diff options
Diffstat (limited to 'old/56289-0.txt')
| -rw-r--r-- | old/56289-0.txt | 3753 |
1 files changed, 0 insertions, 3753 deletions
diff --git a/old/56289-0.txt b/old/56289-0.txt deleted file mode 100644 index ad11bc9..0000000 --- a/old/56289-0.txt +++ /dev/null @@ -1,3753 +0,0 @@ -The Project Gutenberg EBook of The Study of Astronomy, by John Stedman - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: The Study of Astronomy - adapted to the capacities of youth - -Author: John Stedman - -Release Date: January 2, 2018 [EBook #56289] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK THE STUDY OF ASTRONOMY *** - - - - -Produced by Eric Hutton and the Online Distributed -Proofreading Team at http://www.pgdp.net - - - - - - - [Illustration: _Plate I._ - - The COPERNICAN or SOLAR SYSTEM. - - _The comparative Distances of the Planets from the Sun_ - - _T. Conder Sculp^t._] - - - - - THE - - STUDY OF ASTRONOMY, - - ADAPTED TO THE - - CAPACITIES OF YOUTH: - - _IN TWELVE FAMILIAR DIALOGUES_, - - BETWEEN - - A TUTOR AND HIS PUPIL: - - Explaining the General PHÆNOMENA of the HEAVENLY - BODIES, the THEORY of the TIDES, &c. - - _ILLUSTRATED WITH COPPER-PLATES._ - - BY JOHN STEDMAN. - - _LONDON_: - - PRINTED FOR C. DILLY, IN THE POULTRY. - - M.DCC.XCVI. - - - - ------------------------------------------------------------------------- - - - - - ERRATA. - - - Page 20. line 8. _for_ he _read_ the. - - —— 22. — 6. ⎫ - ⎪ - —— 23. — 2. ⎪ — disk — disc. - ⎬ - —— 42. — last ⎪ - ⎪ - —— 79. — 5. ⎭ - - —— 74. — 6. — it axis — its axis. - - —— 78. — 19. _dele_ Mercury. - ------------------------------------------------------------------------- - - - - - PREFACE. - - -It has long been a matter of surprize to those who are interested in the -education of youth, that, among the numerous publications intended for -their improvement, so few attempts have been made to facilitate the -study of Astronomy. - -Many excellent treatises have been written on this important and useful -science; but if it be considered that they abound with technical terms, -unintelligible to juvenile minds, it cannot be expected that they should -derive any great advantage from the perusal of them. - -To remove these difficulties, the Author has endeavoured, whenever he -had occasion to use them, to give such illustrations as to leave no -doubt on the young student’s mind respecting their true meaning. - -The subject appeared to him to be best calculated for dialogues, which -are certainly more agreeable as well as more perspicuous to young -persons, than the discouraging formality of a treatise. And it is -presumed the language will be found natural and easy. - -In the order he has chosen, he has been careful not to introduce any -thing new, till the former part, on which it depends, has been clearly -explained. - -On the whole, it has been his aim to render it as concise and plain as -the nature of the subject will admit; and he flatters himself, that at a -time when the sciences are so universally studied, the introduction now -offered to the public will not be unacceptable. - ------------------------------------------------------------------------- - - - - - CONTENTS. - - - DIALOGUE I. p. 1. - - Introduction. Definition. The sun and planets. A - globe defined. Sun’s distance and magnitude. - Planets, what; their names, periods, and - distances from the sun; their magnitudes, - compared with the earth; called inferior and - superior, why. Comets; derivation of the name. - Solar system; why so called. - - - DIALOGUE II. p. 10. - - Different systems explained. Planets appear like - stars; they shine by reflection; how known - from stars; they never twinkle, why. Stars - shine with their own native light; their - inconceivable distance; are suns, the centers - of other systems. Plurality of worlds. - - - DIALOGUE III. p. 20. - - The earth has the appearance of a star to Venus. - Remote objects appear at equal distances from - us. Our earth is a moon to the moon. The orb - of the moon visible soon after the change; her - disc and bulk compared with the earth; her - mean distance. Sun’s disc compared with hers. - Our sun a star, if seen from a planet of - another system. Stars as far from each other - as the nearest is to us. Stars distinguished - by their apparent magnitude. The Milky Way - innumerable stars. Number of stars visible at - one time to the naked eye. - - - DIALOGUE IV. p. 29. - - Stars divided into constellations; necessary for - ascertaining the situation of the planets, and - of the stars with each other. Planets motion - regular if seen from the sun; irregular as - seen from the earth, the motion being - sometimes direct, sometimes retrograde; at - others they appear stationary. Superior and - inferior conjunction, and opposition, what. - Venus has the different phases of the moon. - Planets, how distinguished from each other. - - - DIALOGUE V. p. 39. - - Ecliptic, what. Inclination of the orbits of the - planets. Nodes of the planets, what. A plane, - what. Planets move in unbounded space. Mercury - and Venus seen on the sun’s disc. Number of - signs in the zodiac. Zodiac, what. A degree, - what. Names of the signs. Number of degrees in - each sign. Sun’s place in the ecliptic. Table - of signs, their characters, &c. To find the - sun’s place in the ecliptic for any day in the - year. - - - DIALOGUE VI. p. 50. - - The orbits of the planets are not true circles, - but somewhat elliptical. Perihelion, aphelion, - and mean distance, what. Attraction, what. - Laws of attraction. Attraction of gravitation, - its effects. Simple motion rectilineal. - Attractive or centripetal, and projectile or - centrifugal forces, what. - - - DIALOGUE VII. p. 61. - - Bodies moving in circles have a tendency to fly - off. Planets kept in their orbits by the joint - action of the centripetal and centrifugal - forces; they describe equal areas in equal - times. Orbits of the comets very elliptical. - The earth in its perihelion in December. - Equation of time. Center of gravity, what; sun - and planets move round it. Sun the center of - the system. - - - DIALOGUE VIII. p. 73. - - The earth revolves on its axis. Cause of day and - night. The motion of the earth so uniform as - not to be perceived. The apparent motion of - the sun caused by the earth’s motion on its - axis. An objection to the earth’s motion - answered. The sun and some of the planets - revolve on their axes. Atmosphere, what; cause - of twilight. Horizon, what; the sun and moon - appear largest near the horizon, why; they - appear above the horizon when below it; caused - by refraction; proved by experiment. - - - DIALOGUE IX. p. 87. - - Inclination of the earth’s axis. An angle, what. - The poles, what. Equinoctial, what. Earth’s - parallelism described. The axis of the earth - points to the same parts of the heavens. - Equator, ecliptic, polar circles, and - meridians, explained. Difference of time - between places lying under different - meridians. Longitude, what. How to reduce - longitude to time, and time to longitude. - Latitude, what. - - - DIALOGUE X. p. 101. - - The seasons. Vernal and autumnal equinoxes. Days - and nights always equal, if the axis of the - earth were perpendicular to the plane of its - orbit. Seasons occasioned by the inclination - of the earth’s axis. Seasons continued. Days - and nights equal at all times under the - equator. The sun above the horizon of the - poles six months; and six months below them - alternately, so that they have but one day and - one night in the year; the longest day under - the polar circles is twenty-four hours. The - sun rises on different points of the compass - at different seasons of the year. Twilight in - the polar regions of long duration. We are - nearest the sun in winter, yet it is our - coldest season, why. The earth divided into - zones; proved to be globular, but is not a - true sphere. - - - DIALOGUE XI. p. 120. - - The moon. Her diameter, synodical and periodical - revolutions. Her phases. Has always the same - side to the earth, and makes a revolution on - her axis every lunation. Has mountains and - valleys, but no seas nor atmosphere; yet may - be inhabited. Her real and apparent motion - described. Eclipses. Of the sun; total and - partial eclipses. Digit, what. Eclipse of the - moon. Penumbra, what. Central and total - eclipse. Why we have not an eclipse at every - full and change of the moon. She does not - always rise with the sun at change; nor when - he sets at full. She is visible when totally - eclipsed. - - - DIALOGUE XII. p. 136. - - Tides. Occasioned by the attraction of the sun - and moon, and their centrifugal forces; - exemplified by an experiment. Spring and neap - tides. Tides not highest directly under and - opposite the moon, but after she has passed - the meridian. They are later and later every - day. Rule for finding the proportional - magnitudes of the planets compared with the - earth; or the proportion that one globe bears - to another. A cube number, what. Table of - roots, squares, and cubes; an example. Rule - for finding the mean distances of the planets - from the sun. Dr. Turner’s rule for extracting - the cube root; an example to explain the rule. - Example to find the mean distance of Mercury - from the sun. Table of diameters, &c. - Conclusion. - ------------------------------------------------------------------------- - - - - - DIALOGUE I. - - - TUTOR. - -Well, Sir! I suppose this early visit is in consequence of my promise, -and your anxiety to become an astronomer. - -PUPIL. It is, Sir.—And as astronomy is a science of which I have a very -imperfect idea, I must beg of you to explain it to me. - -TUTOR. That I shall do with pleasure. But you surely cannot wholly -forget what I have formerly told you. However, as I mean to treat the -subject as if you had no previous knowledge of it, you will have an -opportunity from what you can recollect, to make such remarks, and ask -such questions, as may appear most material to you. - -PUPIL. I thank you, Sir, it is just what I wish. - -TUTOR. By astronomy then is meant a knowledge of the heavenly bodies, -the sun, moon, planets, comets, and stars, respecting their nature, -magnitudes, distances, motions, &c. - -PUPIL. I fear I shall find it a difficult study. - -TUTOR. Have patience.—— - - “The wise and prudent conquer difficulties, - “By daring to attempt them. Sloth and folly - “Shiver and shrink at sight of toil and danger, - “And make the impossibility they fear.” - -PUPIL. This gives me encouragement, and, if you will have patience with -me, I will endeavour to profit by your instructions.——Pray, Sir, what is -the sun? - -TUTOR. The sun, the source of light and heat, has been considered a -globe of fire, round which seven other spherical bodies revolve at -different distances from him, and in different periods of time, from -west by south to east. These are the planets[1]. - - [Footnote 1: From _Planeta_, roving or wandering.] - -PUPIL. Any round ball is a globe, is it not? - -TUTOR. A sphere or globe is defined a round solid body, every part of -whose surface is equally distant from a point within called its center; -and a line drawn from one side through the center to the opposite side, -is called its diameter. - -PUPIL. You say the sun has been considered a globe of fire. Is he not -now thought to be so? - -TUTOR. [2]Doctor Herschell, from some late observations, is of a -different opinion.—But what think you of his magnitude? - - [Footnote 2: See his letter read at the Royal Society, December - 18th, 1794.] - -PUPIL. I really cannot conjecture.—This I know, that when I saw him -through the fog the other day, he appeared about the size of a common -plate. - -TUTOR. You must not always judge by appearances. You will find that -there is a material difference between his real and apparent magnitude, -which I think you will be convinced of when I tell you, that he is no -less than 95 millions of miles from our earth. - -PUPIL. Ninety-five millions of miles! You astonish me. - -TUTOR. You will, I dare say, be no less surprized at being told, that he -is more than a million of times as large as our earth. - -PUPIL. It is almost incredible! And what are the planets? - -TUTOR. The planets are opaque, that is dark bodies, which receive their -light from the sun; and, as I told you, revolve about him. The first, or -that nearest the sun, is called Mercury, the next Venus, then the Earth, -Mars, Jupiter, Saturn, and Georgian, or the Georgium Sidus.[3] These are -called primary planets. - - [Footnote 3: Their characters are, - - Sun, Merc. Venus, Earth, Mars, Jup. Saturn, Georgian, - ☉ ☿ ♀ ♁ ♂ ♃ ♄ ♅ .] - -PUPIL. Are there then any others? - -TUTOR. Yes. There are fourteen others, which move round their respective -primaries as their centers, and with them round the sun, and are called -secondaries, satellites or moons. - -PUPIL. Have all the primaries secondaries? - -TUTOR. Only four of them have moons. The earth, I need not tell you, has -one; Jupiter has four; Saturn seven, besides a stupendous ring which -surrounds his body; and Georgian two. - -PUPIL. In what time, and at what distances, from the sun, do the planets -perform their periodical revolutions? - -TUTOR. _Mercury_ revolves about the sun in 88 days, at the distance of -36 millions of miles. - -_Venus_, at the distance of 68 millions of miles, completes her -revolution in 224 days. - -_Earth_, on which we live, at the distance of 95 millions of miles, -performs its period in one year.[4] - - [Footnote 4: The motion of the earth in its orbit is at the rate of - 68 thousand miles an hour.] - -_Mars_, at the distance of 145 millions of miles, in little less than -two of our years. - -_Jupiter_, at the distance of 494 millions of miles, in near 12 years. - -_Saturn_, at the distance of 906 millions of miles, in about 30 years. - -_Georgian_, discovered a few years since by Dr. Herschell, performs its -period at the distance of 1812 millions of miles, in about 83 years.[5] - - [Footnote 5: As the distances of the planets, when marked in miles, - are a burthen to the memory, astronomers often express their mean - distances in a shorter way, by supposing the distance of the earth - from the sun to be divided into ten parts. Mercury may then be - estimated at four of such parts from the sun, Venus at seven, the - Earth at ten, Mars at fifteen, Jupiter at fifty-two such parts, - Saturn at ninety-five, and Georgian 190 parts. See Plate I. Fig. 1. - - These are calculated by multiplying the respective distances of the - planets by 10, and dividing by 95, the mean distance of the earth - from the sun; and may be set off by any scale of equal parts.] - -PUPIL. What proportion does the earth bear in magnitude to the other -planets? - -TUTOR. The earth is fourteen times as large as Mercury, very little -larger than Venus, and three times as large as Mars. But Jupiter is more -than fourteen hundred times as large as the earth; Saturn above a -thousand times as large, exclusive of his ring; and Georgian eighty-two -times as large. - -PUPIL. Have you any thing else, Sir, to remark concerning the planets? - -TUTOR. There are several other things I intend to make you acquainted -with, namely, their nature, appearances, motions, &c. At present I shall -only say, that Mercury and Venus are called [6]inferior planets, their -orbits or paths described in going round the sun, being within that of -the earth; and the other four, whose orbits are without the earth’s -orbit, [7]superior planets. - - [Footnote 6: Perhaps with more propriety _interior_ or _inward_.] - - [Footnote 7: _Exterior_ or _outward_.] - -PUPIL. There is one thing more I wish to know, if—— - -TUTOR. I suppose you were going to say if not too much trouble; that is -quite unnecessary, as you well know that where I see a desire to learn, -teaching is to me a pleasure.—What is it? - -PUPIL. That you will be so kind as to inform me what the comets are, and -if they have any motion? - -TUTOR. The knowledge we have of comets is very imperfect, as they afford -few observations on which to ground conjecture. They are generally -supposed to be planetary bodies, forming a part of our system: for, like -the planets, they revolve about the sun, but in different directions, -and in extremely long elliptic curves, being sometimes near the sun, at -others staying far beyond the orbit of the outermost planet; whereas the -orbits of the planets are nearly circular. The period of one, which -appeared in 1680, is computed to be 575 years. - -PUPIL. Whence do they derive their name? - -TUTOR. From _Cometa_, a _hairy star_, because they appear with long -tails, somewhat resembling hair: some, however, have been seen without -this appendage, as well defined and round as planets. - -PUPIL. You say _our_ system: what am I to understand by it? - -TUTOR. The word system, in an astronomical sense, means a number of -bodies moving round one common center or point: and, because the planets -and comets revolve about the sun, it is called the _Solar System_ (Plate -I. fig. 2.); and we say _our_ system, as the earth is one of the -planets. Other systems have been invented for solving the appearances -and motions of the heavenly bodies, a description of which I shall leave -till I next see you. - ------------------------------------------------------------------------- - - - - - DIALOGUE II. - - - PUPIL. - -I am afraid, Sir, I am come before you are prepared for me: but the very -great pleasure I received yesterday, induced me to be with you as early -as possible. - -TUTOR. I am glad to see you, and happy to find you are so well pleased -with your difficult study. It will, I assure you, give you more exalted -ideas of the Deity than any that I know of. The Psalmist was undoubtedly -of this opinion when he said, The Heavens declare the glory of God, and -the Firmament sheweth his handy work. - -PUPIL. I will no longer call it a difficult, but a pleasing study, and -feel myself ashamed at having used the expression. I shall now beg you -to explain to me the different systems. - -TUTOR. The system I have been describing to you was known and taught by -Pythagoras, a Greek philosopher, who flourished about 500 years before -Christ, as he found it impossible, in any other way, to give a -consistent account of the heavenly motions. - -This system, however, was so extremely opposite to all the prejudices of -sense and opinion, that it never made any great progress, nor was ever -widely spread in the ancient world. - -Ptolemy, an Egyptian philosopher, who flourished 130 years after Christ, -supposed that the earth was fixed in the center, and that the sun and -the rest of the heavenly bodies moved round it in twenty-four hours, or -one natural day, as this seemed to correspond with the sensible -appearances of the cœlestial motions. This system was maintained from -the time of Ptolemy to the revival of learning in the sixteenth century. - -At length, Copernicus, a native of Poland, a bold and original genius, -adopted the Pythagorean system, and published it to the world in the -year 1530. This doctrine had been so long in obscurity, that the -restorer of it was considered as the inventor. - -Europe, however, was still immersed in ignorance; and the general ideas -of the world were not able to keep pace with those of a refined -philosophy. This occasioned Copernicus to have few abettors, but many -opponents. Tycho Brahe, in particular, a noble Dane, sensible of the -defects of the Ptolemaic system, but unwilling to acknowledge the motion -of the earth, endeavoured, about 1586, to establish a new system of his -own; but, as this proved to be still more absurd than that of Ptolemy, -it was soon exploded, and gave way to the [8]Copernican or true Solar -System. - - [Footnote 8: See Plate I. fig. 2.] - -PUPIL. I confess, I should have thought with Ptolemy, that the earth was -in the center, and that the sun moved round it. - -TUTOR. You must at present content yourself with knowing that it is not -so; and it shall be my business to prove it. - -PUPIL. May I beg the favour of the information you intended respecting -the planets? - -TUTOR. I will grant it with pleasure. The planets are spherical bodies, -which appear like stars, but are not luminous; that is, they have no -light in themselves; though they give us light; for they shine by -reflecting the light of the sun. - -PUPIL. You say, Sir, that they appear like stars; if so, how am I to -know them from stars? - -TUTOR. Very easily: for the stars, or as they are more properly called -fixed stars, always keep the same situation with respect to each other; -whereas the planets, as they move round the sun, must be continually -changing their places among the fixed stars, and with one another. - -PUPIL. Is there any other method of distinguishing them besides what you -have mentioned? - -TUTOR. Yes. The planets never twinkle like the fixed stars, and are seen -earliest in the evening and latest in the morning. - -PUPIL. How is the twinkling of the stars in a clear night accounted for? - -TUTOR. It arises from the continual agitation of the air or atmosphere -through which we view them; the particles of air being always in motion, -will cause a twinkling in any distant luminous body, which shines with a -strong light. - -PUPIL. Then, I suppose, the planets not being luminous, is the reason -why they do not twinkle. - -TUTOR. Most certainly. The feeble light with which they shine is not -sufficient to cause such an appearance. - -PUPIL. Have the stars then light in themselves? - -TUTOR. They undoubtedly shine with their own native light, or we should -not see even the nearest of them: the distance being so immensely great, -that if a cannon-ball were to travel from it to the sun, with the same -velocity with which it left the cannon, it would be more than 1 million, -868 thousand years, before it reached it.