 print." ;K^. 
 
 These advantages are poetically described by our 
 Thomson : 
 
 By dancing meteors then, that ceaseless shake 
 A waving blaze refracted o'er the heavens, 
 And vivid moons, and stars that keener play 
 With double lustre from the glossy waste; 
 Ev'n in the depth of Polar Night, they find 
 A wondrous day : enough to light the chase, 
 Or guide their daring steps to Finland-fairs. 
 
 WINTER, L 859.
 
 102 ASTllONOMY. 
 
 CONVERSATION 7 
 
 Of Mercury. 
 
 TUTOR. Having fully described the earth and 
 the moon, the former a primary planet, and the lat- 
 ter its attendant satellite, or secondary planet, we 
 shall next consider the other planets in their order, 
 with which, however, we are less interested. 
 
 MERCURY, yon recollect, is the planet nearest the 
 sun ; and Venus is the second in order. These are 
 called inferior planets. 
 
 Charles. Why are they thus denominated ? 
 
 Tutor. Because they both revolve in orbits which 
 are included within that of the earth round the sun ; 
 thus (Plate V, Fig. 2), Mercury makes his annual 
 journey round the sun in the orbit a; Venus in , 
 and the earth, farther from that luminary than either 
 of them, makes its circuit in t. 
 
 James. How is this known ? 
 
 Tutor. By observation : for by attentively watch- 
 ng the progress of these bodies, it is found that they 
 are continually changing their places among the 
 fixed stars, and that they are never seen in opposi-
 
 OF MERCURY. 103 
 
 tion to the sun, that is, they are never seen in the 
 western side of the heavens in the morning when he 
 appears in the east ; nor in the eastern part of the 
 heavens in the evening when the sun appears in 
 the west. 
 
 . Charles. Then they may be considered as atten- 
 dants upon the sun? 
 
 Tutor. They may : Mercury is never seen from 
 the earth at a greater distance from the sun, than about 
 28 degrees, or about as far as the moon appears to 
 be from the sun on the second day after its change ; 
 hence it. is that we so seldom see him ; and when we 
 do, it is for so short a time, and always in twilight, 
 that sufficient observations have not been made 
 to ascertain whether he has a diurnal motion on his 
 axis. 
 
 James. Would you then conclude that he has 
 such a motion ? 
 
 Tutor. I think we ought ; because it is known 
 to exist in all those planets upon which observations 
 of sufficient extent have been made, and therefore 
 we may surely infer, without much chance of error, 
 that it belongs also to Mercury, and the Herschel, 
 the former from its vicinity to the sun, and the lat- 
 ter from its great distance from that body, having at 
 present eluded the investigation of the most indefa- 
 tigable astronomers. 
 
 Charles. At what distance is Mercury from the 
 sun?
 
 104 ASTRONOMY. 
 
 Tutor. He revolves round that body at about 37 
 millions of miles distance, in 88 days nearly ; and 
 therefore you can now tell me how many miles he 
 travels in an hour. 
 
 James. I can ; for supposing his orbit circular, 
 I must multiply the 37 millions by 6* ; which will 
 give 222 millions of miles for the length of his orbit ; 
 this I shall divide by 88, the number of days he takes 
 in performing his journey, and the quotient result- 
 ing from this, must be divided by 24, for the num- 
 ber of hours in a day ; and by these operations, I 
 find that Mercury travels at the rate of more than 
 105,000 miles in an hour. 
 
 Charles. How large is Mercury ? 
 
 Tutor. He is the smallest of all the planets. His 
 diameter is something more than 3200 miles in 
 length. 
 
 James. His situation being so much nearer to the 
 sun than ours, he must enjoy a considerably greater 
 share of its heat and light. 
 
 Tutor. So much so, as would indeed infallibly 
 burn every thing belonging to the earth to atoms, 
 were she similarly situated. The heat of the sun at 
 Mercury, must be 7 times greater than our summer 
 heat. 
 
 Charles. And do you imagine that, thus circum- 
 stanced, this planet can be inhabited? 
 
 Tutor. Not by such beings as we are : you and 
 
 See page 40.
 
 OF MERCURY. ]Q5 
 
 I could not long exist at the bottom of the sea ; yet 
 the sea is the habitation of millions of living crea- 
 tures ; why then may there not be inhabitants in 
 Mercury, fitted for the enjoyment of the situation 
 which that planet is calculated to afford ? If there 
 be not, we mnst be at a loss to know why such a 
 body was formed ; certainly it could not be intended 
 for our benefit, for it is rarely even seen by us : 
 
 Ask for what end the heavenly bodies shine? 
 
 Earth for whose use? Pride answers, " Tis for mine : 
 
 suns to light me rise, 
 
 My footstool earth, my canopy the skies." 
 
 POPE. 
 
 But do these worlds display their beams, or guide 
 
 Their orbs, to serve thy use, to please thy pride? 
 
 Thyself but dust, thy stature but a span, 
 A moment thy duration ; foolish man! 
 As well may the minutest emmet say, 
 That Caucasus was raised to pave his way : 
 The snail, that Lebanon's extended wood 
 "Was destined only for his walk and food : 
 The vilest cockle, gaping on the coast 
 That rounds the ample seas, as well may boast, 
 The craggy rock projects above the sky, 
 That he in safety at its foot may lie ; 
 And the whole ocean's confluent waters swell, 
 Only to quench his thirst, or move and blanch his shell. 
 
