A Short History of Astronomy, Arthur Berry [large screen ebook reader .TXT] 📗
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99 Also frequently referred to by the Latin name Cartesius.
100 According to the unreformed calendar (O.S.) then in use in England, the date was Christmas Day, 1642. To facilitate comparison with events occurring out of England, I have used throughout this and the following chapters the Gregorian Calendar (N.S.), which was at this time adopted in a large part of the Continent (cf. chapter II., § 22).
101 From a MS. among the Portsmouth Papers, quoted in the Preface to the Catalogue of the Portsmouth Papers.
102 W. K. Clifford, Aims and Instruments of Scientific Thought.
103 It is interesting to read that Wren offered a prize of 40s. to whichever of the other two should solve this the central problem of the solar system.
104 The familiar parallelogram of forces, of which earlier writers had had indistinct ideas, was clearly stated and proved in the introduction to the Principia, and was, by a curious coincidence, published also in the same year by Varignon and Lami.
105 It is between 13 and 14 billion billion pounds. See chapter X. § 219.
106 As far as I know Newton gives no short statement of the law in a perfectly complete and general form; separate parts of it are given in different passages of the Principia.
107 It is commonly stated that Newton’s value of the motion of the moon’s apses was only about half the true value. In a scholium of the Principia to prop. 35 of the third book, given in the first edition but afterwards omitted, he estimated the annual motion at 40°, the observed value being about 41°. In one of his unpublished papers, contained in the Portsmouth collection, he arrived at 39° by a process which he evidently regarded as not altogether satisfactory.
108 Throughout the Coppernican controversy up to Newton’s time it had been generally assumed, both by Coppernicans and by their opponents, that there was some meaning in speaking of a body simply as being “at rest” or “in motion,” without any reference to any other body. But all that we can really observe is the motion of one body relative to one or more others. Astronomical observation tells us, for example, of a certain motion relative to one another of the earth and sun; and this motion was expressed in two quite different ways by Ptolemy and by Coppernicus. From a modern standpoint the question ultimately involved was whether the motions of the various bodies of the solar system relatively to the earth or relatively to the sun were the simpler to express. If it is found convenient to express them—as Coppernicus and Galilei did—in relation to the sun, some simplicity of statement is gained by speaking of the sun as “fixed” and omitting the qualification “relative to the sun” in speaking of any other body. The same motions might have been expressed relatively to any other body chosen at will: e.g. to one of the hands of a watch carried by a man walking up and down on the deck of a ship on a rough sea; in this case it is clear that the motions of the other bodies of the solar system relative to this body would be excessively complicated; and it would therefore be highly inconvenient though still possible to treat this particular body as “fixed.”
A new aspect of the problem presents itself, however, when an attempt—like Newton’s—is made to explain the motions of bodies of the solar system as the result of forces exerted on one another by those bodies. If, for example, we look at Newton’s First Law of Motion (chapter VI., § 130), we see that it has no meaning, unless we know what are the body or bodies relative to which the motion is being expressed; a body at rest relatively to the earth is moving relatively to the sun or to the fixed stars, and the applicability of the First Law to it depends therefore on whether we are dealing with its motion relatively to the earth or not. For most terrestrial motions it is sufficient to regard the Laws of Motion as referring to motion relative to the earth; or, in other words, we may for this purpose treat the earth as “fixed.” But if we examine certain terrestrial motions more exactly, we find that the Laws of Motion thus interpreted are not quite true; but that we get a more accurate explanation of the observed phenomena if we regard the Laws of Motion as referring to motion relative to the centre of the sun and to lines drawn from it to the stars; or, in other words, we treat the centre of the sun as a “fixed” point and these lines as “fixed” directions. But again when we are dealing with the solar system generally this interpretation is slightly inaccurate, and we have to treat the centre of gravity of the solar system instead of the sun as “fixed.”
From this point of view we may say that Newton’s object in the Principia was to shew that it was possible to choose a certain point (the centre of gravity of the solar system) and certain directions (lines joining this point to the fixed stars), as a base of reference, such that all motions being treated as relative to this base, the Laws of Motion and the law of gravitation afford a consistent explanation of the observed motions of the bodies of the solar system.