[9] - - [Footnote 9: The distance of Syrius is 18,717,442,690,526 miles. A - cannon-ball going at the rate of 1143 miles an hour, would only - reach the sun in about 1,868,307 years, 88 days. - - Adams’s Lectures, vol. 4. page 44.] - -PUPIL. This is wonderful indeed! what then are they supposed to be? - -TUTOR. Suns. - -PUPIL. Suns! the fixed stars suns! - -TUTOR. Yes, suns. - - “One sun by day, by night ten thousand shine.” - -And what will increase your astonishment, each of them is the center of -a system of planets, which move round him.[10] - - [Footnote 10: Dr. Herschell says, that in some clusters of stars he - has observed, they appear too close together to admit any planets to - revolve about them.] - - “Observe how system into system runs.” - - “What other planets circle other suns.” - -PUPIL. I am almost lost.—I used to think they were designed to give us -light. - -TUTOR. This is a vulgar error.—They were doubtless created for a much -nobler purpose, since thousands of them are invisible to us without the -help of a telescope; and we receive more light from the moon than from -all the stars together. - -PUPIL. How do you know they are suns? Is their being luminous a proof of -their being so? - -TUTOR. No. But we know that the sun shines with his own light on all the -planets belonging to our system; and from what I have told you, have the -greatest reason to believe that the stars shine with their own light: we -therefore from analogy conclude, that they are so many suns conveying -light and heat to other worlds[11]. - - [Footnote 11: Dr. Herschell thinks it probable that the sun and - fixed stars may be inhabited.] - -PUPIL. Are there then other worlds besides this we live in? - -TUTOR. Consider.—Has not the earth we inhabit a moon to enlighten it? - -PUPIL. Yes, Sir. - -TUTOR. And have I not told you that Jupiter, Saturn, and Georgian, have -also moons? - -PUPIL. This I well remember. - -TUTOR. For what purpose then do you suppose those orbs were designed? - -PUPIL. Indeed, I cannot tell. - -TUTOR. You surely cannot imagine that they were intended for our use, -since we knew nothing of them till after the invention of telescopes. - -PUPIL. That is what I think no one can suppose. - -TUTOR. And do not all the planets enjoy the benefit of the sun in common -with us? - -PUPIL. Undoubtedly. - -TUTOR. Well, then; of what use would the light and heat be which is -conveyed to them from the sun; or the light which they receive from -their moons if there are no inhabitants? - -PUPIL. I know of none. - -TUTOR. Can you then have any doubt about their being inhabited? - -PUPIL. No, Sir.—But you say that the stars are suns, each of which is -the center of a system of planets or worlds. - -TUTOR. If you are satisfied that the planets belonging to our system are -inhabited, and that the fixed stars are suns, the centers of other -systems, what reasonable objection can you have to all the planets in -the universe being so? - -PUPIL. It is what I cannot comprehend. - -TUTOR. It may be so.—But is not the same Almighty Power, who does -nothing in vain, as capable of making ten thousand worlds if he pleased, -as well as one? - -PUPIL. I will not presume to dispute his power; but are we not told that -all mankind descended from Adam? - -TUTOR. Yes; Moses wrote concerning this earth, he has not made us -acquainted with the inhabitants of the other planets: for aught we know -they might descend from other Adams.—To-morrow evening, I hope to see -you again. - ------------------------------------------------------------------------- - - - - - DIALOGUE III. - - - PUPIL. - -I recollect, Sir, you mentioned last night, that the planets appear like -stars. Our earth is a planet; how can it have the appearance of a star? - -TUTOR. If you were on the planet Venus, the earth would have as much the -appearance of a star as Venus has to us. - -PUPIL. But Venus appears amongst the fixed stars. - -TUTOR. Yes. And so would the earth appear from Venus. - -PUPIL. How can it be? - -TUTOR. Because, in whatever part of the universe we are, we appear to be -in the center of a concave, that is hollow, sphere, where remote objects -appear at equal distances from us: so that, whether we are on the planet -Venus or on the earth, in this particular the effect will be the same. - -PUPIL. Then the light _we_ receive from the sun is by reflection -conveyed to the other planets. - -TUTOR. No doubt of it. And our earth appears as a moon to the -inhabitants of the moon, and undergoes the various changes of that -planet. - -PUPIL. Have you any proof of this, Sir? - -TUTOR. Nothing can be clearer; for, on a fine evening, soon after the -change of the moon, when the earth appears nearly as a full moon to the -moon, and we see a faint streak of light, the whole body of the moon is -visible to us. - -PUPIL. I remember to have seen it. - -TUTOR. You do?—The earth then will appear there thirteen times as large -as the moon does to us; of course it must reflect a strong light on the -body of the moon, and it is by that light we see that part of the moon -which is turned from the sun. - -PUPIL. Is the earth, then, only thirteen times as big as the moon? - -TUTOR. In solidity it is about fifty times as large; but its disc or -face is only thirteen times. - -PUPIL. What is the moon’s distance from the earth? - -TUTOR. 240 thousand miles, which is about 400 times less than that of -the sun. - -PUPIL. And yet she appears as far distant as the sun. - -TUTOR. You are now, I hope, convinced of what I said relative to distant -objects. - -PUPIL. I am, Sir: and I suppose the reason of the moon’s appearing as -large as the sun, is because she is so much nearer to us. - -TUTOR. It is so.—For, at a total eclipse of the sun, which happens when -the moon is in a right line between the sun and the earth, the sun is -obscured from our sight, although his disc is 160 thousand times as -large as that of the moon. In like manner would the moon, when at full, -be hid by placing your cricket-ball in a line between your eye and her, -yet, you know, the ball is not so large as the moon; but being nearer -the eye, it is apparently so. - -PUPIL. This is very clear. But—— - -TUTOR. I conjecture you were going to ask me to explain the nature of -eclipses. - -PUPIL. That was certainly my intention, Sir. - -TUTOR. There are other things you must be made acquainted with before -you will be able to comprehend it, and which I will endeavour to make -you understand before we enter on the subject. - -PUPIL. Whenever you please, Sir. - -TUTOR. You have taken a view of the earth from the planet Venus.—Suppose -I transport you to one of the planets belonging to another system; what -description do you think you should give of it? - -PUPIL. I must consider. What I now call a star would be a sun. The -planets of that system I should see as I now do those belonging to ours: -our sun would be a star; and the earth, with all the other planets, -would be invisible. - -TUTOR. Very well, Sir. Can you then find it difficult to conceive that -all the stars are as far from each other in unbounded space as our sun -is from the nearest star? - -PUPIL. It is hard to conceive: but when I consider that wherever I am, -every remote object appears at an equal distance from me, the difficulty -vanishes. - -TUTOR. That you might form some idea of the immense distance of the -fixed stars, you must recollect, I mentioned the time a cannon-ball -would be in reaching the nearest of them. - -PUPIL. I do, Sir. More than 1,868,000 years. - -TUTOR. You have an excellent memory. I suppose then you know the -distance of the earth from the sun? - -PUPIL. Yes, Sir. I wrote it down; and, it made so strong an impression -on my memory, that I believe I shall never forget it.—95 millions of -miles. - -TUTOR. Now, suppose the earth to be in that part of its orbit which is -nearest to the star, it would be 95 millions of miles nearer to it than -the sun is. - -PUPIL. Certainly. - -TUTOR. And, in the opposite side of its orbit, as much farther from the -star. - -PUPIL. Without doubt. - -TUTOR. Then you find that the earth is 190 millions of miles nearer to -the star at one time of the year than it is at another; and yet the -magnitude of the star does not appear the least altered, nor is its -distance affected by it. - -PUPIL. A proof of its amazing distance.—I was going to ask a silly -question. - -TUTOR. What is it? perhaps not so simple as you may imagine. - -PUPIL. Whether the most conspicuous stars are not supposed to be the -nearest to us? - -TUTOR. Undoubtedly.—And are called stars of the first magnitude; the -next in splendor, stars of the second magnitude; and so on to the sixth -magnitude; and those beyond, which are not visible to the naked eye, are -called telescopic stars. - -PUPIL. The distance of the telescopic stars must be great indeed, beyond -all conception. - -TUTOR. You judge rightly; and their numbers are beyond all computation. -Doctor Herschell says, he has not a doubt but that the broad circle in -the heavens, called the Milky Way, is a most extensive stratum of stars, -he having discovered in it many thousands. Besides, some stars appear to -him double, others treble, &c. not that they are really so, but are -stars at different distances from us, which appear nearly in a right -line. - - “As in the milky-way a shining white - “O’erflows the heav’ns with one continued light, - “That not a single star can shew his rays, - “Whilst jointly all promote the common blaze.” - -PUPIL. I have heard of numbering the stars; but that, I find, is -impossible. - -TUTOR. If you mean that immense host of stars I have been describing, it -is impossible; but, though in a clear winter’s night, without moonshine, -they seem to be innumerable, which is owing to their strong sparkling, -and our looking at them in a confused manner; yet when the whole -firmament is divided as it has been done by the ancients, the number -that can be seen at a time, by the naked eye, is not above a thousand. - -PUPIL. Pray, Sir, how did the ancients divide the firmament? - -TUTOR. I would willingly answer your question; but, as I find I shall -not have time to give you that information I wish, I shall postpone it -till I see you to-morrow evening. - ------------------------------------------------------------------------- - - - - - DIALOGUE IV. - - - TUTOR. - -The ancients, in reducing astronomy to a science, combined the fixed -stars into constellations, allowing several stars to make one -constellation: and, for the better distinguishing and observing them, -they reduced the constellations to the forms of animals, or to the -images of some known things, by which means they were enabled to signify -to others any particular star they meant to notice. Job mentions two of -the constellations, namely, Orion and Pleiades, which shews the study of -astronomy to be very ancient. - -PUPIL. Pray, Sir, how may I know them? - -TUTOR. By studying the use of the cælestial globe, on which they are -drawn. - -PUPIL. Will you be kind enough to instruct me, Sir? - -TUTOR. At some future time I probably may: at present you are not -prepared for it. - -PUPIL. I am satisfied.—Have you any thing more to remark of the -constellations, Sir? - -TUTOR. Yes. The situation of the planets, as they are continually -changing their places, could not be pointed out without first dividing -the stars into constellations: hence, necessity was the mother of -invention. - -PUPIL. And I think a very ingenious one.—If I may be allowed a -comparison, I will suppose the different kingdoms of the world on my -dissected map, to represent so many constellations; then, if I hear of -London, I know it is in England; if of Paris, in France; of Lisbon, in -Portugal; and so on. These I would compare with stars of the first -magnitude, being the chief cities of their respective kingdoms; inferior -cities, stars of the second magnitude; principal towns of the third, &c. - -TUTOR. A very apt comparison indeed. Now if you hear of a traveller -setting off from London to Dover, thence to Calais, Paris, Bern, and so -on to Rome, you know that he must go through part of England, Flanders, -France, Switzerland, and Italy, passing many towns and villages on his -way. - -PUPIL. That is very evident. - -TUTOR. Very well, then; in like manner would the planets, if seen from -the sun, be traced from star to star, from constellation to -constellation, through their whole periods. - -PUPIL. It is not possible to view them from the sun, surely, is it? - -TUTOR. No, certainly. - -PUPIL. Why then do you say if seen from the sun? - -TUTOR. Because it is there only their motions can appear uniform; as -seen from the earth they apparently move very irregularly.—Suppose you -were in the center of a circular course; and, whilst a horse was going -round, you kept your eye on him: cannot you conceive that you should see -him run round the course in a regular manner, moving the whole time the -same way? - -PUPIL. It is not at all difficult to conceive. - -TUTOR. Again. Imagine yourself placed at a considerable distance on the -outside of the course, where you could see the horse the whole time he -was going round, would he appear to move as uniformly as before? - -PUPIL. Certainly not: on the opposite side of the course his motion -would be the same as when I stood in the center of it; when he was -approaching me, I should scarcely see him move; in that part of the -course next to me he would move in a direction contrary to what he did -at first; and again when going from me, his motion would be scarcely -visible. - -TUTOR. This I think will give you a tolerable idea of the irregular -motion of the inferior planets, as seen from the earth. When farthest -from us their motion is said to be direct; when nearest to us -retrograde, because they appear to be moving back again; and, when -approaching, or going from us, we say they are stationary; because, if -then observed in a line with any particular star, they will continue so -for a considerable time: now these appearances could not happen if they -moved round the earth. - -PUPIL. Nothing can be plainer: for if the earth were in the center we -should always see them move the same way. - -TUTOR. When the planet is nearest to us, that is in a line between us -and the sun, we say it is in its inferior conjunction; when farthest -from us, and the sun is between us and the planet, in its superior -conjunction. But the superior planets have alternately a conjunction and -an opposition. - -PUPIL. A conjunction, I suppose, when the sun is between the earth and -the planet, and an opposition when the earth is between the sun and the -planet; that is, when the planet is nearest to us, and appears to be -opposite to the sun? - -TUTOR. You are right.—Therefore, when in conjunction it rises and sets, -nearly with the sun; but in opposition, it rises nearly when the sun -sets, and sets when he rises. - -PUPIL. Why do you say nearly, Sir? - -TUTOR. Because it cannot be exactly, but when the sun, earth, and planet -are in a _right_ line, which seldom happens. - -PUPIL. How do you account for this, Sir? - -TUTOR. At present I fear you will not be able to comprehend what I wish -to explain, as I must use a term you are unacquainted with. The reason -is, that the planets are very seldom in or near their nodes at their -conjunctions or oppositions. - -PUPIL. I do not indeed understand what you mean by the word _nodes_. - -TUTOR. It will be explained to you in due time, and I shall conclude -this evening with a few more remarks relative to the appearance of the -planets. - -PUPIL. Any thing you please, Sir. - -TUTOR. You know that the planets, being opaque bodies, receive their -light from the sun; and that only that part which is turned to the sun -can be enlightened by him, whilst the opposite side must remain in -darkness. - -PUPIL. This is self-evident: if I hold my ball to the candle it will -have the same effect. - -TUTOR. Tell me then how you think they will appear as seen from the -earth. - -PUPIL. If, when you shewed me Venus, she had not appeared perfectly -round, I should say that, both before and after her superior conjunction -I should see her nearly with a full face; when stationary, only half -enlightened, like the moon at first quarter; because, an equal portion -of the dark and bright parts will be turned towards us; the bright part -will be decreasing till her inferior conjunction, when the dark side -will be turned towards us, and consequently invisible; the light will -then increase; and, when she is again stationary, she will appear like -the moon at last quarter. - -TUTOR. When seen through a telescope she has the different appearances -you have mentioned; and when I next see you I will shew you that both -Venus and Mercury may sometimes be seen when in their inferior -conjunctions; the superior planets always appear with nearly a full -face. - -PUPIL. How are the planets distinguished from each other? - -TUTOR. _Mercury_, from his vicinity to the sun, is seldom seen, being -lost in the splendor of the solar brightness. When seen, he emits a very -bright white light. - -_Venus_, known by the names of the morning and evening star, is the -brightest, and to appearance, the largest of all the planets; her light -is of a white colour, and so considerable, that in a dusky place she -projects a sensible shade. She is visible only for three or four hours -in the morning or evening, according as she is before or after the sun. - -_Mars_ is the least bright of all the planets. He appears of a dusky -reddish hue, and much larger at some periods than at others, according -as he is nearer to, or farther from us. - -_Jupiter_ is distinguished by his peculiar magnitude and light. To the -naked eye he appears almost as large as Venus, but not altogether so -bright. - -_Saturn_ shines but with a pale feeble light, less bright than Jupiter, -though less ruddy than Mars. - -_The Georgium Sidus_ cannot be readily perceived without the assistance -of a telescope. - ------------------------------------------------------------------------- - - - - - DIALOGUE V. - - - TUTOR. - -Before I proceed to explain what I promised you, it is necessary you -should be informed that the earth as seen from the sun, in its -periodical revolutions, will describe a circle among the stars which -astronomers call the _ecliptic_, and sometimes _the sun’s annual path_, -because the sun, as seen from the earth, always appears in that line. - -PUPIL. Do not all the planets move in the ecliptic? - -TUTOR. No.