 PRIOR. 
 
 2 E
 
 CONVERSATION XIX, 
 
 Of Venus, 
 
 TUTOR. We now proceed to Venus, the se- 
 cond planet in the order of the solar system, but by 
 far the most beautiful of them all. 
 
 James. How far is Venus from the sun ? 
 Tutor. That planet is 68 millions of miles from 
 the sun, and she finishes her journey in 224J days, 
 consequently she must travel at the rate of 75,000 
 miles in an hour* 
 
 Ckarles. Venus is larger than Mercury, I dare 
 say? 
 
 Tutor. Yes, she is nearly as large as the earth, 
 which she resembles also in other respects, her dia- 
 meter being about 7700 miles in length, and she 
 has a rotation about her axis in 23 hours and 20 
 minutes. The quantity of light and heat which she 
 enjoys from the sun, must be double that which is 
 experienced by the inhabitants of this globe. 
 
 James. Is there also a difference in her seasons, 
 as there is here ?
 
 * OF VENUS, 107 
 
 *?idor. Yes, in a much more considerable de- 
 gree. The axis of Venus inclines about 75 degrees, 
 but that of the earth inclines only 23^ degrees, and 
 as the variety of the seasons in every planet depends 
 on the degree of the inclination of its axis, it is evi- 
 dent that the seasons must vary more with Venus 
 than with us. 
 
 Charles. Venus appears to us larger 'sometimes 
 than at others. 
 
 Tutor. She does ; and this, with other particu- 
 lars, I will explain by means of a figure. Sup- 
 pose s (Plate VII, Fig. 17), to be the sun, T tiie 
 earth in her orbit, and a, b, c, d, e,f, Venus in hers: 
 now it is evident that when Venus is at a, between 
 the sun and earth, she would, if visible, appear 
 much larger than when she is at d in opposition. 
 
 James. That is because she is so much nearer 
 in the former case than in the latter, being in the 
 situation a but 27 millions of miles from the earth 
 T, but at d she is 163 millions of miles off. 
 
 Tutor. Now as Venus passes from a, through 
 b c to d, she may be observed, by means of a good 
 telescope, to have all the same phases as the moon 
 has in passing from new to full : therefore when she 
 is at d she is full, and is seen among the fixed stars 
 in the beginning of Cancer: during her journey from 
 d to e, she proceeds with a direct motion in her 
 orbit, and at e she is seen in Leo, and will appear 
 to an inhabitant of the earth, for a few days, to be
 
 108 ASTRONOMY. 
 
 stationary, not seeming to change her place among 
 the fixed stars, for she is coming toward the earth 
 in a direct line : hut in passing from e to/, though 
 still with a direct motion, yet to a spectator at T, her 
 course will seem to be back again, or retrograde, 
 for she will seem to have gone back from z to y ; 
 her path will appear retrograde till she gets to c t 
 when she will again appear stationary, and after- 
 wards from c to d, and from d to e it will be direct 
 among the fixed stars. 
 
 Charles. When is Venus an evening, and when a 
 morning star ? 
 
 Tutor. She is an evening star all the while she 
 appears east of the sun, and a morning star while 
 she is seen west of him. When she is at a she will 
 be invisible, her dark side being towards us, unless 
 she be exactly in the node, in which case she will 
 pass over the sun's face like a little black spot. 
 
 James. Is that called the transit of Venus r 
 
 Tutor. It is ; and it happens twice only in about 
 120 years. By this phenomenon astronomers have 
 been enabled to ascertain with great accuracy the 
 distance of the earth from the sun ; and having ob- 
 tained this, the distances of the other planets are 
 easily found. By the two transits which happened 
 in 1761 and 1769, it was clearly demonstrated, that 
 the mean distance of the "earth from the sun was 
 between 95 and 96 millions of miles. 
 
 Charles. How do you find the distances of the
 
 OF VENUS. 10.9 
 
 other planets from the sun, by knowing that of the 
 earth*. 
 
 Tutor. I will endeavour to make this plain to 
 you. Kepler, a great astronomer, discovered that 
 all the planets are subject to one general law, which 
 is, that the squares of their periodical times, are pro- 
 portional to the cubes of their distances from the sun. 
 
 James. What do you mean by the periodical 
 times ? 
 
 Tutor. 1 mean the times which the planets take 
 in revolving round the sun ; thus the periodical time 
 of the earth is 365^ days ; that of Venus 224J days ; 
 that of Mercury 88 days. 
 
 Charles. How then would you find the distance 
 of Mercury from the sun? 
 
 Tutor. By the rule of three: I would say, as the 
 square of 365 days (the time which the e9rth takes 
 in revolving about the sun) is to the square of 88 
 days (the time in which Mercury revolves about the 
 sun), so is the cube of 95 millions (the distance in 
 miles of the earth from the sun) to a fourth number. 
 
 James. And is that fourth number the distance 
 in miles of Mercury from the sun ? i 
 
 Tutor. No : you must extract the cube root of 
 that number, and then you will have about 37 mil- 
 lions of miles for the answer, which is the true 
 distance at which Mercury revolves about the sun. 
 
 The remainder of this conversation may be omitted by those young per- 
 sons who are not ready in arithmetical operations. The author, however, 
 knows from experience, that children may, at a very early age, be brought 
 to understand these higher parts of arithmetic.
 
