A Short History of Astronomy, Arthur Berry [large screen ebook reader .TXT] 📗
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48 The Commentariolus and the Prima Narratio give most readers a better idea of what Coppernicus did than his larger book, in which it is comparatively difficult to disentangle his leading ideas from the mass of calculations based on them.
49 Omnis enim quæ videtur secundum locum mutatio, aut est propter locum mutatio, aut est propter spectatæ rei motum, aut videntis, aut certe disparem utriusque mutationem. Nam inter mota æqualiter ad eadem non percipitur motus, inter rem visam dico, et videntem (De Rev., I. v.).
I have tried to remove some of the crabbedness of the original passage by translating freely.
50 To Coppernicus, as to many of his contemporaries, as well as to the Greeks, the simplest form of a revolution of one body round another was a motion in which the revolving body moved as if rigidly attached to the central body. Thus in the case of the earth the second motion was such that the axis of the earth remained inclined at a constant angle to the line joining earth and sun, and therefore changed its direction in space. In order then to make the axis retain a (nearly) fixed direction in space, it was necessary to add a third motion.
51 In this preliminary discussion, as in fig. 40, Coppernicus gives 80 days; but in the more detailed treatment given in Book V. he corrects this to 88 days.
52 Fig. 42 has been slightly altered, so as to make it agree with fig. 41.
53 Coppernicus, instead of giving longitudes as measured from the first point of Aries (or vernal equinoctial point, chapter I., §§ 11, 13), which moves on account of precession, measured the longitudes from a standard fixed star (α Arietis) not far from this point.
54 According to the theory of Coppernicus, the diameter of the moon when greatest was about 1∕8 greater than its average amount; modern observations make this fraction about 1∕13. Or, to put it otherwise, the diameter of the moon when greatest ought to exceed its value when least by about 8′ according to Coppernicus, and by about 5′ according to modern observations.
55 Euclid, I. 33.
56 If P be the synodic period of a planet (in years), and S the sidereal period, then we evidently have (1∕P) + 1 = 1∕S for an inferior planet, and 1 - (1∕P) = 1∕S for a superior planet.
57 Recent biographers have called attention to a cancelled passage in the manuscript of the De Revolutionibus in which Coppernicus shews that an ellipse can be generated by a combination of circular motions. The proposition is, however, only a piece of pure mathematics, and has no relation to the motions of the planets round the sun. It cannot, therefore, fairly be regarded as in any way an anticipation of the ideas of Kepler (chapter VII.).
58 It may be noticed that the differential method of parallax (chapter VI., § 129), by which such a quantity as 12′ could have been noticed, was put out of court by the general supposition, shared by Coppernicus, that the stars were all at the same distance from us.
59 There is little doubt that he invented what were substantially logarithms independently of Napier, but, with characteristic inability or unwillingness to proclaim his discoveries, allowed the invention to die with him.
60 A similar discovery was in fact made twice again, by Galilei (chapter VI., § 114) and by Huygens (chapter VIII., § 157).
61 He obtained leave of absence to pay a visit to Tycho Brahe and never returned to Cassel. He must have died between 1599 and 1608.
62 He even did not forget to provide one of the most necessary parts of a mediæval castle, a prison!
63 It would be interesting to know what use he assigned to the (presumably) still vaster space beyond the stars.
64 Tycho makes in this connection the delightful remark that Moses must have been a skilled astronomer, because he refers to the moon as “the lesser light,” notwithstanding the fact that the apparent diameters of sun and moon are very nearly equal!
65 By transversals.
66 On an instrument which he had invented, called the hydrostatic balance.
67 A fair idea of mediaeval views on the subject may be derived from one of the most tedious Cantos in Dante’s great poem (Paradiso, II.), in which the poet and Beatrice expound two different “explanations” of the spots on the moon.
68 Ludovico delle Colombe in a tract Contra Il Moto della Terra, which is reprinted in the national edition of Galilei’s works, Vol. III.
69 In a letter of May 4th, 1612, he says that he has seen them for eighteen months; in the Dialogue on the Two Systems (III., p. 312, in Salusbury’s translation) he says that he saw them while he still lectured at Padua, i.e. presumably by September 1610, as he moved to Florence in that month.