109 He estimated the annual precession due to the sun to be about 9″, and that due to the moon to be about four and a half times as great, so that the total amount due to the two bodies came out about 50″, which agrees within a fraction of a second with the amount shewn by observation; but we know now that the moon’s share is not much more than twice that of the sun.
110 He once told Halley in despair that the lunar theory “made his head ache and kept him awake so often that he would think of it no more.”
111 December 31st, 1719, according to the unreformed calendar (O.S.) then in use in England.
112 The apparent number is 2,935, but 12 of these are duplicates.
113 By Bessel (chapter XIII., § 277).
114 The relation between the work of Flamsteed and that of Newton was expressed with more correctness than good taste by the two astronomers themselves, in the course of some quarrel about the lunar theory: “Sir Isaac worked with the ore I had dug.” “If he dug the ore, I made the gold ring.”
115 Rigaud, in the memoirs prefixed to Bradley’s Miscellaneous Works.
116 A telescopic star named 37 Camelopardi in Flamsteed’s catalogue.
117 The story is given in T. Thomson’s History of the Royal Society, published more than 80 years afterwards (1812), but I have not been able to find any earlier authority for it. Bradley’s own account of his discovery gives a number of details, but has no allusion to this incident.
118 It is k sin C A B, where k is the constant of aberration.
119 His observations as a matter of fact point to a value rather greater than 18″, but he preferred to use round numbers. The figures at present accepted are 18″·42 and 13″·75, so that his ellipse was decidedly less flat than it should have been.
120 Recherches sur la précession des équinoxes et sur la nutation de l’axe de la terre.
121 The word “geometer” was formerly used, as “géomètre” still is in French, in the wider sense in which “mathematician” is now customary.
122 Principia, Book III., proposition 10.
123 It is important for the purposes of this discussion to notice that the vertical is not the line drawn from the centre of the earth to the place of observation.
124 69 miles is 364,320 feet, so that the two northern degrees were a little more and the Peruvian are a little less than 69 miles.
125 The remaining 8,000 stars were not “reduced” by Lacaille. The whole number were first published in the “reduced” form by the British Association in 1845.
126 A mural quadrant.
127 The ordinary approximate theory of the collimation error, level error, and deviation error of a transit, as given in textbooks of spherical and practical astronomy, is substantially his.
128 The title-page is dated 1767; but it is known not to have been actually published till three years later.
129 For a more detailed discussion of the transit of Venus, see Airy’s Popular Astronomy and Newcomb’s Popular Astronomy.
130 Some other influences are known—e.g. the sun’s heat causes various motions of our air and water, and has a certain minute effect on the earth’s rate of rotation, and presumably produces similar effects on other bodies.
131 The arithmetical processes of working out, figure by figure, a non-terminating decimal or a square root are simple cases of successive approximation.
132 “C’est que je viens d’un pays où, quand on parle, on est pendu.”
133 Longevity has been a remarkable characteristic of the great mathematical astronomers: Newton died in his 85th year; Euler, Lagrange, and Laplace lived to be more than 75, and D’Alembert was almost 66 at his death.
134 This body, which is primarily literary, has to be distinguished from the much less famous Paris Academy of Sciences, constantly referred to (often simply as the Academy) in this chapter and the preceding.
135 E.g. Mélanges de Philosophie, de l’Histoire, et de Littérature; Éléments de Philosophie; Sur la Destruction des Jésuites.
136 I.e. he assumed a law of attraction represented by μ∕r2 + ν∕r3.
137 This appendix is memorable as giving for the first time the method of variation of parameters which Lagrange afterwards developed and used with such success.
138 That of the distinguished American astronomer Dr. G. W. Hill (chapter XIII., § 286).
139 They give about ·78 for the mass of Venus compared to that of the earth.
140 The orbit might be a parabola or hyperbola, though this does not occur in the case of any known planet.
141 On the Calculus of Variations.
142 The establishment of the general equations of motion by a combination of virtual velocities and D’Alembert’s principle.
143 Théorie des Fonctions Analytiques (1797); Resolution des Équations Numériques (1798); Leçons sur le Calcul des Fonctions (1805).
144 Théorie Analytique des Probabilités.
145 The
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