 ASTRONOMY. 
 
 CONVERSATION XX, 
 
 Of Mars. 
 
 TUTOR. Next to Veuus is the earth and her 
 satellite the moon, but of these sufficient notice has 
 already been taken, and therefore we shall pass ou 
 to the planet Mars, which is known in the heavens 
 by a dusky red appearance. Mars, together with 
 Jupiter, Saturn, and the Herschel, are called supe- 
 rior planets, because the orbit of the earth is en- 
 closed by their orbits. 
 
 Charles. At what distance is Mars from the sun? 
 
 Tutor. About 144 millions of miles; the length 
 of his year is equal to 687 of our days, and there- 
 fore he travels at the rate of more than 53 thousand 
 miles in an hour: his diurnal rotation on his axis 
 is performed in 24 hours and 39 minutes, which 
 makes his figure that of an oblate spheroid. 
 
 James. How is the diurnal motion of this planet 
 discovered r 
 
 Tutor. By means of a very large spot which is 
 seen distinctly on his face, when he is in that part 
 of his orbit which is opposite to the sun and earth.
 
 OF MARS. Ill 
 
 Charles. Is Mars as large as the earth? 
 
 Tutor. No: his diameter is only 4189 miles in 
 length, which is but little more than half the length 
 of the earth's diameter. And owing to his distance 
 from the sun he will not enjoy one-half of the light 
 and heat which we enjoy. 
 
 James. And yet, I believe, he has not the benefit 
 of a moon. 
 
 Tutor. No moon has ever been discovered be- 
 longing either to Mercury, Venus, or Mars. 
 
 Charles. Do the superior planets exhibit similar 
 appearances of direct and retrograde motion to those 
 of the inferior planets? 
 
 Tutor. They do: suppose s (Plate VII, Fig. 18), 
 the sun ; a, b, d,f y g, h, the earth, in different parts 
 of its orbit, and m Mars in his orbit. When the 
 earth is at , Mars will appear among the fixed 
 stars at x: when by its annual motion the earth has 
 arrived at &, d, and/, respectively, the planet Mars 
 will appear in the heavens at y, z, and w: when 
 the earth has advanced to g, Mars will appear sta- 
 tionary at o: to the earth in its journey from^ to h 9 
 the planet will seem to go backwards or retrograde 
 in the heavens from o to z, and this retrograde mo- 
 tion will be apparent till the earth has arrived at , 
 when the planet will again appear stationary. 
 
 James. I perceive that Mars is retrograde when 
 in opposition, and the same is, I suppose, applica- 
 ble to the other superior planets ; but the retro-
 
 112 ASTRONOMY. 
 
 grade motion of Mercury and Venus is when those 
 planets are in conjunction. 
 
 Tutor. You are right: and you see the reason, 
 I dare say, why the superior planets may be in the 
 west in the morning when the sun rises in the east, 
 and the reverse. 
 
 Charles. For when the earth is at d t Mars may 
 be at n, in which case the earth is between the sun 
 and the planet: I observe also that the planet Mars, 
 and consequently the other superior planets, are 
 much nearer the earth at one time than at others. 
 
 Tutor. The difference with respect to Mars is 
 no less than 190 millions of miles, the whole length 
 of the orbit of the earth. This will be a proper 
 time to explain what is meant by the Heliocentric 
 longitude of the planets. 
 
 James. I do not know the- meaning of the word 
 heliocentric. 
 
 Tutor. It is a term used to express the place of 
 any heavenly body as seen from the sun; whereas 
 the geocentric place of a planet, is the position 
 which it has when seen from the earth. 
 
 Charles. "Will you show us by a figure in what 
 this difference consists? 
 
 Tutor. I will: let s (Plate VII, Fig. 19), repre- 
 sent the place of the sun, b Venus in its orbit, a the 
 earth in hers, and c Mars in his orbit, and the out- 
 ermost circle will represent the sphere of fixed stars. 
 Now to a spectator on the earth a, Venus will ap-
 
 OF MAR& 113 
 
 pear among the fixed stars in the beginning of Scor- 
 pio, but as viewed from the sun, she will be seen 
 beyond the middle of Leo. Therefore the Geocen- 
 tric longitude of Venus will be in Scorpio, but her 
 Heliocentric longitude will be in Leo. Again, to a 
 spectator at , the planet Mars, at c, will appear 
 among the fixed stars, towards the end of the sign 
 of Pisces ; but as viewed from the sun he will be 
 seen at the beginning of the sign Aries: conse- 
 quently ihe gtocenlric longitude of Mars is in Pisces ; 
 but his heliocentric longitude is in Aries.
 
 114 ASTRONOMY. 
 
 CONVERSATION XXL 
 
 ,WIJ<K. lii'-ff- ,o J; t *'?it v^!<f oil; ? A i*; v> 
 
 - mg 
 
 O/' Jupiter* 
 
 TUTOR. We now come to Jupiter, the largest 
 of all the planets, which is easily kuovvii by his pe 
 culiar magnitude and brilliancy. 
 
 Charles. Is Jupiter larger than Venus ? 
 
 Tutor. Though he does not appear so large, yet 
 the magnitude of Venus bears hut a. very small pro- 
 portion to that of Jupiter, whose diameter is 90,000 
 miles in length, consequently his bulk will exceed 
 the bulk of Venus 1500 times; his distance from 
 the sun is estimated at more than 490 millions of 
 miles. 
 