—On account of the obliquity of their orbits, they are, in -every revolution, one half of their periods above the ecliptic, and the -other half below it. - -PUPIL. I think I comprehend your meaning; but shall be obliged to you, -Sir, if you can make it clearer to me. - -TUTOR. I have here a little design, (Plate II. Fig. 1.) which will -answer our purpose: where S represents the sun; ABCD, the orbit of the -earth; and EFGH, the orbit of one of the inferior planets, suppose -Venus. - - [Illustration: _Plate II._ - - _T. Conder Sculp^t._] - -PUPIL. Now I understand it perfectly: the half EHG rises above, and the -other half EFG sinks below it, from the points EG, which I perceive are -in a line with the orbit of the earth. But pray, Sir, have you any name -for that dotted line? - -TUTOR. Yes, it is called the _line_ of the nodes; and the points EG the -_nodes_ of the planet: the latter is called the ascending node, because, -when the planet is in G, it is ascending or rising above the orbit of -the earth; or, which is the same thing, above the ecliptic: and when in -E, it is descending or sinking below it, whence _it_ is called the -descending node. But you must remember that the orbits of all the -planets do not cross or intersect the ecliptic in the same points; but -that their nodes or intersections are at different parts of it. - -PUPIL. How can the orbit of the earth and the ecliptic be the same? - -TUTOR. They are very different; but being in the same plane, if the -orbit of any planet inclines to one it must incline equally to the -other. - -PUPIL. You will, I fear, Sir, think me very stupid: but I must beg of -you to inform me what you mean by a plane? - -TUTOR. Any flat surface is a plane. You may therefore suppose the edge -of a round tea-table to represent the ecliptic, and a circle within it, -drawn from the center of the table, the orbit of the earth: will they -not be both in the same plane? - -PUPIL. Certainly. - -TUTOR. You must not imagine, when I am speaking to you of the plane of -the ecliptic, or plane of the earth’s orbit, that it is a visible flat -surface, or, in speaking of the orbits of the planets, I mean solid -rings.—No. The planets perform their revolutions with the utmost -regularity, in unbounded space; and, like a bird thro’ the air, leave no -track behind them. - -PUPIL. How then are they retained in their orbits? - -TUTOR. The question, I confess, is natural, and is what I expected; but -I must of necessity postpone it to another opportunity; and shall now -fulfil the promise I made of shewing you in what manner the inferior -planets may be seen when in their inferior conjunctions. Cast your eye -again on the little design I gave you, and consider, if Venus were in -her ascending node at G, when the earth is at _b_; or, in her descending -node, at E, when the earth is at _a_, what the effect would be. - -PUPIL. She would be in a line with the sun. - -TUTOR. And, on the sun’s disc, she would appear a dark round spot, -passing over it. These appearances, which are called transits, happen -very seldom: because she is very seldom in or near her nodes at her -inferior conjunctions. There was one in June 1761, one in June 1769; and -the next will be in the year 1874. And as Mercury is seen in the same -manner, it is a proof that their orbits must be within that of the -earth. - -PUPIL. I thank you, Sir, and shall be obliged to you to inform me how -many constellations the earth pastes over in every revolution? - -TUTOR. Twelve, which correspond with the months of the year, and are -called the twelve signs of the zodiac. - -PUPIL. What is the zodiac? - -TUTOR. That part of the heavens which contains the twelve signs, and -which you may conceive to be a zone or belt extending eight degrees on -each side the ecliptic, in which the planets constantly revolve: so that -no planet is ever seen more than eight degrees either north or south, -that is above or below the ecliptic. - -PUPIL. What am I to understand by a degree? - -TUTOR. All circles, whether great or small, are supposed to be divided -into 360 equal parts, called degrees, and each degree into 60 equal -parts, called minutes: therefore, if I speak of a circle in the heavens, -the circumference of the earth, or any other circle, by a degree is -meant the 360th part of that circle; and a minute the 60th part of a -degree. - -PUPIL. What are the names of the twelve signs? - -TUTOR. The first is called Aries, which you know signifies a Ram; -Taurus, the Bull; Gemini, the Twins; Cancer, the Crab; Leo, the Lion; -Virgo, the Virgin; Libra, the Balance; Scorpio, the Scorpion; -Sagittarius, the Archer; Capricorn, the Goat; Aquarius, the -Water-bearer; and Pisces, the Fishes. - -PUPIL. Do you wish me to commit these to memory, Sir? - -TUTOR. It is very requisite; but as I know you are fond of verse, you -shall hear what Doctor Watts says— - - The Ram, the Bull, the heav’nly Twins, - And next the Crab the Lion shines, - The Virgin, and the Scales: - The Scorpion, Archer, and Sea-goat, - The Man that holds the Water-pot, - And Fish with glitt’ring tails. - -PUPIL. I like it much, as it will assist my memory. - -TUTOR. As the twelve signs correspond with the months of the year, the -earth must pass over nearly one degree every day, one sign every month, -and in twelve months complete a whole circle, or 360 degrees; therefore -every sign must contain 30 degrees, because 30 multiplied by 12 is equal -to 360. - -PUPIL. It must be so. - -TUTOR. You must remember, that when the earth is in any sign, as seen -from the sun, the sun will be in the opposite sign, as seen from the -earth: for instance, if the earth be in Aries, the sun will be in Libra; -if in Taurus, the sun will be in Scorpio, &c. therefore, as by the -earth’s annual motion, the sun _appears_ to move, we always speak of the -sun’s, not the earth’s place, in the ecliptic.—You do not seem to -understand me? - -PUPIL. Not perfectly, Sir. - -TUTOR. Take this orange, and put it in the middle of the round table -before us, and place an apple on the opposite side next the window: the -orange may represent the sun, the apple the earth, and the window the -sign Aries. Now go round the table to the apple; look at the orange, and -tell me to what part of the room the eye will be directed. - -PUPIL. To the part opposite to the window, Sir. - -TUTOR. If then you suppose the door, which is opposite to the window, to -be the sign Libra, the sun will be in Libra when the earth is in -Aries—will it not? - -PUPIL. It is very plain. - -TUTOR. I shall now give you a table of the signs, their characters, the -corresponding months, and the days of the month the sun enters each -sign, by means of which, if you reckon a degree for a day, you may find -the sun’s place, nearly, for any day in the year. - -PUPIL. This will give me much pleasure, and I shall be happy to have it. - - THE TABLE. - - NORTHERN SIGNS. - - Aries, Taurus, Gemini, Cancer, Leo, Virgo. - ♈ ♉ ♊ ♋ ♌ ♍ - March, April, May, June, July, Aug. - 20, 20, 21, 21, 23, 23. - - SOUTHERN SIGNS. - - Libra, Scorpio, Sagittarius, Capricorn, Aqua. Pisces. - ♎ ♏ ♐ ♑ ♒ ♓ - Sept. October, November, Decem. Jan. Feb. - 23, 23, 21, 21, 20, 18. - -PUPIL. Why do you write northern and southern signs, Sir? - -TUTOR. Because they are situated north and south of a circle in the -heavens, called the equinoctial, which circle crosses the ecliptic in -the points Aries and Libra, and extends 23-1/2 degrees on each side of -it; and which I shall have occasion to mention to you another time. - -PUPIL. When you think proper, Sir, I shall be glad to have it explained -to me. - -TUTOR. Look at your table, and tell me what sign and what degree the sun -is in the 30th of March, and 20th of October. - -PUPIL. The sun enters Aries the 20th of March, of course he must be 10 -degrees in that sign the 30th; and, as he does not enter Scorpio till -the 23d of October, he must want three degrees of completing the sign -Libra; he must therefore, on the 20th of October, be in 27 degrees of -Libra. - -TUTOR. Very well.—Do you learn the table, as you will have a farther use -for it. - ------------------------------------------------------------------------- - - - - - DIALOGUE VI. - - - PUPIL. - -Since I was last with you, Sir, I have been thinking of what you then -told me, that the planets perform their revolutions in open space: I -have not the least idea how this can be; if convenient, I shall be happy -to have it explained. - -TUTOR. It will be necessary first to inform you, that the orbits or -paths described by the revolution of the planets round the sun, are not -true circles (as Plate II. fig. 2.) but somewhat elliptical, that is, -longer one way than the other, as fig. 3. - -PUPIL. This is exceedingly plain. - -TUTOR. In a circle, the periphery or circumference is equally distant -from a point within called its center, as A; but an ellipsis has two -points called the focuses or foci, as B C. In one of these, called its -lower focus, is the sun: so that you see in every revolution of the -planet it must be nearer to the sun in one part of its orbit, than it is -in another. - -PUPIL. I see it clearly. - -TUTOR. Now let S (Plate II. fig. 4.) represent the sun, A B C D a planet -in different parts of its orbit; when it is nearest to the sun, as at A -it is said to be in its _perihelion_; when at B its _aphelion_; but when -at C or D its middle or mean distance, because the distance S C or S D -is the middle between A S the least and B S the greatest distance; and -half the distance between the two focuses is called the _eccentricity_ -of its orbit, as S E or E F. - -PUPIL. This I will endeavour to understand; but I find it will take me -some time to be perfected in it. - -TUTOR. You may study it at your leisure, as it will not prevent our -proceeding to the thing proposed, namely, the laws which govern the -motion of the planets, or ATTRACTION OF GRAVITATION. - -PUPIL. By attraction I think you mean that property in bodies whereby -they have a tendency to approach each other. I remember you told me that -the magnet I had the other day attracted the needle. - -TUTOR. Yes. And you may recollect that when I took a feather suspended -by a thread, and put it near the conductor of the electrical machine, it -was strongly attracted by it, and adhered to it as long as the machine -was kept in motion. - -PUPIL. I remember it well. But what am I to understand by attraction of -gravitation? - -TUTOR. The sun, being the largest body, _attracts_ the earth and all the -other planets, they _gravitate_ or have a tendency to approach the sun; -the earth being larger than the moon _attracts_ her, and she -_gravitates_ towards the earth; the planets are attracted by and -gravitate towards each other; a stone when thrown from the earth, by its -attraction and the gravitating power or weight of the stone, is brought -to the earth again; the waters in the ocean gravitate towards the center -of the earth; and it is by this power we stand on all parts of the earth -with our feet pointing to the center. - -PUPIL. This information affords me great pleasure. - -TUTOR. Having mentioned attraction of magnetism, electricity, and -gravitation, it may not be amiss to inform you of another kind, called -_attraction of cohesion_. - -PUPIL. Any thing which tends to my improvement, I shall be obliged to -you to communicate. - -TUTOR. By attraction of cohesion is meant that property in bodies which -connects or firmly unites the different particles of matter of which the -body is composed. - -PUPIL. Pray, Sir, inform me what you mean by the _laws_ of attraction? - -TUTOR. You are to understand, 1st. That _attraction decreases as the -squares of the distances between the centers of the attracting bodies -increase_. - -PUPIL. I must beg you, Sir, to explain to me the meaning of the squares -of the distances. - -TUTOR. Any number multiplied into itself is a square number, thus 1 is -the square of 1; 4 is the square of 2; 9 is the square of 3, and so on, -because 1 multiplied into itself is 1; 2 by 2 is 4; 3 by 3 is 9, &c. Now -suppose, that when the planet is at B (Plate II. fig. 4.) it is twice as -far from the sun as it is at A: how much more will it be attracted by -the sun at A than at B? - -PUPIL. You say, Sir, that the distance is twice as great at B as at A? - -TUTOR. I do. - -PUPIL. Then as the square of the distance 2 is 4, the decrease of -attraction at B, the planet at A will be attracted with four times the -force it would be at B.—Am I right, Sir? - -TUTOR. Perfectly so. And if the distance at B were three times as great -as at A, it would be attracted with a force nine times as great. - -PUPIL. I perceive it must be so. - -TUTOR. I shall now give you the 2d law, namely, That _bodies attract one -another with forces proportionable to the quantities of matter they -contain_. - -PUPIL. Do all bodies of the same magnitude contain equal quantities of -matter? - -TUTOR. No, certainly: For a ball of cork may be as large as one of lead, -and yet not contain the same quantity of matter, because it is more -porous, and not so compact or dense a body as the lead; neither will a -ball of lead of the same magnitude as one of gold contain an equal -quantity of matter.—So the sun, though a million of times as big as the -earth, contains a quantity of matter only 200,000 as great, therefore -attracts the earth with a force 200,000 as great as the earth attracts -him. - -PUPIL. I think this is clear. - -TUTOR. We will now suppose that in the river are two boats of equal -bulk, at the distance of twenty yards from each other, and that a man in -one boat pulls a rope which is fastened to the other, what effect will -be produced, or where do you think the boats will meet? - -PUPIL. Had you not told me that bodies attract one another with forces -which are proportioned to the quantities of matter they contain, I -should say the boat to which the rope is fastened would come to that in -which the man stands: but as I imagine you mean to apply this to -attraction, by the above rule, they will meet at a point which is half -way between them. - -TUTOR. If one boat were three times the bulk of the other, how then? - -PUPIL. The lightest would move three times as far as the heaviest, or 15 -yards whilst the heaviest moved only 5. - -TUTOR. Upon my word you reason philosophically. In both cases you are -perfectly right. - -PUPIL. As the sun is so immense a body that his quantity of matter is so -much greater than the planets, I am at a loss to know why they are not -by the power of attraction drawn to him. - -TUTOR. And so they would if the attractive power were not counteracted -by another of equal force. - -PUPIL. Did you not say, Sir, that the planets are kept in their orbits -by attraction? - -TUTOR. I did. But you find that by attraction _only_ the sun would draw -all the planets to himself. - -PUPIL. That is evident. But I wish to know what this counteracting power -you speak of is? - -TUTOR. I will tell you presently.—You must remember that _simple_ motion -is naturally rectilineal, that is, all bodies, if there were nothing to -prevent them, would move in strait lines. - -PUPIL. Then as the planetary motion is circular, it cannot be simple? - -TUTOR. No. It is a _compound_ of the two forces I have been mentioning: -the one is called the attractive or centripetal force; the other, the -projectile or centrifugal force. - -PUPIL. The former I clearly comprehend, but not the latter. I can -conceive, that if two bodies approach each other by attraction they must -move in a right line. - -TUTOR. If you shoot a marble on a smooth piece of ice, in what direction -will it run? - -PUPIL. Strait forward. - -TUTOR. This is a projectile force.—Could you, do you think, shoot it in -any other direction? - -PUPIL. No, Sir. - -TUTOR. Then is not this motion also rectilineal? - -PUPIL. It is. - -TUTOR. When you strike a ball with your cricket-bat, or throw a stone -with your hand, is it not projected or thrown forward by the force of -the bat or hand? - -PUPIL. Certainly. - -TUTOR. And does it not move in a strait line? - -PUPIL. At first it appears to do so; but afterwards it inclines towards -and falls to the earth. - -TUTOR. Cannot you account for this? - -PUPIL. I suppose it must be drawn to the earth by attraction. - -TUTOR. You are right. The attraction of the earth, and the resistance of -the atmosphere or air through which it moves, retards its progress, or -it would continue moving in a strait line, with a velocity equal to that -which was at first impressed upon it. In like manner the beneficent -Creator of the Universe impressed a force on all the planets which -should be equal to that of the attractive power of the sun, that one -might not overcome the other. - -PUPIL. This wants explaining. - -TUTOR. I would willingly gratify you, but as I have much more to say on -the subject, I fear it will be too great a burthen on your memory; it -will therefore be better to postpone it. - -PUPIL. As you please, Sir. - ------------------------------------------------------------------------- - - - - - DIALOGUE VII. - - - TUTOR. - -Having at our last meeting explained to you the nature of the attractive -and projectile forces, I shall proceed to shew you that it is by the -joint action or combination of these two forces that the planets are -retained in their orbits. - -PUPIL. I am all anxiety, as I wish to be informed how, or in what manner -they can act against each other, to produce that effect. - -TUTOR. Answer me a few questions, and you will soon know. - -PUPIL. As many as you please, Sir. - -TUTOR. If you whirl a stone in a sling, what will be its motion? - -PUPIL. Circular. - -TUTOR. Is you let it suddenly slip out of the sling, will it continue -its circular motion? - -PUPIL. No, Sir, but fly off in a strait line. - -TUTOR. This line you must remember is what mathematicians call the -tangent of a circle, as A _a_, B _b_, &c. (Plate II. fig. 5.) for all -bodies moving in a circle have a natural tendency to fly off in that -direction. Thus a body at A will tend towards _a_; at B towards _b_, and -so on; but the central force acting against it preserves its circular -motion. - -PUPIL. By the central force here you mean the action of the hand, do you -not? - -TUTOR. Yes. For, as soon as the stone is released and that power is -lost, it assumes its natural, that is, its rectilineal motion.