70 Historia e Dimostrazioni intorno alle Macchie Solari.
71 Acts i. 11. The pun is not quite so bad in its Latin form: Viri Galilaci, etc.
72 Spiritui sancto mentem fuisse nos docere, quo modo ad Coelum eatur, non autem quomodo Coelum gradiatur.
73 From the translation by Salusbury, in Vol. I. of his Mathematical Collections.
74 The only point of any importance in connection with Galilei’s relations with the Inquisition on which there seems to be room for any serious doubt is as to the stringency of this warning. It is probable that Galilei was at the same time specifically forbidden to “hold, teach, or defend in any way, whether verbally or in writing,” the obnoxious doctrine.
75 This is illustrated by the well-known optical illusion whereby a white circle on a black background appears larger than an equal black one on a white background. The apparent size of the hot filament in a modern incandescent electric lamp is another good illustration.
76 Actually, since the top of the tower is describing a slightly larger circle than its foot, the stone is at first moving eastward slightly faster than the foot of the tower, and therefore should reach the ground slightly to the east of it. This displacement is, however, very minute, and can only be detected by more delicate experiments than any devised by Galilei.
77 From the translation by Salusbury, in Vol. I. of his Mathematical Collections.
78 The official minute is: Et ei dicto quod dicat veritatem, alias devenietur ad torturam.
79 The three days June 21-24 the only ones which Galilei could have spent in an actual prison, and there seems no reason to suppose that they were spent elsewhere than in the comfortable rooms in which it is known that he lived during most of April.
80 Equivalent to portions of the subject now called dynamics or (more correctly) kinematics and kinetics.
81 He estimates that a body falls in a second a distance of 4 “bracchia,” equivalent to about 8 feet, the true distance being slightly over 16.
82 Two New Sciences, translated by Weston, p. 255.
83 The astronomer appears to have used both spellings of his name almost indifferently. For example, the title-page of his most important book, the Commentaries on the Motions of Mars (§ 141), has the form Kepler, while the dedication of the same book is signed Keppler.
84 The regular solids being taken in the order: cube, tetrahedron, dodecahedron, icosahedron, octohedron, and of such magnitude that a sphere can be circumscribed to each and at the same time inscribed in the preceding solid of the series, then the radii of the six spheres so obtained were shewn by Kepler to be approximately proportional to the distances from the sun of the six planets Saturn, Jupiter, Mars, Earth, Venus, and Mercury.
85 Two stars 4′ apart only just appear distinct to the naked eye of a person with average keenness of sight.
86 Commentaries on the Motions of Mars, Part II., end of chapter XIX.
87 An ellipse is one of several curves, known as conic sections, which can be formed by taking a section of a cone, and may also be defined as a curve the sum of the distances of any point on which from two fixed points inside it, known as the foci, is always the same.
Thus if, in the figure, S and H are the foci, and P, Q are any two points on the curve, then the distances S P, H P added together are equal to the distances S Q, Q H added together, and each sum is equal to the length A A′ of the ellipse. The ratio of the distance S H to the length A A′ is known as the eccentricity, and is a convenient measure of the extent to which the ellipse differs from a circle.
88 The ellipse is more elongated than the actual path of Mars, an accurate drawing of which would be undistinguishable to the eye from a circle. The eccentricity is 1∕3 in the figure, that of Mars being 1∕10.
89 Astronomia Nova αἰτιολογητος seu Physica Coelestis, tradita Commentariis de Motibus Stellae Martis. Ex Observationibus G. V. Tychonis Brahe.
90 It contains the germs of the method of infinitesimals.
91 Harmonices Mundi Libri V.
92 There may be some interest in Kepler’s own statement of the law: “Res est certissima exactissimaque, quod proportionis quae est inter binorum quorumque planetarum tempora periodica, sit praecise sesquialtera proportionis mediarum distantiarum, id est orbium ipsorum.”—Harmony of the World, Book V., chapter III.
93 Epitome, Book IV., Part 2.
94 Introduction to the Commentaries on the Motions of Mars.
95 Substantially the filar micrometer of modern astronomy.
96 Galilei, at the end of his life, appears to have thought of contriving a pendulum with clockwork, but there is no satisfactory evidence that he ever carried out the idea.
97 In modern notation: time oπf oscillation = 2π√(l∕g).
98 I.e. he obtained the familiar formula (v2)∕r, and
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