 James. Then he is five times farther from the 
 sun than the earth, and consequently, as light and 
 heat diminish in the same proportion as the squares 
 of the distances from the illuminating body increase, 
 the inhabitants of Jupiter enjoy but a twenty-fifth 
 part of the light and heat of the sun that we enjoy. 
 
 Tutor. Another thing remarkable in this planet 
 is, that it revolves on its axis, which is perpendicu- 
 lar to its orbit, in 10 hours, and in consequence of
 
 OF JUPITER. J15 
 
 this swift diurnal rotation, his equatorial diameter 
 is 6000 miles greater than his polar diameter. 
 
 Ckarles. Since then a variety in the seasons of a 
 planet depends upon the inclination of the axis to 
 its orbit, and since the axis of Jupiter has no incli* 
 nation, there can be no difference in his seasons, 
 nor any in the length of his days and nights. 
 
 Tutor. You are right, his days and nights are 
 always five hours each in length ; and at his equa- 
 tor, and its neighbourhood, there is perpetual 
 summer; and an everlasting winter in the polar 
 regions, 
 
 James. What is the length of his year ? 
 
 Tutor. Jt is equal to nearly 12 of ours, for he 
 takes 12 years, 314 days, and 10 hours, to make a 
 revolution round the sun, consequently he travels 
 at the rate of more than 28,000 miles in an hour. 
 
 This noble planet is accompanied with four satel- 
 lites, which revolve about him at different distances, 
 and at different periodical times : t\\e first in about 
 1 day and 18 hours ; the second in 3 days 13 hours ; 
 the third m 7 days 3 hours; and the Jourth in 16 
 days and 16 hours. 
 
 Charles. And are these satellites, like our moon, 
 subject to be eclipsed ? 
 
 Tutor. They are ; and their eclipses are of 
 considerable importance to astronomers, in ascer- 
 taining with accuracy the longitude of different places 
 on the earth.
 
 118 ASTRONOMY* 
 
 By means of the eclipses of Jupiter's satellites, 
 a method has also been obtained of demonstrating 
 that the motion of light is progressive, and not in- 
 stantaneous, as was once supposed. Hence it is 
 found, that the velocity of light is nearly 11,000 
 times greater than the velocity of the earth in its 
 orbit, and more than a million times greater than 
 that of a ball issuing from a cannon. Rays of light 
 come from the sun to the earth in 8 minutes, that 
 is at the rate of 12 millions of miles in a minute 
 nearly. 
 
 James. Who discovered these satellites ? 
 
 Tutor. They were first seen by Galileo in 1710. 
 He took them for telescopic stars, but farther ob- 
 servations convinced him and others, that they 
 were planetary bodies. 
 
 The relative situation of these small bodies 
 changes at every instant. They are sometimes seen 
 to pass over the face of the planet, and project a 
 shadow in the form of a black spot, which de- 
 scribes a line across it. 

 
 OF SATURN. 117 
 
 . ;ihI e 
 
 CONVERSATION XXII. 
 
 
 
 TUTOR. AVe are now arrived at Saturn in our 
 descriptions, which, till within these twenty years, 
 was esteemed the most remote planet of the solar 
 system. 
 
 Charles. How is he distinguished in the heavens ? 
 
 Tutor. Hfe shines with a pale dead light, very 
 unlike the brilliant Jupiter, yet his magnitude seems 
 to vie with that of Jupiter himself. The diame? 
 ter of Saturn is nearly 80 thousand miles in length: his 
 distance from the sun is more than 900 millions of 
 miles, and he performs his journey round that lumi- 
 nary in a little less than 30 of our years, consequent- 
 ly he must travel at a rate not much short of 21,000 
 miles an hour. 
 
 James. His great distance from the sun must 
 render an abode on Saturn extremely cold and dark 
 too, in comparison of what we experience here. 
 
 Tutor. His distance from the sun being between 
 9 and 10 times greater than that of the earth, he 
 enjoys about 90 times less light and heat; it has 
 2 H
 
 . 
 
 H8 ASTRONOMY 
 
 nevertheless been calculated, that the light of the 
 sun at Saturn is 500 times greater than that which 
 we enjoy from OUT full moon. 
 
 diaries. The day-light at Saturn, then, cannot be 
 very contemptible : I should hardly have thought 
 that the light of the sun here was 500 times greater 
 than that experienceld from a full moon. 
 
 Tutor. So much greater is our meridian light 
 than this, that during the sun's absence behind a 
 cloud, when the light is much less strong than when 
 we behold him in all his glorious splendour, it is- 
 reckoned that our day-light is 90,000 times greater 
 than the light of the moon at its full. 
 
 James. But Saturn has several moons, 1 believer 
 
 Tutor. He is attended by seven Satellites, or 
 moons, whose periodical times differ very much ; 
 the one nearest to him performs a revolution round 
 the primary planet in 22 hours and a half; and that 
 which is most remote takes 79 days and 7 hours for 
 his monthly journey: this last satellite is known 
 to turn on its axis, and in its rotation is subject ta 
 the same law which our moon obeys, that is, it 
 revolves on its axis in the same time in which it 
 revolves about the planet. 
 