—Again. If -you are left at liberty, cannot you run strait forward? - -PUPIL. Yes, Sir. - -TUTOR. Now, suppose one of your companions were to fasten a rope round -your body, and at the extent of it were to stand still and hold it -tight, with a force equal to that with which you run, could you, do you -think, move in a strait line, that is, in a tangent of a circle? - -PUPIL. No, Sir. I must run in a circle. - -TUTOR. Why? - -PUPIL. Because, whilst the rope is extended I am prevented running in -any other direction. - -TUTOR. Just so it is with the planets: the attractive or centripetal -force of the sun being equal to that of the projectile or centrifugal -force of the planets, they are by attraction prevented moving on in a -strait line, and, as it were, drawn towards the sun; and by the -projectile force from being overcome by attraction. They must therefore -revolve in circular orbits. - -PUPIL. What I have so long wished is now accomplished. I understand it -perfectly. - -TUTOR. What I have now explained relates not only to the primary planets -which have the sun for their center of motion; but, you must remember -that the secondary planets are governed by the same laws, in revolving -about their respective primaries; for, as by the attractive power of the -sun combined with the projectile force of the primary planets they are -retained in their orbits; so also the action of the primaries upon their -respective secondaries together with their projectile force, will -preserve them in their orbits. - -PUPIL. Pray, Sir, what have you else to observe? - -TUTOR. Have I not told you that the orbits of the planets are not true -circles, but a little elliptical? - -PUPIL. Yes, Sir; and I shall be glad to know the reason of it. - -TUTOR. If the attractive power of the sun were uniformly the same in -every part of their orbits they would be true circles, and the planets -would pass over _equal_ portions of their orbits in _equal_ times; that -is, they would move from B to C, (Plate II. fig. 5.) in the same time as -from A to B, &c. - -PUPIL. That is clear, but as their orbits are elliptical, when the -planets are farthest from the sun, the velocity with which they move -must be lessened as the attraction is decreased. - -TUTOR. And they must consequently pass over _unequal_ parts of their -orbits in _equal_ portions of time. And, as _a double velocity will -balance a quadruple or fourfold power of gravity or attraction_, it -follows, that as the centripetal force is four times as great at A as at -B (Plate II. fig. 4.) the centrifugal force will be twice as great, and -would carry a planet from A to _a_ in the same time it would from B to -_b_, and in its orbit from A to _c_ as soon as from B to _d_, and -thereby describe the area, or space contained between the letters A S -_c_, in the same time as the area or space B S _d_. For according to the -laws of the planetary motions, in their periodical revolutions, _they -always describe equal areas in equal times_. - -PUPIL. The orbits of the comets being very elliptical, the irregularity -of their motions must be exceedingly great. - -TUTOR. Great, indeed!—One of them passed so near the sun as to acquire a -heat which Sir Isaac Newton computed to be two thousand times hotter -than red hot iron.[12] - - [Footnote 12: Dr. Herschel is of opinion, that bodies near the sun - do not acquire so great a degree of heat as has been generally - imagined.] - -PUPIL. Astonishing! If they pass so near the sun, the centripetal force -must act powerfully on the body of the comet. - -TUTOR. And that force, you know, must be equalled by the projectile -force; so you find they move when near the sun with amazing -celerity.—But when arrived at their aphelion, where the influence of the -sun is weak, what a transition! - -PUPIL. Wonderful, indeed!—Their motion is excessively slow, and the sun -must appear little more than a fixed star. Surely they cannot be -inhabited, can they? - -TUTOR. We cannot speak positively; but, as they differ so much from the -planets, which we have reason to suppose are so, it is imagined they are -designed for some purpose unknown to us. - -PUPIL. When is the earth in its perihelion? - -TUTOR. In December; and our summer half year is longer than the winter -half, by about eight days. - -PUPIL. I suppose this is occasioned by the inequality of the earth’s -annual motion. - -TUTOR. It is; and this inequality is the cause of the difference of time -between the sun and a well regulated clock; the latter keeps equal time, -whilst the former is constantly varying. - -PUPIL. I have often seen in the almanack clock fast, clock slow, but did -not know the meaning of it: I imagine it is that the clock should be so -much faster or slower than the time by the sun as is there mentioned. - -TUTOR. It is: but there are tables calculated to shew the difference of -time for every day in the year; so that if you know the exact times of -the day by the sun, and have one of these tables, you will see what the -time should be by the clock, to a second, which is not shewn in a common -almanack. - -PUPIL. In speaking of the annual or yearly motion of the earth, you have -no where mentioned the cause of the seasons; will it be agreeable to do -it now, Sir? - -TUTOR. The vicissitudes of the seasons, the cause of day and night, &c. -shall be the subject of future lessons: we shall find sufficient to -employ us at present. - -PUPIL. I think you told me just now that the earth is nearest the sun in -December; that is our winter; this seems a little mysterious. - -TUTOR. It may appear so to you now, by-and-by you will be of a different -opinion. I shall explain this matter to you with that of the seasons, -&c. - -PUPIL. I fear I have interrupted you.—As you said you had sufficient -employment for us, I shall be glad to know what it is. - -TUTOR. Hitherto I have spoken of the sun’s being fixed, and that the -planets revolve about him as a center. Instead of which the sun and -planets move round one common center, called the center of gravity. - -PUPIL. What is this center of gravity? - -TUTOR. Have you never seen a person raise a heavy weight by means of a -long pole or leaver, which it was not in his power to lift without it? - -PUPIL. Yes, Sir, and it excited my astonishment. - -TUTOR. Now, suppose the weight to see raised to be 10 Cwt. and the prop -on which the leaver rested 1 foot from the body to be raised; and the -person at the other end of the leaver 10 feet from the prop; with what -weight must he press to raise the 10 Cwt.? - -PUPIL. I think that very easy; for, as he is ten times as far from the -prop as the weight is, a pressure of 1 Cwt. which is one-tenth of the -weight to be raised will do it. - -TUTOR. To be sure; and yet you say you were astonished when you saw it! -Every thing we do not understand at first appears difficult.—To apply -this to our present purpose. You see that a weight of 1 Cwt. at 10 feet -from a prop, will balance another of 10 Cwt. at one foot from it. Now, -instead of a prop let the two weights be nicely poised on a center, -round which they may freely turn; the heaviest would move in a circle, -whose radius, or distance from the center would be one foot, whilst the -lightest would move in one 10 feet from the center in the same time. - -PUPIL. Is the center round which they move the center of gravity? - -TUTOR. It is; and round an imaginary point as a center the sun and -planets move, always preserving an equilibrium. If the earth were the -only attendant on the sun, as his quantity of matter is 200,000 times as -great as that of the earth, he would revolve in a circle a 200,000th -part of the earth’s distance from him, in the same time as the earth is -making one revolution in its orbit, or in one year; but, as the planets -in their orbits must vary in their positions, the center of gravity -cannot be always at the same distance from the sun. - -PUPIL. If it were, the balance could not be preserved. - -TUTOR. Clearly so. But you must know that the quantity of matter in the -sun so far exceeds that of all the planets together, that even if they -were all in a line on one side of him he would never be more than his -own diameter distant from his center of gravity; therefore, astronomers -consider the sun as the center of the system, and express themselves -accordingly. - -PUPIL. As you told me the secondary planets are governed by the same -laws as the primaries, I imagine they also with their primaries move -round a center of gravity. - -TUTOR. They do so.—The earth and moon, Jupiter with his satellites, -Saturn and his attendants, revolve about their respective centers; -these, with the sun and the rest of the planetary system, make their -circuits round their center; every system in the universe is supposed to -revolve in like manner; and all these together to move round one _common -center_.—How are we lost in contemplating the omniscience of the Deity! -How difficult to conceive so many millions of bodies of dead matter -constantly in motion, so nicely balanced and governed by such unerring -laws!—Well may we say with the Psalmist, “Lord! how manifold are thy -works, in wisdom hast thou made them all.” - ------------------------------------------------------------------------- - - - - - DIALOGUE VIII. - - - TUTOR. - -I shall now, agreeably to my promise, explain to you the cause of day -and night, and then proceed with the vicissitudes of the seasons. - -PUPIL. That is what I much wish to know; and had you not told me that -the earth moved round the sun every year, I should have found no -difficulty in accounting for the succession of day and night, since the -sun appears to rise and set every day. - -TUTOR. That is true; but I think I must have convinced you that so -immense a body as the sun cannot revolve about the earth; as well may -you suppose that in roasting a bird it is necessary that the fire should -move round it. - -PUPIL. That I think would be very absurd, as it is much easier for the -bird on the spit to turn to the fire, than for the fire to go round the -bird. - -TUTOR. You are certainly right, and if the earth revolve on its axis -every twenty-four hours, will not the different parts of it be -alternately turned to the sun, as the bird on the spit is to the fire? - -PUPIL. I do not clearly comprehend what you mean by the axis of the -earth; for, as it moves in open space and has no support, it can have -nothing to resemble the spit on which it turns. - -TUTOR. Certainly not. By the earth’s axis is meant an imaginary line -passing through its center, on which it is supposed to turn; as your -ball if rolled on the ground would revolve on an axis whilst it was -moving forward. - -PUPIL. I can now answer your question in the affirmative: and, as our -year consists of 365 days, I imagine the earth must make as many -revolutions on its axis whilst it is going once round the sun. - -TUTOR. Undoubtedly: and as only one half of a spherical body can at any -time be enlightened by a luminous body, that part of the earth only -which is turned to the sun, can receive the benefit of his enlivening -rays, when it will be day; whilst the opposite part will be involved in -darkness, and it will be night. - -PUPIL. I perceive it must be so. But, if the earth move in the manner -you describe, I cannot conceive how it is that we are not sensible of -its motion. - -TUTOR. If the motion of the earth were irregular it would be -perceptible; but as it meets with no obstruction the motion must be so -uniform as not to be perceived. - -PUPIL. Had I recollected this, I need not have given you this -trouble.—But I am continually meeting with fresh difficulties. - -TUTOR. You have only to mention what they are, and I shall take a -pleasure in removing them. - -PUPIL. I thank you, Sir; and shall be obliged to you to inform me, how -the motion of the earth can cause the sun to appear to move? - -TUTOR. When in a carriage which went smoothly on the road, or in a boat -whose motion was scarcely perceptible on the water, did you never fix -your attention on the objects you passed? - -PUPIL. Yes, often, Sir. - -TUTOR. And had you not known that you really moved, and that the trees, -&c. were immoveable in the ground, what then would have been your -opinion? - -PUPIL. That the trees, &c. moved in a direction contrary to that in -which I was moving. - -TUTOR. Is not this sufficient to convince you that the apparent motion -of the sun may be occasioned by the revolution of the earth on its axis? - -PUPIL. It is:—But if so large a body as the earth make a revolution on -its axis in 24 hours, it must move with great velocity. - -TUTOR. It does so; and the inhabitants of London by this motion are -carried at the rate of 560 miles an hour[13]. - - [Footnote 13: The hourly motion under the equator is 900 miles.] - -PUPIL. What an astonishing rapidity! - -TUTOR. Now, the sun with the rest of the heavenly bodies must move round -the earth, or the earth must revolve on its axis in 24 hours, to cause -that appearance. - -PUPIL. That is plain. - -TUTOR. Well then, great as you may suppose the velocity of the earth on -its axis to be, if the sun move round the earth his hourly motion will -be nearly 25 millions of miles; and beyond conception would be that of -the fixed stars. Which now do you think is most probable, that the sun -and stars should move round the earth, or that they, by the simple -motion of the earth, should appear to be in motion? - -PUPIL. The latter, to be sure, Sir.—I have one difficulty remaining, -which is this; if a lark rise from a field near London and remain in the -air a quarter of an hour, if the earth move at the rate of 560 miles an -hour, it will go 140 miles whilst the lark is suspended, and yet it -continues over the field,—how can this be? - -TUTOR. This objection to the motion of the earth has been made by those -who were older and who thought themselves wiser too than yourself. They -either did not know or did not consider, that the atmosphere which -surrounds the earth is a part of itself, and gravitates towards it, and -therefore partakes of the earth’s motion and carries the lark along with -it. Besides, as the Sun, Venus, Mars, and Jupiter are known to revolve -on their axes, we have reason to suppose that the other planets, -together with the earth, must have the same motion[14]. - - [Footnote 14: Dr. Herschell says that several of the fixed stars - revolve on their axes.] - -PUPIL. How is it known that they do revolve on their axes; and in what -time do they perform their revolutions? - -TUTOR. By the assistance of telescopes dark spots have been seen on the -disc of the sun, by the motion of which it is found that he revolves on -his axis in 25-1/4 days; Venus performs her diurnal revolution in about -23 ho. 21 min.; Mars goes round his axis in 24 ho. 39 min.; and Jupiter -in 9 ho. 56 min.; as to the rest, no spot or any fixed point has been -discovered to ascertain the length of their day; Mercury being too near -the sun, and Saturn and the Georgium Sidus too remote for our -observations. - -PUPIL. I can no longer doubt of the earth’s motion: and, if it will not -be improper, a description of the atmosphere will give me pleasure. - -TUTOR. That I can have no objection to. The atmosphere is a thin, -invisible fluid, most dense or heavy near the earth, but grows gradually -rarer or lighter the higher we ascend, so much so, that at the tops of -some high mountains it is difficult to breathe. It serves not only to -suspend the clouds, furnish us with wind and rain, and answer the common -purposes of breathing, but is also the cause of the morning and evening -twilight, and of all the glory and brightness of the firmament. - -PUPIL. How, pray? - -TUTOR. If there were no atmosphere, the sun would yield no light but -when our eyes were directed towards him; and the heavens would appear -dark and as full of stars as on a dark winter’s night; but the -atmosphere being strongly illuminated by the sun, reflects the light -back upon us, and makes the whole heavens to shine so strongly, that the -faint light of the stars is obscured, and they are rendered invisible. - -PUPIL. I find then the atmosphere is of more use than I imagined. But -how is it the cause of the twilight? - -TUTOR. The atmosphere is about 45 miles above the surface of the earth, -therefore the sun’s rays falling upon the higher parts of it before -rising, by reflection causes a faint light, which increases till he -appears above the horizon; and in the evening it decreases after he -sets, till he is 18 degrees below the horizon, where the morning -twilight begins, and the evening twilight ends. - -PUPIL. By the horizon, I think you mean that distant boundary of our -sight where the heavens and the earth seem to join all around us, as it -appears from an eminence. - -TUTOR. The very same. ’Tis that imaginary circle which intercepts from -our view the sun, moon, and stars each night; and when, by the rotation -of the earth, they appear to descend below it, we say they are set; as -on the contrary, each morning, when they appear above it, we say they -rise. - - “To find the spacious line, cast round thine eyes, - “And where the earth’s high surface joins the skies, - “Where stars first set, and first begin to shine, - “There draw the fancy’d image of this line.” - -PUPIL. A very pleasing description, indeed. - -TUTOR. You will remember that this is called the _rational horizon_; but -that which respects land and water is called the _sensible horizon_. The -former divides the heavens into two equal parts, and is 90 degrees -distant from a point directly over our heads, called the _zenith_, and -the opposite point of the heavens directly under our feet, called the -_nadir_.—But I must resume the subject of the atmosphere. - -PUPIL. Had I not thought you had finished your description of the -atmosphere, I should not have presumed to interrupt you. - -TUTOR. What I have told you respecting the horizon is necessary for you -to be acquainted with; therefore, the suspension is immaterial.—You -must, I make no doubt, have observed the sun and moon at rising and -setting to appear larger than when higher above the horizon. - -PUPIL. I have, frequently, Sir. - -TUTOR. And cannot you tell the reason of it? - -PUPIL. No, Sir. - -TUTOR. The reason is this: In viewing them, when near the horizon, you -see them through a thicker medium than when they are higher, that is, -you see them through a greater quantity of the atmosphere; and you not -only see them larger, but really above the horizon whilst they are -actually below it. - -PUPIL. How do you account for this, Sir? - -TUTOR. Light, like material bodies, if it meet with no obstruction, will -move in right lines; now, the rays of the sun in coming to the earth -must pass through a great quantity of the atmosphere, which being a -fluid, refracts or bends the rays of light, by which refraction it is -that we are favoured with the sight of the sun 3-1/4 minutes every -morning before he rises above the horizon, and every evening after he -sinks below it, which in one year amounts to more than 40 hours. This -refraction is greatest near the horizon, and ends in the zenith. - -PUPIL. Pray, Sir, can you make this clearer by an experiment? - -TUTOR. I have just thought of one. Take a bason filled with water, and a -strait stick or piece of wire; put it perpendicularly into the water, -that is, that it lean neither way, and there will be no refraction; -incline it a little towards the edge of the bason and it will appear a -little bent at the surface of the water; incline it still more, and the -refraction will be greater. - -PUPIL. I have often seen this appearance when I have put my stick into -water, but did not before know the cause. - -TUTOR. You may try one more experiment. Pour the water out of the bason, -and set the bason on the floor; put a guinea into it, and let it -represent the sun.—Why do you smile? - -PUPIL. Because I have not the sun’s representative to try the experiment -with. - -TUTOR. Well, well, put a shilling into the bason and call it the moon, -and it will answer the same purpose:—Walk backward till you just lose -sight of it, then the right line from your eye continued over the edge -of the bason must pass beyond the money at the bottom of it. - -PUPIL. That is evident. - -TUTOR. Keep your position, and desire some friend to pour the water -gently into the bason so as not to remove the money, and you will -clearly distinguish it. Now, if you call the edge of the bason the -horizon, the water the atmosphere, and the shilling the moon, is it not -clear that you will see it above the horizon, when it is really below -it? - -PUPIL. I think so, Sir. - -TUTOR. Well, try the experiment, and let me know the result when I next -see you. - ------------------------------------------------------------------------- - - - - - DIALOGUE IX. - - - TUTOR. - -I presume, Sir, you have made the experiment I recommended to you. - -PUPIL. I have, Sir; and am so well convinced of what you told me, that -nothing farther need be said on the subject. - -TUTOR. As that is the case, I shall proceed.