 Besides the seven moons, Saturn is encompass- 
 ed with two broad rings, which are probably of 
 considerable importance in reflecting the light of the 
 sun to that planet ; the breadth of the inner ring is 
 20,000 miles, that of the outer ring 7200 mifes, and
 
 OP SATURN. 119 
 
 the vacant space between the two rings is 2839 
 miles. These rings give Saturn a very different ap- 
 pearance to any of the other planets. Plate VIII, 
 Fig. 20, is a representation of Saturn as seen through 
 a good telescope. 
 
 James. Is it known of what nature the ring is? 
 
 Tutor. Dr. Herschel thinks it no less solid than 
 that of the planet itself, and he has found that it 
 casts a strong shadow upon the planet. The light 
 of the ring is brighter than that of the planet ; for 
 the ring appears sufficiently bright for observation, 
 at times when the telescope scarcely affords light 
 enough to give a fair view of Saturn. 
 
 Charles. Is it known whether Saturn turns on 
 its axis r 
 
 r j **** w?tf *sfit ' : "wta 
 
 Tutor. According to Dr. Herschel it has a rota- 
 tion about its axis in 12 hours 1.3 J minutes: this he 
 computed from the equatorial diameter being longer 
 than the polar diameter in the proportion of 11 to 
 10. Dr. Herschel has also discovered that the 
 ring, just mentioned, revolves about the planet in 
 10 hours and a half.
 
 120 ASTRONOMY,: 
 
 . <T. > 
 
 . . 
 
 CONVERSATION XXIII. 
 
 kPWi^'V** 
 
 - 
 i-::j 
 
 Jl . 
 
 O/ *7<e Herschel Planet. 
 
 TUTOR. We have but one other planet to 
 describe, that is the Herschel. 
 
 James. "Was it discovered by Dr. Herschel? 
 
 Tutor. It was, on the 13th of March, 1781, and 
 therefore by astronomers, in general, it is denomi- 
 nated the Herschel planet : though by the doctor 
 himself it was named the Georgium Sid us, or 
 Georgian star, in honour of his present majesty 
 George the Third, who has been a liberal patron to 
 this great and most indefatigable astronomer. 
 
 Charles. I do not think that I have ever seen 
 this planet. 
 
 Tutor. Its apparent diameter is too small to be 
 discerned readily by the naked eye, but it may be 
 easily discovered in a clear night, when it is above 
 the horizon, by means of a good telescope. 
 
 James. Is it owing to the smallness of this pla- 
 net, or to its great distance from the sun, that we 
 cannot see it with the naked eye ?
 
 OF THE HERSCHEL PLANET. 121 
 
 Tutor. Both these causes are combined: in 
 comparison of Jupiter and Saturn it is small, his 
 diameter being less than 35 thousand miles in 
 length ; and his distance from the sun is estimated 
 at more than 1800 millions of miles from that lumi- 
 nary, around which, however, he performs his 
 journey in 82 of our years, consequently he must 
 travel at the rate of 16,000 miles an hour. 
 
 Ckarles. But if this planet has been discovered 
 only 22 years, how is it known that it will complete 
 its revolution in 82 years ? 
 
 Tutor. By a long series of observations it was 
 found to move with such a velocity, as would carry 
 it round the heavens in that period. Moreover, 
 v/hen it was first discovered, it was in Gemini, and 
 in August, 1803, it had advanced to the 1 lth of 
 Libra, more than a fourth part of its journey ; and 
 in June, 1809, it was in the 8th of Scorpio. 
 James. How many moons has the Herschel? 
 Tutor. He is attended by six satellites, or moons, 
 of which, the one nearest to the planet performs his 
 revolution round the primary in 5 days and 23 
 hours, but that which is the most remote from him 
 takes 107 days and 16 hours for his journey. 
 
 CJiarles. Is there any idea formed as to the light 
 and heat enjoyed by this planet ? 
 
 Tutor. His distance from the sun is 19 times 
 greater than that of the earth, consequently, since the 
 2 I
 
 122 ASTRONOMY. 
 
 square of 19 is 361, the light and heat experienced 
 by the inhabitants of that planet must be 361 times 
 less than ive derive from the rays of the sun. 
 
 The proportion of light enjoyed by the Herschel 
 has been estimated at about equal to the effect of 
 249 of our full moons. 
 
 -'i'> a*m- ^. 
 
 IIW &''OIi Ol 
 

 
 OF THE SMALLER PLANETS. J->3 
 
 '* 
 
 -'{-w-tfo *.! :-: 
 
 ,, : CONVERSATION XXIV. 
 - -^3!*- 
 
 , 
 O/' //ie smaller Planets. 
 
 CHARLES. You mentioned that besides the 
 Herschel, four other planetary bodies Lad been 
 recently discovered. How are their orbits situated 
 with respect to those of the other planets? 
 
 Tutor. Those small planets called asteroids re- 
 volve in orbits between those of Mars and Jupiter, 
 and two of them at nearly the same distance from 
 the sun : 
 
 Vesta is distant,. . *. ->'.'. .225,435,000 miles 
 
 Juno, . : . J .^. '.'V . 253,380,485 
 
 Ceres, : . .262,903,570 
 
 Pallas, 262,921,240 
 
 Vesta was discovered in 1807 at Bremen, a town 
 of Germany, by an astronomer named Olbers. Juno 
 was discovered at the same place in 1804, by an- 
 other astronomer named Harding. Ceres was dis- 
 covered by Piazzi, a Sicilian astronomer at Palermo 
 in 1801 ; and Pallas also by Olbers of Bremen in 
 1802. Observers differ very widely respecting the
 
 124 .ITI ASTRONOMY. 
 
 size of these asteroids, but no estimate makes their 
 united size equal to that of Mars, which is little 
 more than \ of the size of the earth. 
 