—I dare say you do not -forget what the plane of the ecliptic is. - -PUPIL. I do not, Sir; but have a perfect recollection of it. - -TUTOR. Now, remember, that the axis of the earth is not upright or -perpendicular to the plane of the ecliptic, but inclines to, or leans -towards it, 23-1/2 degrees, and makes an angle with it of 66-1/2 -degrees. - -PUPIL. An angle signifies a corner; but that cannot be the meaning here. - -TUTOR. That is what is generally understood by an angle: but, in -geometry, it means the meeting of any two lines which incline to one -another, in a certain point. Now, if you conceive the axis of the earth -to be one line, and the plane of the ecliptic the other, the point where -they meet or cross each other will form an angle. - -PUPIL. I think I understand it; but how can it contain 23-1/2 or 66-1/2 -degrees? - -TUTOR. You know what a degree is. - -PUPIL. If I remember right it is the 360th part of a circle. - -TUTOR. It is so: and the measure of an angle is an arc or part of the -circumference of a circle, whose angular point is the center: and so -many 360th parts as any arc contains, so many degrees the measure of the -angle is said to be; thus, Z C P (Plate III. fig. 1.) makes an angle of -23-1/2 degrees, because the arc Z P contains 23-1/2 360th parts of the -whole circle. Then if A B represent the plane of the ecliptic, and N C S -the axis of the earth, as D N contains the same number of degrees as Z -P, will not its inclination from a perpendicular be 23-1/2 degrees? - - [Illustration: _Plate III._ - - _T. Conder Sculp^t._] - -PUPIL. Nothing can be plainer. - -TUTOR. For the same reason, as P B contains 66-1/2 parts of the whole -circle, the axis of the earth makes an angle of 66-1/2 degrees with the -plane of the ecliptic. And, if you add 23-1/2 to 66-1/2 the sum will be -90, which is the measure Z B, or the fourth part of the circle, and -makes what is called a right angle, at the point or center C. - -PUPIL. It is very clear:—but what do the other letters refer to? - -TUTOR. The extremities of the earth’s axis are called the poles, N the -north, and S the south pole, and P the north-pole star, to which, and to -the opposite part of the heavens, the axis always points. These -extremities in the heavens appear motionless, whilst all other parts -seem in a continual state of revolution: the circle of motion appears to -increase with the distance from the apparently motionless points to that -circle in the heavens which is at an equal distance between them, called -the equinoctial, represented by the letters Æ Q; and is the same I -promised some time ago to explain to you. - -PUPIL. I recollect it: and as the line A B represents the plane of the -ecliptic, I suppose the line Æ Q is the plane of the equinoctial, which -I see crosses it as you then told me. - -TUTOR. You are right: and it makes an angle with it of 23-1/2 degrees. -It is called the equinoctial, because when the sun appears there, that -is, in Aries or Libra, the days and nights are equal in all parts of the -world, which I shall shew you in due time; and shall now explain to you -what I have just mentioned, that the axis of the earth always points to -the same parts of the heavens. I am apprehensive you will think it -strange that this should be the case, and the axis keep parallel to -itself. - -PUPIL. What am I to understand by the axis being parallel to itself? - -TUTOR. Two lines are said to be parallel when they do not incline to but -keep at equal distances from each other; so that if they were infinitely -continued, they would never meet. Now, if you can conceive a line drawn -parallel to the earth’s axis in any part of its orbit, it will be -parallel to it in every other part of it. A little drawing I have by me, -(Plate III. fig 2.) where the earth is represented in four different -parts of its orbit, I think will make this plain to you. - -PUPIL. I comprehend your meaning clearly. But, as the orbit of the earth -is 190 millions of miles in diameter, I have not the least conception -how it can incline to the same points. Had you not told me to the -contrary, I should have thought it must move round them in every -revolution of the earth about the sun. - -TUTOR. That such a motion would be perceptible is evident, if the fixed -stars were near the earth; but, compared with their distance, 190 -millions of miles is but a mere point: therefore, the axis always -inclines to the same points of the heavens. - -PUPIL. This is a greater proof of the inconceivable distance of the -stars than what you mentioned before, and I thought that very -astonishing: - - Wonders on wonders constantly arise, - Whene’er we view the earth, or sea, or skies. - -TUTOR. It is very true. And the more we search, the more we have cause -to admire the works of the Almighty. - -PUPIL. Pray, Sir, what is the next thing you propose? - -TUTOR. To make you acquainted with the other circles you see in the -figure (Plate III. fig. 1.) as it is very necessary you should know -them. - -PUPIL. Will you be kind enough to tell me their names, Sir, and I will -endeavour to remember them? - -TUTOR. That line which divides the globe into two equal parts, called -the northern and southern hemispheres, which answers to the equinoctial -in the heavens, and is equally distant from the two poles, is called the -_equator_; the other which crosses it, as I before told you, is the -_ecliptic_; the smaller circle, north of the equator, is the _tropic of -Cancer_; that south of it, the _tropic of Capricorn_; the circles next -the poles are called the _polar circles_; or that next the north pole, -the _arctic circle_, and that next the south pole, the _antarctic -circle_; each of which is 23-1/2 degrees distant from its respective -pole, as are the tropics from the equator. - -PUPIL. You have not mentioned the lines which cross the other circles, -and terminate in the poles; what are they called? - -TUTOR. They are called _meridians_, because when any of them, as the -earth revolves on its axis, is opposite to the sun, it is mid-day or -noon along that line. Twenty-four of these lines are usually drawn on -the globe to correspond with the twenty-four hours of the day; but you -are not to suppose there are no more than twenty-four; for every place -that lies ever so little east or west of another place has a different -meridian.—To make this clearer to you, we will suppose the upper 12 -(Plate III. fig. 1.) to be opposite the sun, it will of course be noon -along that line; the next meridian marked 1, being 15 degrees east, will -have passed the meridian 1 hour, consequently it will there be one in -the afternoon, and so on, according to the order of the figures, till -you come to the lower 12, which being the part of the earth turned -directly from the sun, it will be midnight on that meridian; on the next -meridian, as you proceed round, it will be one in the morning, the next -two, and so on till you arrive at the upper twelve, where you set off. -So you see there must be a continual succession of day and night. This -difference of time between places lying under different meridians is -what is called longitude. - -PUPIL. I think I have heard of a Mr. Harrison, who made a time-keeper -for determining the longitude. Shall I trespass at all if I beg a little -farther information on this subject? - -TUTOR. It is my wish at all times to satisfy your curiosity, when I can -do it with propriety. I shall therefore comply with your request.—Mr. -Harrison’s time-keeper, and those made since by other artists, are so -constructed, that the heat and cold of different climates will not -affect them; for, all metals are more or less expanded by heat, and -contracted by cold; for which reason it is, that a clock or watch made -in the usual way will not keep equal time. Now, all that is required of -these time-keepers to ascertain the longitude is this: Suppose a captain -of a vessel sailing from London to the West Indies, we will say -Kingston, in Jamaica. On his passage thither he makes an observation, -and finds the sun on the meridian, or that it is twelve o’clock in that -situation, when by his time-keeper it is two in the afternoon in London, -whence he concludes he is 30 degrees west of London. - -PUPIL. I must beg you to explain this to me, as I do not understand why -two hours of time should be equal to 30 degrees of longitude. - -TUTOR. You must consider, that as the earth makes a complete revolution -on its axis in 24 hours, it must pass over 360 degrees in that time: -now, if you divide 360 by 24, the quotient 15, will be the number of -degrees passed over in one hour; 30 degrees will be equal to two hours, -&c. The difference of time between London and his situation is two -hours, consequently the difference of longitude must be 30 degrees: and, -it must be west, because the sun had passed the meridian of London; for, -as the earth revolves from west by south to east, one place which lies -east of another must come first to the meridian or opposite to the sun. -Therefore, when longitude is reckoned from London, if the place lie east -of that meridian the time will be before; if west, after London. - -PUPIL. I see it clearly; and as 60 minutes make an hour, if I divide it -by 15, the quotient 4 will be the minutes answering to one degree. - -TUTOR. You are right: and for the same reason, 4 seconds of time are -equal to one minute of longitude, which you know is the 60th part of a -degree.—Our captain when arrived at Kingston, finds the difference of -time between it and London 5 ho. 6 min. 32 sec. Can you tell me the -longitude of Kingston? - -PUPIL. If I bring the hours and minutes to minutes, and divide by 4, the -quotient I think will be degrees, will it not? - -TUTOR. It will: and the seconds of time divided by 4, will be minutes of -longitude. Now try if you can do it. - -PUPIL. Five hours 6 minutes, multiplied by 60 will be 306 minutes, this -divided by 4, will give 76 degrees and 2 over, which 2 is half a degree, -or 30 minutes: and 32 seconds of time divided by 4, will be 8 minutes of -longitude, the sum of which is 76 degrees 38 minutes for the longitude -of Kingston. - -TUTOR. Very well.—I have just now thought of another method of reducing -time to longitude, and longitude to time, which you may probably find -easier. However, when you are in possession of both, you may use which -you please. - -PUPIL. That which is easiest must, I think, be best. - -TUTOR. I will give it you, and let me have your opinion of it. - - To reduce time to longitude. - - Multiply the hours, minutes, and seconds of time by 15, or - rather by the factors as they are called, namely 3 and 5, - carrying one for every 60 in the minutes and seconds, and - setting down the remainder, thus: - - ho. min. sec. - 5 6 32 difference of - 3 time. - ──────────────── - 15 19 36 - 5 - ──────────────── - Degrees 76 38 0 longitude. - ════════════════ - - Divide the degrees and minutes of longitude by 5 and 3 and the - quotient will be the difference of time. - -PUPIL. I give this the preference. - -TUTOR. As longitude is seldom mentioned without being accompanied with -latitude, that you may not be ignorant of its meaning when you meet with -it, I shall just tell you that it is the distance of any place from the -equator, reckoned in degrees and minutes on the meridian, and is either -north or south as the place lies north or south of the equator. The -latitude of any place is equal to the elevation of the pole above the -horizon. The latitude of the heavenly bodies is reckoned from the -ecliptic, and terminates in the arctic and antarctic circles: and their -longitude begins at the point Aries. - -PUPIL. What is the measure of a degree? - -TUTOR. A degree of latitude is 60 geographical, or 69-1/2 English miles: -and a degree of longitude on the equator is equal to it, because the -equator as well as the meridians divides the globe into two equal parts. -But a degree of longitude decreases as you approach the poles: for at -the poles the meridians meet in a point, consequently a degree there can -have no dimension. To-morrow I will shew you the cause of the seasons. - ------------------------------------------------------------------------- - - - - - DIALOGUE X. - - - PUPIL. - -I think, Sir, when you left me last night you told me our next business -would be to explain the nature of the seasons? - -TUTOR. I did so, and am persuaded you will find no great difficulty in -comprehending it.—Cast your eye on the little drawing I gave you, (Plate -III. fig. 2.) where the earth is represented as situated at the four -quarters of the year, namely, Spring, Summer, Autumn, and Winter.—But -before we proceed to an explanation it will be necessary to remark, -that, in the little scheme the eye is supposed to be elevated above the -plane of the earth’s orbit, and that we see it very obliquely. The orbit -by this means appears very elliptical; and, the enlightened hemisphere, -or that half of the earth which is turned to the sun in the spring, and -the darkened hemisphere, or that turned from him in the autumn, are -there represented. - -PUPIL. This I understand. - -TUTOR. Well then, we will begin with the spring.—In this situation of -the earth the equator is exactly opposed to the sun: and, as he always -enlightens a hemisphere, or half of its surface, his rays will reach to -both the poles: whence, from the diurnal revolution of the earth, the -day and night are equal all over the globe. - -PUPIL. This I remember you told me happened when the sun was in Aries -and Libra. The sun is now entering Aries: and, as we are in the rays of -the sun one half of the diurnal revolution, and in the shadow of the -earth, or dark, the other half, the day and night must be equal. - -TUTOR. Certainly. And as the sun enters Aries in the equinoctial, it is -then called the _Vernal_, that is, _Spring Equinox_. When the sun enters -the opposite sign Libra, the same effects are produced, and it is then -called the _Autumnal Equinox_. - -PUPIL. You have passed on from Spring to Autumn. - -TUTOR. I have so.—We will now return, and trace the earth in its orbit -from spring to summer.—You have already seen that the north and south -poles are both enlightened, and that the day and night are equal at the -equinoxes. If the axis of the earth were perpendicular to the plane of -the earth’s orbit, this would constantly be the case, and we should have -no diversity of seasons: for, the sun being over the equator, the poles -must be perpetually enlightened, and of course we should have equal day -and night at all times of the year. - -PUPIL. That is plain. I suppose then that it is to the inclination of -the earth’s axis we are indebted for the increase and decrease of days. - -TUTOR. It is occasioned by the inclination of the earth’s axis and its -preserving its parallelism, which I explained to you last evening.—As -the sun is now in the first point of Aries, the earth you know must be -in the beginning of Libra, it being the opposite sign.—Now fix your -attention on the scheme, and imagine the earth to be advancing in its -orbit through Libra, Scorpio, and Sagittarius: and at the first degree -of Capricorn give me your opinion of the earth’s position. - -PUPIL. The north pole is turned to the sun, the south pole from him, and -the tropic of Cancer is opposite to him. - -TUTOR. How many degrees are the tropics from the equator, or, in other -words, what is the inclination of the earth’s axis? - -PUPIL. Twenty-three degrees and a half. - -TUTOR. And so far are the rays of the sun cast beyond the north pole, -and fall short of the south pole: so that the whole of the arctic circle -is enlightened, and the antarctic circle involved in darkness. - -PUPIL. What conclusion am I to draw from this? - -TUTOR. That in the northern half of the globe it is the longest day, or -summer, and in the southern half the shortest, or winter, whilst under -the equator the days and nights are equal. - -PUPIL. I used to think that when it was winter or summer here it was so -in every part of the world. - -TUTOR. You now find your mistake. For as the earth is making its -progress from Libra, the north pole is approaching the sun, and the -south pole receding from him: consequently the length of the day is -increasing in the northern hemisphere and decreasing in the -southern.—The sun has now been three months above the horizon of the -north pole, and the same time below that of the south pole, and in three -months more, when the earth arrives at Aries, the scene will be -reversed: the sun will be over the equator, both poles will be again -enlightened, and the day and night will be equal in every part of the -globe. The sun will now be rising to the south and setting to the north -pole. This is our Autumn. - -PUPIL. And as the earth is advancing towards winter, the south pole will -be turning to the sun, and the north pole from him, whence I conclude -that when the earth is in Cancer it must be summer, south of the -equator, when it is our winter. - -TUTOR. Most assuredly. For you see that the sun is over the tropic of -Capricorn, which you know is as much south of the equator as the tropic -of Cancer is north of it, where the sun was in our summer. The antarctic -circle is now enlightened, and the arctic obscured in shade; but, under -the equator there is neither increase nor decrease, the days and nights -being each twelve hours. - -PUPIL. It is now our winter, the sun has been three months above the -horizon of the south pole, and will continue so till the vernal equinox, -when he will again rise to the north pole, and so on in regular -succession. - -TUTOR. It must be plain then to you that there can be but one day and -one night at each of the poles, reckoning the time the sun is above or -below their respective horizons; under the arctic and antarctic circles, -the longest day is twenty-four hours, and in the shortest the sun is -just visible in the horizon at noon. The longest day decreases in length -the nearer we approach the equator, where I before observed there is no -variation, because the circle bounding light and darkness, in every -position of the earth, divides the equator into two equal parts; and, it -must be observed, that the longest day and longest night are equal to -each other in every part of the globe. - -PUPIL. If the longest day under the arctic circle be just twenty-four -hours, the sun must rise in the north. - -TUTOR. He does so, makes a complete circle and sets in the [15]north -again. From the arctic circle to the equator, he rises north of the east -and sets north of the west: at the equator he rises due east and sets -due west, thence southward to the antarctic circle, he rises south of -the east, and sets south of the west: and under the antarctic circle, as -I observed just now, he is visible in the horizon in the south at noon. - - [Footnote 15: Here it must be observed that there will be a little - variation from sun-rising to sun-setting, as the earth is advancing - in its orbit.] - -PUPIL. We usually say, the sun rises in the east and sets in the west. - -TUTOR. At the equinoxes it must be so in all parts of the globe, the -poles excepted: in every other situation, except under the equator, -there is a continual change. What I have now told you, respecting the -northern hemisphere, will be reversed at our shortest day: that is, in -the northern hemisphere the sun will rise south of the east and set -south of the west; and, in the southern hemisphere the contrary, the sun -will be in the horizon, at noon, under the arctic circle, and the day -will be twenty-four hours under the antarctic circle. - -PUPIL. Pray Sir, are the regions within the polar circles inhabited? If -they are, their situation, in winter, must, I think, be dreadful. - -TUTOR. It is foreign to my present purpose to speak of the inhabitants -of the earth, as that more properly belongs to Geography. Thus much -however I shall tell you, that, although it must be very cold and -dreary, they are not so long deprived of light as you may imagine; for, -even under the poles, when the sun is hidden from them, they are but a -short time in total darkness, for, you must recollect, that the twilight -continues till the sun is eighteen degrees below the horizon; and the -sun’s greatest depression, you know, can be but twenty three degrees and -a half, equal to the inclination of the earth’s axis. Besides this, the -moon is above the horizon of the poles a fortnight together; being half -her period north, and the other half south, of the equator; and, as the -moon at full is in the sign opposite to the sun, the tropical full moons -must be twenty-four hours above the horizon at the polar circles. - -PUPIL. This description is very pleasing, as I had no idea of their -being favoured with so much light in the absence of the sun: and, I -find, as the sun is longer above the horizon in summer than in winter, -the moon, on the contrary, continues longer with us in winter, when we -most need her assistance, than she does in summer. - -TUTOR. As you seem to understand what I have been explaining, I shall -shew you, that the reason why it is hottest when we are farthest from -the sun is, that in winter when we are nearest to him the days are -shorter, his rays sail very obliquely on us, and are more dispersed than -they are in summer, when he not only remains longer above the horizon, -but being higher, his rays fall more direct on us, by which means the -earth becomes so much heated that it has not time in the short nights to -get cold again.—When the earth is nearest the sun it is summer in the -southern hemisphere, therefore it is reasonable to suppose that the heat -there must far exceed ours in the same latitude; but to counteract this -their summer is shorter by eight days than ours: and it is well known -that it is much colder near the poles in the southern than in the -northern hemisphere: but this is accounted for from there being more -land to retain the heat in the latter than in the former. - -PUPIL. My doubts on this head being now removed, I must beg you to give -me such other information as you may think proper. - -TUTOR. As there are different degrees of heat and cold, the earth has -been divided into five zones, namely, one torrid, two temperate, and two -frigid zones. - -PUPIL. How are they distinguished? - -TUTOR. The torrid zone is all that space surrounding the globe contained -between the tropics, having the equator running through the middle of -it. It is so called on account of its excessive heat, for, twice every -year the sun is vertical to the inhabitants, that is, he shines directly -on their heads, and casts no shadow, but under their feet, at noon. - -PUPIL. We find it sometimes extremely hot here in our summer; surely, in -the torrid zone it must be almost insupportable? - -TUTOR. They are inured to it from their infancy.—But we are departing -from our subject.—The temperate zones are comprehended between the -tropics and polar circles, that between the tropic of Cancer and the -arctic circle is called the north temperate zone, and that between the -tropic of Capricorn and the antarctic circle the south temperate zone. - -PUPIL. I suppose they are called temperate because the heat is not so -intense as in the torrid zone? - -TUTOR. True. Neither is the cold so severe as in the frigid zones, which -are those regions comprized within the polar circles, and are -denominated north and south, as they are contiguous to the north or -south poles. - -PUPIL. Why are they called frigid? - -TUTOR. They are called frigid or frozen zones, because near the poles -there are perpetual fields of ice, the heat of the sun, even in summer, -being insufficient to dissolve it.—Now try if you can tell me the -breadth of each zone in degrees. - -PUPIL. The torrid zone being twenty-three degrees and a half on each -side the equator must be forty-seven degrees, which must also be the -breadth of the frigid zones, as the polar circles are distant -twenty-three degrees and a half from the poles, which are their centers. -And, as from the equator to either pole is ninety degrees, from the -equator to the tropics twenty-three and a half, and from the polar -circle to the pole twenty-three and a half, if the sum of these, that -is, forty-seven, be taken from ninety, the remainder, forty-three, will -be the breadth of each of the temperate zones. - -TUTOR. Very well. - -PUPIL. From what you have told me I have no doubt but that the earth is -globular, but I have no proof of it: I must therefore beg your -assistance. - -TUTOR. That it cannot be an extended plane, as some have imagined, is -very evident; for, if it were, the angle made with that plane and the -north pole star would be always equal, for reasons I have before given -you: neither can it be cylindrical, that is like a garden roller, as -others have supposed.—If a person travel northward the pole star becomes -more elevated, and if he could penetrate to the north pole of the earth -the star would be in the zenith, or directly over his head: on the -contrary, if he travel southward, it is more and more depressed till he -arrives at the equator, where the star is in the horizon; as he proceeds -it disappears, and other stars rise to his view, invisible to us. Here -then you see it must be circular northward and southward. - -PUPIL. I am convinced it must be so. - -TUTOR. And it is as certain that it is so east and west: for, navigators -have often sailed round it steering the same course: that is, if they -sail an easterly or westerly course at setting off, by continuing the -same course they will return to the port whence they departed. This you -know they could not do if it were not round, any more than an insect -could, by crossing a round table, arrive at the place it set out from; -but, by going round the edge it would be still going forward and come -again to the point it had left. - -PUPIL. It is very evident. - -TUTOR. Again. In every direction, if a ship be seen at a distance, the -first things observed are the top-mast and rigging, whilst the hull or -body of the ship is hidden behind the convexity, that is roundness of -the water, just as you would see a man coming over a hill, you would -first see his head, he would be rising more and more to your view till -he arrived at the top, where he would be full in sight. - -PUPIL. I am at a loss to account for the convexity of the water. How can -its surface be round? - -TUTOR. Have you never observed the drops of water falling from the eaves -of a house? - -PUPIL. Often, Sir. - -TUTOR. Of what shape were they? - -PUPIL. Globular.—But what is the cause of their being so? - -TUTOR. Attraction.—For as every particle of water which composes the -drop tends to the same center, every part of the surface must be -equidistant from the center, it must therefore be spherical. In like -manner if you separate quicksilver, each portion will form itself into a -globe. - -PUPIL. All this is very clear. And, for the same reason, the water in -the ocean must be convex; for, I remember you told me that it gravitated -towards the center of the earth. - -TUTOR. Once more.—I think you must have seen an eclipse of the moon. - -PUPIL. I have, Sir. - -TUTOR. Of what figure was the darkened part? - -PUPIL. Circular. - -TUTOR. Take this ball, and hold it before the candle between your finger -and thumb, so that the shadow may be thrown on the wall, and in all -positions you will find it circular. - -PUPIL. It is so. - -TUTOR. Apply this crown piece in the same manner, with the flat side to -the candle. - -PUPIL. It is a circle. - -TUTOR. Turn it a little obliquely. - -PUPIL. It is now an ellipsis. - -TUTOR. Now turn the edge to the candle. - -PUPIL. The shadow is a strait line. - -TUTOR. You now see that no other body than that of a globe can in all -positions cast a circular shadow. - -PUPIL. I do, Sir. - -TUTOR. The darkness on the disc of the moon at the time of an eclipse is -the shadow of the earth, which in all situations is circular; the earth, -therefore, which casts the shadow, must be a globe. - -PUPIL. It must be so.—But—— - -TUTOR. The earth is mountainous.—It is so: but remember that the highest -mountain bears no greater proportion to the bulk of the earth than the -small irregularities on the peel of an orange bears to that fruit: that -objection therefore is soon removed. And yet it is not a true sphere. - -PUPIL. What then? - -TUTOR. A spheroid, that is, it is a little flattened at the poles, and -is in shape not unlike an orange or a turnip. This you will not be -surprized at when I tell you that the equatorial parts are about four -thousand miles from the center of motion. - -PUPIL. I suppose then you infer that as the centrifugal force is greater -the farther it is removed from the center, that the parts near the poles -have a tendency to fly off towards the equator. - -TUTOR. I do. And as we have finished this part of our subject, I shall -take leave of you. - ------------------------------------------------------------------------- - - - - - DIALOGUE XI. - - - TUTOR. - -I now propose giving you a description of the moon, and I doubt not it -will afford you some degree of pleasure. - -PUPIL. Indeed it will, as I know little more than that she is a -secondary planet or satellite, revolving round the earth, and with it -round the sun. - -TUTOR. You know her mean distance from the earth. - -PUPIL. I did not recollect that: 240 thousand miles. - -TUTOR. Right. Her diameter is about 2161 miles, and her bulk about a -fiftieth part of the earth’s. Her axis is almost perpendicular to the -plane of the ecliptic, consequently she can have no diversity of -seasons. - -PUPIL. What is her period? - -TUTOR. The time she takes to revolve from one point of the heavens to -the same again is called her _siderial_ or _periodical revolution_, and -is performed in 27 days, 7 hours, 43 minutes; but _synodical -revolution_, or the time taken up to revolve from the sun to the same -apparent situation with respect to the sun again, or from change to -change, is 29 days, 12 hours, and 44 minutes. - -PUPIL. I do not clearly comprehend it. - -TUTOR. If the earth had no annual motion, the period of the moon would -be uniformly 27 days, 7 hours, 43 minutes; but you are to consider that -whilst the moon is revolving round the earth, the earth is advancing in -its orbit, and of course she must be so much longer in completing her -synodical revolution as the difference of time between that and her -siderial revolution. This I will make clear to you in a few -minutes.—What is the situation of the hour-hand and minute-hand of a -watch at twelve o’clock? - -PUPIL. They will be in conjunction. - -TUTOR. And will they be in conjunction at one? - -PUPIL. No, Sir. - -TUTOR. Yet the minute-hand has made a complete revolution: but before -they can be in conjunction again the minute-hand must move forward till -it overtakes the hour-hand. - -PUPIL. I now understand it, and must beg you to explain to me the -different phases of the moon. - -TUTOR. Take this ivory ball, and suspend it by the string with your hand -between your eye and the candle. Let the candle represent the sun, the -ball the moon, and your head the earth. In this situation, as the candle -enlightens only one half of the ball, the part turned from you will be -enlightened, and the part turned to you will be dark. This will be a -representation of the moon at change, and as no part of her enlightened -hemisphere is turned to the earth, she can reflect no light upon it, and -consequently is invisible to us. She now rises and sets nearly with the -sun.—Turn yourself a little to the left, and you will observe a streak -of light like what is called the new moon. - -PUPIL. I see it clearly. - -TUTOR. Move round one quarter. - -PUPIL. One half of the side next me is now enlightened. - -TUTOR. You may conceive it to be the moon at first quarter.—Go on, and -you will see the light increase till the ball is opposite to the candle, -when the side next you will be wholly illumined, and will give you a -just idea of the moon at full, which now rises about the time of -sun-setting, being opposite to the sun: and, the farther she advances in -her orbit the later she rises. - -PUPIL. It is plain it must be so. She rises with the sun at change, -being then in conjunction: and as she revolves in her orbit the same way -as the earth does on its axis, the earth will have farther to revolve -each day before it can see the moon. At the full she is in opposition, -and of course rises when the sun sets: and so continues to rise later -and later, till the change again. - -TUTOR. You imagine that the moon rises exactly with the sun when she is -at change; and when he sets, at full. I will presently convince you of -your mistake; and would have you now proceed with your ball. Place it -again opposite to the candle, and as you turn round you will find the -light gradually decrease as it before increased, that the side that was -before enlightened is now dark, and the dark side light. When you have -gone three quarters round, one half of the side next you will be -enlightened, and will resemble the moon at last quarter. As you go on -the darkened part will increase, till you arrive at the place you set -off from, where the light is quite obscured. - -PUPIL. I have now completed the circuit, and am much delighted with it, -as by this simple contrivance I can perceive the various changes of the -moon, and that the western side is enlightened from the change to the -full, and the eastern side from the full to the change. - -TUTOR. I find then it has fully answered the purpose intended. - -PUPIL. Indeed it has. But if you will give me leave I will use the ball -again. - -TUTOR. By all means. - -PUPIL. I perceive, as I move round, that the same side of the ball is -turned towards me whilst every part is turned to the candle. Is it so -with the moon? - -TUTOR. It is: and as every part of the moon is turned to the sun, she -makes one revolution on her axis whilst she makes one in her orbit. - -PUPIL. This is very singular. If the same side of the moon be always -turned to the earth, the opposite side of course can never see it. - -TUTOR. And they must likewise be deprived of the earth as a moon. - -PUPIL. True. But how is it known that the same side of the moon is -always opposed to the earth? - -TUTOR. The moon, like our earth, consists of mountains and valleys, -which, when seen through a good telescope, are very beautiful. The -mountainous parts appear as lucid spots and bright streaks of light: and -as the same spots, &c. are constantly turned to the earth, she must keep -the same side to the earth. - -PUPIL. It is very clear. Are there no seas? - -TUTOR. It was formerly imagined that the dark parts were seas, but later -observations prove that they are hollow places or caverns, which do not -reflect the light of the sun. Besides, if there were seas there would -consequently be exhalations, and if exhalations, clouds and vapours, and -an atmosphere to support them. That there are no clouds is evident, -because when our atmosphere is clear, and the moon above our horizon in -the night-time, all her parts appear constantly with the same clear, -serene, and calm aspect. - -PUPIL. Has the moon then no atmosphere? - -TUTOR. If she has it is imperceptible to us: for, when she approaches -any star, we cannot discover with our best telescopes any change of -colour or diminution of lustre in the star till the instant it is lost -behind her: whence it is clear, that she can have no such gross medium -as our atmosphere to surround her. - -PUPIL. May we not then doubt whether she be inhabited or not, as without -air we cannot breathe? - -TUTOR. The same Almighty Being who created us and gave us air to -breathe, may have provided a different way for their existence. It does -not hold good that, because we could not live there, she is not -inhabited. Fish will live a considerable time in water under an -exhausted receiver: and, I have heard of a toad being found in a block -of marble. Your doubt therefore, I think, ought not to be admitted. - -PUPIL. I am satisfied. And must now beg to be informed how I may observe -the moon’s motion. - -TUTOR. Her real motion round the earth, may be easily known by remarking -when she is near any particular star. Thus, suppose you see her west, -that is to the right of it, she will be approaching, then in conjunction -with, and afterwards pass it towards the east. Her apparent motion is -that of rising and setting, which is occasioned by the rotation of the -earth on its axis. - -PUPIL. I remember not long since, when you shewed me Jupiter, that the -moon was west of him: the next evening I saw her almost appear to touch -him, and soon after at a great distance from him easterly. I now see -that her real motion is from west by south to east, and her apparent -motion from east by south to west. - -TUTOR. If you have no objection, I will now explain the cause of -eclipses. - -PUPIL. So far from it, that it will give me the greatest pleasure. - -TUTOR. Take your ivory ball, suspend it as before, in a right line -between your eye and the candle.—Can you see the candle? - -PUPIL. No, Sir. - -TUTOR. For what reason. - -PUPIL. Because the ball prevents the light coming to me. - -TUTOR. This then represents an eclipse of the sun, which can never -happen but when the moon is between the sun and the earth, which must be -at the change: for, as light passes in a right line, the sun is hidden -to that part of the earth which is under the moon, and therefore he must -be eclipsed. If the whole of the sun be obscured by the body of the -moon, the eclipse is total: if only a part be darkened, it is a partial -eclipse; and so many twelfth parts of the sun’s diameter, as the moon -covers, so many digits are said to be eclipsed. - -PUPIL. May not the word digit be applied to the moon as well as the sun? - -TUTOR. It may: for it means a twelfth part of the diameter of either the -sun, or the moon. - -PUPIL. As you have now shewn me the cause of an eclipse of the sun, I am -anxious to have that of the moon explained. - -TUTOR. We must again have recourse to your little ball.