 It has not hitherto been ascertained by obser- 
 vation that they turn on their axis ; but the periods 
 in which they revolve round the sun are as follows : 
 Vesta ... ..... 3 years and 240 days. 
 
 Juno ........ 4 --- 130 - 
 
 Ceres & Pallas 4 -- 221 
 James. Has there been any attempt to account 
 for the existence of those small planets, so close to 
 each other, and yet so distant from any of the great 
 planets ? 34 , jj ^, j^r^-t silrw 
 
 Tutor. Olbers and some other able astronomers 
 think they discover in the phenomena of those as- 
 teroids grounds for believing, that they are the 
 fragments of a large planet which has been burst 
 asunder by some internal force, similar to that which 
 I shall one day prove to you lias served to raise the 
 mountains of the earth to their present elevation. 
 
 c (fiaflidttf j $ T&H ai'b&ft*KK)8fVe:n-J? /:}&' Y 
 
 i>uiit.i4dtQ inttCLsu sstf'OiHiJ^e, M ./j , Yi,um*> 'ia
 
 OF COMETS. 
 
 , : :i;'iJ . ' * 
 
 CONVERSATION XXV. 
 
 u V " 'o^^ ^i;;T?cti 
 
 .tei*i .^.-"/i *it * -ia^H-.^ 
 
 O/ Cornels. 
 
 TUTOR. Besides the seven great and four 
 small primary planets, and the eighteen secondary 
 ones or satellites, which we have been describing, 
 there are other bodies belonging to the solav system, 
 called comets. 
 
 Charles. Do comets resemble the planets in any 
 respects ? 
 
 Tiitor. Like them they are supposed to revolve 
 about the sun in elliptical orbits, and to describe 
 equal areas in equal times ; but they do not appear 
 to be adapted for the habitation of animated beings 
 like man, owing to the great degrees of heat and cold 
 to which, in their course, they must be subjected. 
 
 The comet seen by Sir Isaac Newton, in the 
 year 1680, was observed to approach so near the 
 sun, that its heat was estimated by that great 
 man, to be 2000 times greater than that of red-hot 
 iron. 
 
 James. It must have been a very solid body to 
 2L
 
 i;>G . ASTRONOMY. 
 
 have endured such a heat without being entirely 
 dissipated. 
 
 Tutor. So indeed it should seem ; and a body 
 thus heated must retain its heat a long time ; foe 
 a red-hot globe of iron, of a single inch in diameter, 
 exposed to the open air, will scarcely lose its heat 
 in an hour; and it is said, that a globe of red-hot 
 iron, as large as our eayth, would scarcely cool in 
 50,000 years. See Eufield's Institutes of Nat f Phil. 
 p. 296. 2d edit. 
 
 C/wles. Are the periodical times of the comets 
 Jtnowq? 
 
 Tutor. Not with any degree of certainty ; it was 
 supposed that the periods of three of them had been 
 distinctly ascertained. The first of these appeared 
 in the years 1531, 16Q7, and 1(J32, and it was ex- 
 pected to return every 75th year; and one which, 
 as had been predicted by J)r. Halley, appeared in 
 1753, was supposed to be the same. 
 
 The second of them appeared in 1 533, and 1661, 
 pnd it was expected that it would again make its 
 appearance in 1789, but in this, the astronomers of 
 the present day have been disappointed. ,,j 
 
 The third was that which appeared in 1680, and 
 its period being estimated at 575 years, cannot upoa 
 that supposition, return until the year 2255. This 
 last comet at ils greatest distance is eleven thousand 
 two hundred millions of miles from the sun, ancj 
 its least distance from the sun's centre was but four
 
 .OF COMETS, 127 
 
 hundred and ninety thousand miles ; in this part 
 of its orbit it travelled at the rate of 880,000 mites 
 in an hoar, v )*? 
 
 James. Do all bodies move faster or slower in 
 proportion as they are nearer to, or more distant 
 .from, their centre of motion ? 
 
 Tutor. They do, for if you look back upon the 
 last six or seven lectures, you will see that the 
 Herschel, which is the most remote planet in the 
 solar system, travels at the rate of 16,000 miles an 
 hour; Saturn, the next nearer in the order, 21,000 
 jniles ; Jupiter 28,000 miles; Mars 5-3,000 miles; 
 the earth 65,000 miles ; Venus 75,000 miles; and 
 Mercury at the rate of 105,000 miles in an hour. 
 But here we come to a comet, whose progressive 
 motion in that part of its orbit which is nearest to 
 the sun, is more than -equal to eight times the velo- 
 city of Mercury. 
 
 Charles. Were not comets formerly dreaded, as 
 awful prodigies intended to alarm the world ? 
 
 Tutor. Comets are frequently accompanied with 
 n luminous train called the tail, which is supposed 
 to be nothing more than vapour rising from the 
 body in a line opposite to the sun, but which, to 
 uninformed people, has been a source of terror 
 and dismay. 
 
 Charles* Do comets shine by their own light? 
 
 Tv.tor. It was, till within these few years, sup* 
 obed that comets borrowed all their light from the
 
 128 
 
 sun ; but the appearance of two very brilliant comets, 
 of latd, seems to have overturned that theory. One 
 of these was visible, for several weeks, in 1807, and 
 the other from September to the end of the 
 year 1811. Previously to the appearance of these, 
 it was generally supposed that the light of comets, 
 like that of the moon and planets, was reflected 
 light only. A new theory is now adopted by Dr. 
 Herschel, and other eminent astronomers, who have 
 liad capital opportunities, in both the instances 
 referred to, for accurate observations. Dr. Hers- 
 chel says, with respect to the comet in 1807, " we 
 are authorized to conclude, that the body of the 
 comet, on its surface, is self-luminous, from what- 
 ever cause this quality may be derived. The viva* 
 city of the light of the comet also, had a much 
 greater resemblance to the radiance of the fixed 
 stars, than to the mild reflection of the sun's .beams 
 from the moon. S1 
 
 The same inference has been drawn from the ob- 
 servations made on the comet of 181 1, which dis- 
 tinctly exhibited, to very powerful telescopes, the 
 several parts of which the comet is composed, 
 ; Charles. What are those parts? 
 
 Tutor. They are the nucleus, the head, the comet, 
 and the tail. 
 
 The nucleus is a very small, brilliant, and dia- 
 mond-like substance in the centre, so small as to be 
 incapable of. being measured.
 
 OF COMETS. 129 
 
 x : t> a ' 
 
 The head includes all the very bright surrounding 
 light: inferior telescopes, that will "not render the 
 nucleus visible, are often able to exhibit the head 
 thus described. The head of the comet of 1807 
 was ascertained to be 538 miies in diameter : that of 
 J811 to be about the size of the moon. 
 
 The coma is the hairy or nebulous appearance sur- 
 rounding the head. 
 
 The taily which, in some comets extends through 
 an immense space, it is thought may be more satis- 
 factorily accounted for, by supposing it to consist 
 of radiant matter, such as the matter of the aurora 
 borealis, than when we unnecessarily ascribe the 
 light to a reflection of the sun's illuminations thrown 
 upon vapours supposed to arise from the body of 
 the comet. The tail of the comet, in 1807, was 
 ascertained to be more than nine millions of miles 
 in length; and that in 1811 was full 33 millions in 
 length. 
 
 James. Was this comet at a great distance from 
 the earth ? 
 
 Tutor. On the 15th of September, its distance 
 from the sun was more than 95 millions of miles; 
 and its distance from the earth, at the same time, 
 was upwards of 142 millions of miles,
 
 jfjw 
 ct 
 
 CONVERSATION XXVI. 
 
 .i i'-'JOI 9ill tu SIv.e; -^ JUiK* rf >'i*6l 
 
 ^ ; . t \i;. : ..' 
 
 .h/^$4 srit -uvbrtWVT 
 
 O/ /^ Sun. 
 
 
 TUTOR. Having given you a particular de- 
 scription of the planets which revolve about the 
 sun, and also of the satellites which travel round 
 the primary planets as central bodies, while they 
 are carried at the same time with these bodies round 
 the sun, we shall conclude our account of the 
 solar system by taking some notice of the suu 
 himself. 
 
 James. You told us a few days ago, that the 
 s'uii has a rotation^on its axis how is that known? 
 
 Tutor. By the spots on his surface it is knowu 
 that he completes a revolution from west to east oil 
 his axis in about 25 days, two days less than his 
 apparent revolution, in consequence of the earth's 
 motion in Her orbit, in the same direction. 
 
 Charles. Is the figure of the sun globular? 
 
 Tutor. No ; the motion about its axis renders 
 it spheroidical, having its diameter at the equator 
 larger than that which passes through the poles.
 
 OF THE SUN. . 131 
 
 The sun's diameter is equal to 100 diameters of 
 the earth, aud therefore his bulk must be a million 
 of times greater than that of the earth, but the den- 
 sity of the matter of which it is composed is four 
 times less than the density of our globe.' 
 
 We have already seen that by the attraction of 
 the sun, the planets are retaiued in their orbits, and 
 that to him they are indebted for light, heat, and 
 motion. 

 
 132 ASTRONOMY, 
 
 u'^'j .301 6? ?*fjpo tHl! 
 
 * CONVERSATION XXVII. 
 
 O/ Me 
 
 TUTOR. We will now put an end to our astro- 
 nomical conversations by referring again to the fixed 
 stars, which, like our sun, shine by their own light. 
 
 diaries. Is it then certain that the fixed stars 
 are of themselves luminous bodies ; and that the 
 planets borrow their light from the sun ? 
 
 Tutor. By the help of telescopes it is known 
 that Mercury, Venus, and Mars, shine by a borrow- 
 ed light ; for like the moon, they are observed to 
 have different phases according as they are differ- 
 ently situated with regard to the sun. The immense 
 distances of Jupiter, Saturn, and the Herschel pla- 
 net, do not allow the difference between the perfect 
 and imperfect illumination of their disks or phases 
 to be perceptible. 
 
 Now the distance of the fixed stars from the earth 
 is so great, that reflected light would be much too 
 weak ever to reach the eye of an observer here. 
 