—Turn yourself -round till it is opposite to the candle in a line with your head, and -you will see that no light can be thrown on it from the candle, because -your head is between them. In like manner the rays of the sun are -prevented falling on the moon, by the interposition of the earth: she -must therefore be eclipsed. - -PUPIL. I see it clearly. And as an eclipse of the sun happens when the -moon is at change, that of the moon must be when she is at full; for, it -is then only the earth’s shadow can fall on the moon, the earth being at -no other time between the sun and her. - -TUTOR. The diameter of the shadow is about three times that of the moon, -and consequently the moon must be totally eclipsed whilst she continues -in it. On the contrary, the shadow of the moon at an eclipse of the sun, -covers so small a part of the earth’s surface, that the sun is totally -or centrally eclipsed to but a small part of it; and its duration is -very short. But a faint or partial shadow surrounds this darkened shade, -in which the sun is more or less eclipsed, as the place is nearer to or -farther from its center; this partial shadow is called the _penumbra_. I -have prepared for you a little drawing, representing an eclipse both of -the sun and moon, which I think will enable you better to understand -what I have been explaining. (Plate IV. Fig. 1 and 2.) In the former, -_p. p._ is the penumbra. - - [Illustration: _Plate IV._ - - _T. Conder Sculp^t._] - -PUPIL. In what does a central differ from a total eclipse? - -TUTOR. An eclipse of the sun may be central, and not total; for, those -who are under the point of the dark shadow, will see the edge of the sun -like a fine luminous ring, all around the dark body of the moon when the -sun is eclipsed at the moon’s greatest distance from the earth; but when -she is nearest the earth at an eclipse of the sun, the eclipse is total. -When the penumbra first touches the earth, the general eclipse begins; -when it leaves the earth, the general eclipse ends. An eclipse of the -moon always begins on the moon’s eastern side, and goes off on her -western side; but an eclipse of the sun begins on the sun’s western -side, and goes off on his eastern side. When the moon is eclipsed in -either of her nodes, the eclipse is both central and total. - -PUPIL. Pray, what is the reason we have not an eclipse at every full and -change of the moon? - -TUTOR. For the same reason that Mercury and Venus are not seen to pass -over she sun’s disc at every inferior conjunction. - -PUPIL. Is the orbit of the moon then inclined to the plane of the -ecliptic? - -TUTOR. It is: and no eclipse of the sun can happen but when the moon is -within 17 degrees of either of her nodes: neither can there be one of -the moon, unless she be within 12 degrees. At all other new moons she -passeth either above or below the sun, as seen from the earth: and at -all other full moons above or below the earth’s shadow, according as she -is north or south of the ecliptic. You now see that the moon must -sometimes rise before and sometimes after the sun at change, and before -or after he sets at full. - -PUPIL. I do, Sir, and am much obliged to you for this pleasing account -of the moon, and of eclipses: and if you have any thing farther to -observe, it will afford me additional pleasure. - -TUTOR. You may, at some time or other, have an opportunity of seeing a -total eclipse of the moon; it will therefore be necessary to prepare you -for a phænomenon which otherwise you might be much surprized at, and -that is, that after the moon is immersed in the earth’s shadow, she is -still visible. - -PUPIL. This is a phænomenon that I am not able to account for; for, the -moon being an opaque body, she cannot shine by her own light[16], and -the rays of the sun are prevented falling on her by the interposition of -the earth, she cannot therefore shine by reflection. - - [Footnote 16: Dr. Herschell supposes the moon and the rest of the - planets may have some inherent light: the side of the planet Venus, - turned from the sun, having been seen, as we see the moon soon after - the change.] - -TUTOR. It is by reflection that we see her; for the rays of the sun -which fall upon our atmosphere are refracted or bent into the earth’s -shadow, and so falling upon the moon are reflected back to us. If we had -no atmosphere, she would be totally dark, and of course invisible to us. - -PUPIL. What is her appearance? - -TUTOR. It is that of a dusky colour, somewhat like tarnished copper.—I -have one thing more to remark before we quit this subject, which is, -that the moon’s nodes have a retrograde or backward motion, in a -direction contrary to the earth’s annual motion, and go through all the -signs and degrees of the ecliptic in little less than nineteen years, -when there will be a regular period of eclipses, or return of the same -eclipses for many ages. - -PUPIL. Pray, Sir, what do you propose for our next subject? - -TUTOR. The ebbing and flowing of the sea, or cause of the tides. - ------------------------------------------------------------------------- - - - - - DIALOGUE XII. - - - TUTOR. - -In order to explain the cause of the tides, I have since I saw you last -prepared a little drawing for you, (Plate IV. fig. 3.) where S -represents the sun, M the moon at change, E the center of the earth, and -A B C D its surface, covered with water. It is obvious, from the -principles of gravitation, that if the earth were at rest the water in -the ocean would be truly spherical, if its figure were not altered by -the action of some other power. But, daily experience proves that it is -continually agitated. - -PUPIL. What is the cause of this agitation? - -TUTOR. The attraction of the sun and moon, particularly the latter: for, -as she is so much nearer the earth than the sun, she attracts with a -much greater force than he does, and consequently raises the water much -higher, which, being a fluid, loses as it were its gravitating power, -and yields to their superior force. - -PUPIL. What proportion does the attractive power of the sun bear to that -of the moon? - -TUTOR. As three to ten. So when the moon is at change, the sun and moon -being in conjunction, or on the same side of the earth, the action of -both bodies is on the surface of the water, the moon raising it ten -parts,[17] and the sun three, the sum of which is thirteen parts, -represented by B _b_. Now it is evident, that if thirteen parts be added -by the attractive power of those bodies, the same number of parts must -be drawn off from some other part, as A _a_, C _c_. It will now be -high-water under the moon at _b_, and its opposite side _d_, and -low-water at _a_ and _c_. - - [Footnote 17: By part here I do not mean any specific measure.] - -PUPIL. That the attraction of the sun and moon must occasion a swelling -of the waters on the side next them, I can readily conceive, and that -this swell must cause a falling off at the sides: but that the tide -should rise as high on the side opposite to the sun and moon, in a -direction contrary to their attraction, is what I am not able to account -for. - -TUTOR. This difficulty will be removed when you consider that all bodies -moving in circles have a constant tendency to fly off from their -centers. Now, as the earth and moon move round their center of gravity, -that part of the earth which is at any time opposite to the moon will -have a greater centrifugal force than the side next her, and at the -earth’s center the centrifugal force exactly balances the attractive -force: therefore, as much water is thrown off by the centrifugal force -on the side opposite to the moon, as is raised on the side next her by -her attraction. Hence, it is plain, that at D, fig. 3, the centrifugal -force must be greater than at the center E, and at E than B, because the -part D is farther from the center of motion than the part B. On the -contrary, the part B being nearer the moon than the center E, the -attracting power must there be strongest, and weakest at D. And, as the -two opposing powers balance each other at the earth’s center, the tides -will rise as high on that side from the moon, by the excess of the -centrifugal force, as they rise on the side next her by the excess of -her attraction. - -PUPIL. In this explanation you have mentioned nothing of the sun. - -TUTOR. From what I have already said it must be plain to you that if -there were no moon the sun by his attraction would raise a small tide on -the side next him; and, it is as evident that the tides opposite would -be raised as high by the centrifugal force: for the sun and earth, as -well as the earth and moon, move round their center of gravity. This may -be exemplified by an easy experiment. Take a flexible hoop, suppose of -thin brass, tie a string to it and whirl it round your head, and it will -assume an elliptical shape; the tightness of the string drawing out the -side next to your hand, and the centrifugal force throwing off the -other. - -PUPIL. This I clearly comprehend. - -TUTOR. I shall now refer you to the next figure, (fig. 4.) where F -represents the moon at full: the sun and moon are in opposition, and yet -the tide is as high on each side as in the former case. I wish you to -shew me the cause. - -PUPIL. I will use my endeavour to do it, Sir. - -TUTOR. Then I doubt not you will accomplish it. - -PUPIL. When the moon is at full, ten parts of water are raised from that -side of the earth next her, by her attraction; and, as the side which is -next her is opposite to the sun, three parts must be thrown off by his -centrifugal force, the sum of which will be thirteen parts next the -moon.—From the side opposite to the moon, and under the sun, ten parts -are thrown off by her centrifugal force, and three raised by his -attraction, making thirteen, the same as before. - -TUTOR. I could not have done it better. These are called _Spring Tides_. -But when the moon is in her quarters, the action of the sun and moon are -in opposition to each other; that is, they act in contrary directions -(see fig. 5.) The moon of herself would raise the water ten parts under -her, and throw off ten parts by her centrifugal force on the opposite -side; but, the sun being then in a line with the low-water, his action -keeps the tides from falling so low there, and consequently from rising -so high under and opposite to her. His power, therefore, on the -low-water being three parts, leaves only seven parts for the high water, -under and oppose the moon. These are called _Neap Tides_. - -PUPIL. This is very plain. - -TUTOR. You would naturally suppose that the tides ought to be highest -directly under and opposite to the moon: that is, when the moon is due -north and south. But we find, that in open seas, where the water flows -freely, the moon is generally past the north and south meridian when it -is high-water. For, if the moon’s attraction were to cease when she was -past the meridian, the motion of ascent communicated to the water before -that time would make it continue to rise for some time after: as the -heat of the day is greater at three o’clock in the afternoon than it is -at twelve; and it is hotter in July and August than in June, when the -sun is highest and the days are longest. - -PUPIL. These are convincing reasons. And, pray what time after the moon -has passed the meridian, is it high-water? - -TUTOR. If the earth were entirely covered with water, so that the tides -might regularly follow the moon, she would always be three hours past -the meridian of any given place when the tide was at the highest at that -place. But, as the earth is not covered with water, the tides do not -always answer to the same distance of the moon from the meridian at the -same places, because the regular course of the tides is much interrupted -by the different capes and corners of the land running out into the -oceans and seas in different directions, and also by their running -through shoals and channels. But, at whatever distance the moon is from -the meridian on any given day, at any place, when the tide is at its -height there, it will be so again the next day, much about the time when -the moon is at the like distance from the meridian again. - -PUPIL. Are not the tides later every day than they were the preceding -day? - -TUTOR. Yes; and the reason is obvious: for, whilst the earth is -revolving on its axis in twenty-four hours, the moon will be advancing -in her orbit; therefore the earth must turn as much more than round its -axis before the same place which was under her can come to the same -place again with respect to her, as she has advanced in her orbit during -that interval of time, which is 50 minutes. This being divided by 4, -gives 12-1/2 minutes; so that it will be 6 hours 12-1/2 minutes from -high to low-water, and the same time from low to high-water: or 12 hours -25 minutes from high-water to high-water again. - -PUPIL. This I understand perfectly well. - -TUTOR. I have now finished my description of the tides, and having a -little time to spare, if you wish to know how to find the proportionate -magnitude of the planets with that of the earth, and to calculate their -distances from the sun, I will employ it that way. - -PUPIL. At our first conference I remember you shewed me the proportion -that the other planets bear to the earth, with their periods and -distances from the sun; but to have it in my power to make the -calculations myself, will certainly give me great pleasure. - -TUTOR. To find what proportion any planet bears to the earth; or, that -one globe bears to another, you must observe that, _all spheres or -globes are in proportion to one another as the cubes of their -diameters_. So that you have nothing more to do than to cube the -diameter of each, and divide the greatest by the least number, and the -quotient will shew you the proportion that one bears to the other. - -PUPIL. The operation appears very simple; but, as I do not know what a -cube number is, I cannot perform it. - -TUTOR. You cannot forget what a square number is. - -PUPIL. The product of any number multiplied into itself is a square -number, as 4 is the square of 2. - -TUTOR. Any square number multiplied by its root, or first power, will be -a cube number. Thus 4 multiplied by 2 will be 8, which is the cube of 2; -9 is the square or second power, and 27 the cube or third power of 3, -&c. This you will perhaps better understand by - - A TABLE OF - - Roots. 1. 2. 3. 4. 5. 6. 7. 8. 9. - Squares. 1. 4. 9. 16. 25. 36. 49. 64. 81. - Cubes. 1. 8. 27. 64. 125. 216. 343. 512. 729. - -PUPIL. I do, Sir; and am now prepared for an example. - -TUTOR. The diameter of the sun is 893552 miles, of the earth 7920 miles; -how much does the sun exceed the earth in magnitude? - -PUPIL. The cube of 893522, the sun’s diameter, is 713371492260872648; -and of 7920, the earth’s, 496793088000. And 713371492260872648 divided -by 496793088000 is equal to 1435952, and so many times is the bulk of -the sun greater than that of the earth. - -TUTOR. This one example may suffice, as I intend by and by to give you a -table of diameters, &c.; you may then calculate the rest at your -leisure. - -PUPIL. I shall now, Sir, be glad to have the other explained. - -TUTOR. The periods of the planets, or the times they take to complete -their revolutions in their orbits, are exactly known; and the mean -distance of the earth from the sun has been also ascertained. Here, -then, we have the periods of all, and the mean distance of one, to find -the distances of the rest; which may be found by attending to the -following proportion: - - As the square of the period of any one planet, - Is to the cube of its mean distance from the sun; - So is the square of the period of any other planet, - To the cube of its mean distance. - -The cube root of this quotient will be the distance sought. - -PUPIL. Here again I find myself at a loss, as I have not learnt to -extract the cube root. - -TUTOR. I will give you [18]Doctor Turner’s rule, which I think will -answer your purpose. - - [Footnote 18: Young Geometrician’s Companion.] - -“First, having set down the given number, or resolvend, make a dot over -the unit figure, and so on over every third figure (towards the left -hand in whole numbers, but towards the right hand in decimals); and so -many dots as there are, so many figures will be in the root. - -Next, seek the nearest cube to the first period; place its root in the -quotient, and its cube set under the first period. Subtract it -therefrom; and to the remainder bring down one figure only of the next -period, which will be a dividend. - -Then, square the figure put in the quotient, and multiply it by 3, for a -divisor. Seek how often this divisor may be had in the dividend, and set -the figure in the quotient, which will be the second place in the root. - -Now, cube the figures in the root, and subtract it from the two first -periods of the resolvend; and to the remainder bring down the first -figure of the next period, for a new dividend. Square the figures in the -quotient, and multiply it by 3, for a new divisor; then proceed in all -respects as before, till the whole is finished.” - -The following example will, I trust, make it clear to you. - - EXAMPLE. - -It is required to find the cube root of 15625. - - . . - 15625 (25 - 8 - ───── - 12) 76 - 15625 - ───── - ..... - ═════ - -Point every third figure, and the first period will be 15; the nearest -cube to which, in the table I gave you just now, you will find to be 8, -and its root 2; the 8 you must place under the 15, and the 2 in the -quotient: take 8 from 15 and 7 will remain, to which bring down 6, the -first figure of the next period, and you have 76 for a dividend. The -figure put in the quotient is 2, the square of which is 4, which -multiplied by 3 is 12, for a divisor. Now 12 in 76 will be 5 times; cube -25, and you will have 15625, which, subtract from the resolvend, and -nothing will remain; which shews that the resolvend is a cube number, -and 25 its root. - -PUPIL. You say 12 in 76 is 5 times; I should have said 6 times. - -TUTOR. In common division it would be so; but as the cube of 26 would be -greater than the resolvend from which you are to subtract it, it can go -but 5 times. - -PUPIL. Now, Sir, I think I have a sufficient knowledge of the rule to -solve a problem. - -TUTOR. The earth’s period is 365 days, and its mean distance from the -sun 95 millions of miles; the period of Mercury is 88 days—what is his -mean distance? - -PUPIL. As the distance of the earth is given, I must make the square of -365 the first term, the cube of 95 the second, and the square of 88 the -third term of the proportion. - -TUTOR. Certainly.—Take your slate, or a piece of paper, prepare your -numbers, and make your proportion. - -PUPIL. I find the square of 365 = 133225; of 88 = 7744; and the cube of -95 = 857375. - -Then 133225 : 857375 :: 7744 to a fourth term. - -I now multiply the second and third terms together, and divide the -product by the first, the quotient 49836 is the cube of the mean -distance of Mercury from the sun in millions of miles, and the fourth -term sought. - -TUTOR. So far you are right. Now extract the root. - - . . - 49836 (36 3 36 - 27 3 36 - ─── ── ───── - 27) 228 Sq. of 3 = 9 216 - 46656 Mul. by 3 108 - ───── ── ───── - 3180 Divisor 27 1296 - ═════ ══ 36 - ───── - 7776 - 3888 - ───── - Cube of 36 = 46656 - ═════ - -PUPIL. The root I find to be 36, which is the mean distance of Mercury -from the sun, in millions of miles. - -TUTOR. You now see, that although 27 in 228 will go 8 times, yet here it -will go but 6 times; and, as there is a remainder, it shews you that the -resolvend is not a cube number. - -PUPIL. I see it clearly. - -TUTOR. You now seem perfect in the rule; I shall therefore not trouble -you with any more examples, but shall give you the table I promised you. - - ┌─────────────────────────────────────────────────────────────────────┐ - │ TABLE. │ - ├──────────┬──────────┬───────────────┬───────────────┬───────────────┤ - │ Names │Diameters,│ Magnitude, │ Periods, │ Mean Distance │ - │ of the │in English│ compared │ in │ from the Sun, │ - │ PLANETS. │ Miles. │with the Earth.│Years and Days.│ in Mil. of │ - │ │ │ │ │ Miles. │ - ├──────────┼──────────┼───────────────┼───────────────┼───────────────┤ - │Sun │ [A]893522│ 1435952 │ —— │ —— │ - │ │ │ │ │ │ - │Mercury │ 3261│ 1/14 │ 0 —— 88 │ 36 │ - │ │ │ │ │ │ - │Venus │ 7699│ 5/49 │ 0 —— 224 │ 68 │ - │ │ │ │ │ │ - │Earth │ 7920│ 1 │ 1 or 365 │ 95 │ - │ │ │ │ │ │ - │Moon │ 2161│ 1/49 │ —— │ —— │ - │ │ │ │ │ │ - │Mars │ 5312│ 1/3 │ 1 and 322 │ 145 │ - │ │ │ │ │ │ - │Jupiter │ 90255│ 1479 │ 11 —— 314 │ 494 │ - │ │ │ │ │ │ - │Saturn │ 80012│ 1031 │ 29 —— 167 │ 906 │ - │ │ │ │ │ │ - │Georgian │ 34217│ 82 │ 83 —— 121 │ 1812 │ - └──────────┴──────────┴───────────────┴───────────────┴───────────────┘ - - [Footnote A: The Diameters were taken from Adams’s Lectures, Vol. IV. - p. 39.] - -PUPIL. I shall take the first opportunity of calculating the rest, in -which I am certain I shall have great satisfaction. - - * * * * * - -TUTOR. I have now conducted you through the elementary parts of -astronomy, have given you a general view of the system of the world, and -prepared you to pursue the study with profit and pleasure.—In your -future researches, the more accurate you are, the more you will discover -of regularity, symmetry, and order in the constitution of the frame of -nature. - - “Hail, Sov’reign Goodness! all-productive Mind! - “On all thy works thyself inscrib’d we find; - “How various all, how variously endow’d, - “How great their number, and each part how good! - “How perfect then must the Great Parent shine, ⎫ - “Who, with one act of energy divine, ⎬ - “Laid the vast plan, and finish’d the design!” ⎭ - - - THE END. - - - - ------------------------------------------------------------------------- - - - - - Directions to the Bookbinder. - - Plate I. _to face the_ Title. - ———— II. —— _page_ 40. - ———— III. —— —— 88. - ———— IV. —— —— 131. - ------------------------------------------------------------------------- - - Transcriber’s note: - -All instances of ‘disk’ changed to ‘disc’ - -Errata, instance of ‘disk’ on page 79 added, “—— 79. — 5. ⎭” - -Page 11, ‘Years’ changed to ‘years,’ “130 years after Christ” - -Page 20, ‘h e’ changed to ‘the,’ “would have as much the appearance” - -Page 24, ‘cannon ball’ changed to ‘cannon-ball,’ “the time a cannon-ball -would” - -Page 63, comma changed to full stop after ‘TUTOR,’ “TUTOR. Why?” - -Page 65, ‘a’ changed to ‘_a_,’ “carry a planet from A to _a_” - -Page 74, ‘itaxis’ changed to ‘its axis,’ “if the earth revolve on its -axis every” - -Page 78, ‘Mercury’ struck after ‘Sun,’ “Sun, Venus, Mars, and Jupiter -are known to revolve on their axes” - -Page 93, ‘cancer’ changed to ‘Cancer,’ “is the _tropic of cancer_; that” - -Page 93, ‘capricorn’ changed to ‘Capricorn,’ “the _tropic of capricorn_” - -Page 115, ‘othes’ changed to ‘other,’ “and other stars rise to his” - -Page 115, ‘bnt’ changed to ‘but,’ “out from; but, by going round” - -Page 116, ‘it’s’ changed to ‘its,’ “How can its surface be round” - -Page 128, full stop inserted after ‘eclipses,’ “explain the cause of -eclipses.” - - - - - -End of the Project Gutenberg EBook of The Study of Astronomy, by John Stedman - -*** END OF THIS PROJECT GUTENBERG EBOOK THE STUDY OF ASTRONOMY *** - -***** This file should be named 56289-0.txt or 56289-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/5/6/2/8/56289/ - -Produced by Eric Hutton and the Online Distributed -Proofreading Team at http://www.pgdp.net - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. Special rules, set forth in the General Terms of Use part -of this license, apply to copying and distributing Project -Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm -concept and trademark. Project Gutenberg is a registered trademark, -and may not be used if you charge for the eBooks, unless you receive -specific permission. If you do not charge anything for copies of this -eBook, complying with the rules is very easy. You may use this eBook -for nearly any purpose such as creation of derivative works, reports, -performances and research. They may be modified and printed and given -away--you may do practically ANYTHING in the United States with eBooks -not protected by U.S. copyright law. Redistribution is subject to the -trademark license, especially commercial redistribution. - -START: FULL LICENSE - -THE FULL PROJECT GUTENBERG LICENSE -PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK - -To protect the Project Gutenberg-tm mission of promoting the free -distribution of electronic works, by using or distributing this work -(or any other work associated in any way with the phrase "Project -Gutenberg"), you agree to comply with all the terms of the Full -Project Gutenberg-tm License available with this file or online at -www.gutenberg.org/license. - -Section 1. General Terms of Use and Redistributing Project -Gutenberg-tm electronic works - -1.A. By reading or using any part of this Project Gutenberg-tm -electronic work, you indicate that you have read, understand, agree to -and accept all the terms of this license and intellectual property -(trademark/copyright) agreement. If you do not agree to abide by all -the terms of this agreement, you must cease using and return or -destroy all copies of Project Gutenberg-tm electronic works in your -possession. If you paid a fee for obtaining a copy of or access to a -Project Gutenberg-tm electronic work and you do not agree to be bound -by the terms of this agreement, you may obtain a refund from the -person or entity to whom you paid the fee as set forth in paragraph -1.E.8. - -1.B. "Project Gutenberg" is a registered trademark. It may only be -used on or associated in any way with an electronic work by people who -agree to be bound by the terms of this agreement. There are a few -things that you can do with most Project Gutenberg-tm electronic works -even without complying with the full terms of this agreement. See -paragraph 1.C below. There are a lot of things you can do with Project -Gutenberg-tm electronic works if you follow the terms of this -agreement and help preserve free future access to Project Gutenberg-tm -electronic works. See paragraph 1.E below. - -1.C. The Project Gutenberg Literary Archive Foundation ("the -Foundation" or PGLAF), owns a compilation copyright in the collection -of Project Gutenberg-tm electronic works. Nearly all the individual -works in the collection are in the public domain in the United -States. If an individual work is unprotected by copyright law in the -United States and you are located in the United States, we do not -claim a right to prevent you from copying, distributing, performing, -displaying or creating derivative works based on the work as long as -all references to Project Gutenberg are removed. Of course, we hope -that you will support the Project Gutenberg-tm mission of promoting -free access to electronic works by freely sharing Project Gutenberg-tm -works in compliance with the terms of this agreement for keeping the -Project Gutenberg-tm name associated with the work. You can easily -comply with the terms of this agreement by keeping this work in the -same format with its attached full Project Gutenberg-tm License when -you share it without charge with others. - -1.D. The copyright laws of the place where you are located also govern -what you can do with this work. Copyright laws in most countries are -in a constant state of change. If you are outside the United States, -check the laws of your country in addition to the terms of this -agreement before downloading, copying, displaying, performing, -distributing or creating derivative works based on this work or any -other Project Gutenberg-tm work. The Foundation makes no -representations concerning the copyright status of any work in any -country outside the United States. - -1.E. Unless you have removed all references to Project Gutenberg: - -1.E.1. The following sentence, with active links to, or other -immediate access to, the full Project Gutenberg-tm License must appear -prominently whenever any copy of a Project Gutenberg-tm work (any work -on which the phrase "Project Gutenberg" appears, or with which the -phrase "Project Gutenberg" is associated) is accessed, displayed, -performed, viewed, copied or distributed: - - This eBook is for the use of anyone anywhere in the United States and - most other parts of the world at no cost and with almost no - restrictions whatsoever. You may copy it, give it away or re-use it - under the terms of the Project Gutenberg License included with this - eBook or online at www.gutenberg.org. If you are not located in the - United States, you'll have to check the laws of the country where you - are located before using this ebook. - -1.E.2. If an individual Project Gutenberg-tm electronic work is -derived from texts not protected by U.S. copyright law (does not -contain a notice indicating that it is posted with permission of the -copyright holder), the work can be copied and distributed to anyone in -the United States without paying any fees or charges. If you are -redistributing or providing access to a work with the phrase "Project -Gutenberg" associated with or appearing on the work, you must comply -either with the requirements of paragraphs 1.E.1 through 1.E.7 or -obtain permission for the use of the work and the Project Gutenberg-tm -trademark as set forth in paragraphs 1.E.8 or 1.E.9. - -1.E.3. If an individual Project Gutenberg-tm electronic work is posted -with the permission of the copyright holder, your use and distribution -must comply with both paragraphs 1.E.1 through 1.E.7 and any -additional terms imposed by the copyright holder. Additional terms -will be linked to the Project Gutenberg-tm License for all works -posted with the permission of the copyright holder found at the -beginning of this work. - -1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm -License terms from this work, or any files containing a part of this -work or any other work associated with Project Gutenberg-tm. - -1.E.5. Do not copy, display, perform, distribute or redistribute this -electronic work, or any part of this electronic work, without -prominently displaying the sentence set forth in paragraph 1.E.1 with -active links or immediate access to the full terms of the Project -Gutenberg-tm License. - -1.E.6. You may convert to and distribute this work in any binary, -compressed, marked up, nonproprietary or proprietary form, including -any word processing or hypertext form. However, if you provide access -to or distribute copies of a Project Gutenberg-tm work in a format -other than "Plain Vanilla ASCII" or other format used in the official -version posted on the official Project Gutenberg-tm web site -(www.gutenberg.org), you must, at no additional cost, fee or expense -to the user, provide a copy, a means of exporting a copy, or a means -of obtaining a copy upon request, of the work in its original "Plain -Vanilla ASCII" or other form. Any alternate format must include the -full Project Gutenberg-tm License as specified in paragraph 1.E.1. - -1.E.7. Do not charge a fee for access to, viewing, displaying, -performing, copying or distributing any Project Gutenberg-tm works -unless you comply with paragraph 1.E.8 or 1.E.9. - -1.E.8. You may charge a reasonable fee for copies of or providing -access to or distributing Project Gutenberg-tm electronic works -provided that - -* You pay a royalty fee of 20% of the gross profits you derive from - the use of Project Gutenberg-tm works calculated using the method - you already use to calculate your applicable taxes. The fee is owed - to the owner of the Project Gutenberg-tm trademark, but he has - agreed to donate royalties under this paragraph to the Project - Gutenberg Literary Archive Foundation. Royalty payments must be paid - within 60 days following each date on which you prepare (or are - legally required to prepare) your periodic tax returns. Royalty - payments should be clearly marked as such and sent to the Project - Gutenberg Literary Archive Foundation at the address specified in - Section 4, "Information about donations to the Project Gutenberg - Literary Archive Foundation." - -* You provide a full refund of any money paid by a user who notifies - you in writing (or by e-mail) within 30 days of receipt that s/he - does not agree to the terms of the full Project Gutenberg-tm - License. You must require such a user to return or destroy all - copies of the works possessed in a physical medium and discontinue - all use of and all access to other copies of Project Gutenberg-tm - works. - -* You provide, in accordance with paragraph 1.F.3, a full refund of - any money paid for a work or a replacement copy, if a defect in the - electronic work is discovered and reported to you within 90 days of - receipt of the work. - -* You comply with all other terms of this agreement for free - distribution of Project Gutenberg-tm works. - -1.E.9. If you wish to charge a fee or distribute a Project -Gutenberg-tm electronic work or group of works on different terms than -are set forth in this agreement, you must obtain permission in writing -from both the Project Gutenberg Literary Archive Foundation and The -Project Gutenberg Trademark LLC, the owner of the Project Gutenberg-tm -trademark. Contact the Foundation as set forth in Section 3 below. - -1.F. - -1.F.1. Project Gutenberg volunteers and employees expend considerable -effort to identify, do copyright research on, transcribe and proofread -works not protected by U.S. copyright law in creating the Project -Gutenberg-tm collection. Despite these efforts, Project Gutenberg-tm -electronic works, and the medium on which they may be stored, may -contain "Defects," such as, but not limited to, incomplete, inaccurate -or corrupt data, transcription errors, a copyright or other -intellectual property infringement, a defective or damaged disk or -other medium, a computer virus, or computer codes that damage or -cannot be read by your equipment. - -1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right -of Replacement or Refund" described in paragraph 1.F.3, the Project -Gutenberg Literary Archive Foundation, the owner of the Project -Gutenberg-tm trademark, and any other party distributing a Project -Gutenberg-tm electronic work under this agreement, disclaim all -liability to you for damages, costs and expenses, including legal -fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT -LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE -PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE -TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE -LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR -INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH -DAMAGE. - -1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a -defect in this electronic work within 90 days of receiving it, you can -receive a refund of the money (if any) you paid for it by sending a -written explanation to the person you received the work from. If you -received the work on a physical medium, you must return the medium -with your written explanation. The person or entity that provided you -with the defective work may elect to provide a replacement copy in -lieu of a refund. If you received the work electronically, the person -or entity providing it to you may choose to give you a second -opportunity to receive the work electronically in lieu of a refund. If -the second copy is also defective, you may demand a refund in writing -without further opportunities to fix the problem. - -1.F.4. Except for the limited right of replacement or refund set forth -in paragraph 1.F.3, this work is provided to you 'AS-IS', WITH NO -OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT -LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE. - -1.F.5. Some states do not allow disclaimers of certain implied -warranties or the exclusion or limitation of certain types of -damages. If any disclaimer or limitation set forth in this agreement -violates the law of the state applicable to this agreement, the -agreement shall be interpreted to make the maximum disclaimer or -limitation permitted by the applicable state law. The invalidity or -unenforceability of any provision of this agreement shall not void the -remaining provisions. - -1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the -trademark owner, any agent or employee of the Foundation, anyone -providing copies of Project Gutenberg-tm electronic works in -accordance with this agreement, and any volunteers associated with the -production, promotion and distribution of Project Gutenberg-tm -electronic works, harmless from all liability, costs and expenses, -including legal fees, that arise directly or indirectly from any of -the following which you do or cause to occur: (a) distribution of this -or any Project Gutenberg-tm work, (b) alteration, modification, or -additions or deletions to any Project Gutenberg-tm work, and (c) any -Defect you cause. - -Section 2. Information about the Mission of Project Gutenberg-tm - -Project Gutenberg-tm is synonymous with the free distribution of -electronic works in formats readable by the widest variety of -computers including obsolete, old, middle-aged and new computers. It -exists because of the efforts of hundreds of volunteers and donations -from people in all walks of life. - -Volunteers and financial support to provide volunteers with the -assistance they need are critical to reaching Project Gutenberg-tm's -goals and ensuring that the Project Gutenberg-tm collection will -remain freely available for generations to come. In 2001, the Project -Gutenberg Literary Archive Foundation was created to provide a secure -and permanent future for Project Gutenberg-tm and future -generations. To learn more about the Project Gutenberg Literary -Archive Foundation and how your efforts and donations can help, see -Sections 3 and 4 and the Foundation information page at -www.gutenberg.org - - - -Section 3. Information about the Project Gutenberg Literary Archive Foundation - -The Project Gutenberg Literary Archive Foundation is a non profit -501(c)(3) educational corporation organized under the laws of the -state of Mississippi and granted tax exempt status by the Internal -Revenue Service. The Foundation's EIN or federal tax identification -number is 64-6221541. Contributions to the Project Gutenberg Literary -Archive Foundation are tax deductible to the full extent permitted by -U.S. federal laws and your state's laws. - -The Foundation's principal office is in Fairbanks, Alaska, with the -mailing address: PO Box 750175, Fairbanks, AK 99775, but its -volunteers and employees are scattered throughout numerous -locations. Its business office is located at 809 North 1500 West, Salt -Lake City, UT 84116, (801) 596-1887. Email contact links and up to -date contact information can be found at the Foundation's web site and -official page at www.gutenberg.org/contact - -For additional contact information: - - Dr. Gregory B. Newby - Chief Executive and Director - gbnewby@pglaf.org - -Section 4. Information about Donations to the Project Gutenberg -Literary Archive Foundation - -Project Gutenberg-tm depends upon and cannot survive without wide -spread public support and donations to carry out its mission of -increasing the number of public domain and licensed works that can be -freely distributed in machine readable form accessible by the widest -array of equipment including outdated equipment. Many small donations -($1 to $5,000) are particularly important to maintaining tax exempt -status with the IRS. - -The Foundation is committed to complying with the laws regulating -charities and charitable donations in all 50 states of the United -States. Compliance requirements are not uniform and it takes a -considerable effort, much paperwork and many fees to meet and keep up -with these requirements. We do not solicit donations in locations -where we have not received written confirmation of compliance. To SEND -DONATIONS or determine the status of compliance for any particular -state visit www.gutenberg.org/donate - -While we cannot and do not solicit contributions from states where we -have not met the solicitation requirements, we know of no prohibition -against accepting unsolicited donations from donors in such states who -approach us with offers to donate. - -International donations are gratefully accepted, but we cannot make -any statements concerning tax treatment of donations received from -outside the United States. U.S. laws alone swamp our small staff. - -Please check the Project Gutenberg Web pages for current donation -methods and addresses. Donations are accepted in a number of other -ways including checks, online payments and credit card donations. To -donate, please visit: www.gutenberg.org/donate - -Section 5. General Information About Project Gutenberg-tm electronic works. - -Professor Michael S. Hart was the originator of the Project -Gutenberg-tm concept of a library of electronic works that could be -freely shared with anyone. For forty years, he produced and -distributed Project Gutenberg-tm eBooks with only a loose network of -volunteer support. - -Project Gutenberg-tm eBooks are often created from several printed -editions, all of which are confirmed as not protected by copyright in -the U.S. unless a copyright notice is included. Thus, we do not -necessarily keep eBooks in compliance with any particular paper -edition. - -Most people start at our Web site which has the main PG search -facility: www.gutenberg.org - -This Web site includes information about Project Gutenberg-tm, -including how to make donations to the Project Gutenberg Literary -Archive Foundation, how to help produce our new eBooks, and how to -subscribe to our email newsletter to hear about new eBooks. - |