 James. Is the distance ascertained with any de- 
 gree of precision ?
 
 OP THE FIXED STARS. 133 
 
 ' *.- * ' - " 
 
 Tutor. It is not : but it is known with certainty 
 to be so great, that the whole length of the earth's 
 orbit, viz. 190 millions of miles, is but a point in 
 comparison of it ; and hence it is inferred that the 
 distance of the nearest fixed star cannot be less than 
 a hundred thousand times the length of the earth's 
 orbit*: that is, a hundred thousand times 190 mil- 
 lions of miles, or 19,000,000,000,000 miles : this dis- 
 tance being immensely great, the best method of 
 forming some clear conception of it, is to compare 
 it with the velocity of some moving body, by which 
 it may be measured. The swiftest motion with which 
 we are acquainted is that of light, which, as we 
 have seen, is at the rate of 12 millions of miles in a 
 minute; and yet light would be about 3 years in,' 
 passing from the nearest fixed star to the earth. A 
 cannon-ball, which may be made to move at the rate 
 of 20 miles in a minute, would be eighteen hundred 
 thousand years in traversing the distance. Sound, 
 the velocity of which is 13 miles in a minute, would 
 be more than 2 million 7 hundred thousand years in 
 passing from the star to the earth. So that if it were 
 possible for the inhabitants of the earth, to see the 
 light ; to hear the sound ; and to receive the ball 
 of a cannon discharged at the nearest fixed star : 
 they would not perceive the light of its explosion for 
 3 years after it had been fired ; nor receive the ball 
 till 1800 thousand years had elapsed ; nor hear the 
 
 See Enfield's Institutes of Natural Philosophy, p. 34T. 2d Ed- 
 2 N
 
 ,; -.-; . f.-% 
 
 134 ASTRONOMY. H1 'JO 
 
 report for 2 millions and 7 hundred thousand yeirs 
 after the explosion,^ <rfo> 
 
 CJtqrles. Are the fixed stars at different distances 
 from the earth ? 
 
 Tutor. Their magnitudes, as you know, appear 
 to be different from one another, which difference 
 may arise either from a diversity in their real .mag- 
 nitudes, or in their distances, or from both these 
 causes acting conjointly. It is the opinion of Dr. 
 Herschel, that the different apparent magnitudes of 
 the stars arise from the different distances at which 
 they are situated, and therefore he concludes that 
 stars of the seventh magnitude, are at seven times 
 the distance from us that those of the first magni- 
 tude are. 
 
 By. the assistance of his telescopes he is able to 
 discover stars which he estimates to be at 497 times 
 the distance of Sirius the Dogstar : from which he 
 infers, that with more powerful instruments he should 
 be able to discover stars at still greater distances. 
 
 James. I recollect that you told us once, that it 
 had been supposed by some astronomers, that there 
 might be fixed stars at so great a distance from us, 
 that the rays of their light had not yet reached the 
 earth, though they had been travelling at the rate 
 of 12 millions of miles in a minute, from the first 
 creation to the present time. 
 
 Tutor. I did ; it was one of the sublime specu- 
 lations of the celebrated Huygens-
 
 OF THE FIXED STAKS. 135 
 
 Charles. What can' be 'the- use of these fixed 
 stars? not to enlighten the earth, for a single ad- 
 ditional moon would give us much more light than 
 them all, especially if it were so contrived as to 
 afford us its assistance at those intervals when our 
 present moon is below the horizon. ' i;3_im 
 
 Tutor. You are right: they could not have been 
 created for our use, since thousands, and even mil- 
 lions, are never seen but by the assistance of glasses, 
 to which but few of our race have access. Your 
 minds indeed are too enlightened to imagine, like 
 children unaccustomed to reflection, that all things 
 were created for the enjoyment of man. The earth 
 on which we live is but one of seven great primary 
 planets circulating perpetually round the sun as a 
 centre, and with these are connected eighteen se- 
 condary planets or moons, all of which are proba- 
 bly teaming with living beings, capable, though in 
 different ways, of enjoying the bounties of the great 
 First Cause. 
 
 The fixed stars then are probably suns, which, 
 like our sun, serve to enlighten, warm, and sustain o- 
 ther systems of planets and their dependent satellites. 
 
 James. Would our sun appear as a fixed star at 
 any great distance ? 
 
 Tutor. It certainly would: and Dr. Herschel 
 thinks there is no doubt, but that it is one of the 
 heavenly bodies belonging to that tract of the hea- 
 vens known by the name of the Milky Way.
 
 136 ASTRONOMY. 
 
 Charles.. I know the milky way in the heavens, 
 but 1 little thought that J had .any concern with it' 
 otherwise than as an observer; 
 
 Tutor. The rhilky way consists of fixed stars, 
 too small to be discerned with the naked eye ; 
 and if our sun be. one of them, the earth and other 
 planets are closely connected with this part of the 
 heavens. t *% 
 
 Gentlemen, it is time that we take our leave of 
 this subject for the present. But in all your studies 
 and pursuits, never- forget, that "J ^ 
 
 - -yon cannot go 
 
 Where UNIVERSAL LOVE not smiles around, 
 Sustaining all yon orbs, and all their snns j 
 From seeming evil still educing good, 
 And better thence again, and better still, 
 In infinite progression. 
 
 THOMSON. 
 
 HI r i ;? . :-
 

 
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