Adding together a and c, we get 12.671840, which quantity is to 5 places of decimals the same as b. From this it follows that for an enormous period of time the 3 interior satellites cannot all be eclipsed at the same time; for in the simultaneous eclipses of II and III, I will always be in conjunction with Jupiter, and so on. Making use of his own tables, Wargentin has calculated that simultaneous eclipses of the 3 satellites cannot take place before the lapse of 1,317,900 years, and an alteration of only 0.33" in the annual motion of II would suffice to render the phenomenon for ever impossible. D'Arrest pointed out the commensurability, within a few hours, of 5187 revolutions of I, 2583 of II, 1281 of III, and 548 of IV, in 25o 55a, when the same geometric configuration will recur. The exact figures are given by him as follow: Revolutions. Days : Between satellites III and IV the following comparatively coarse approximation subsists. Seven times the period of the former (50d 1h 57m 53°520) exceeds by only 21m 1978 three times the period of the latter (50d 1h 36m 33.813). Moreover the periods of I, II, and III stand in the ratio of 1, 2 and 4, as near as may be. The following special elements are given by Hind. "The line of apsides of the IIIrd satellite revolves in about 137, and that of the IVth in about 516. The lines of nodes of the 3 exterior satellites revolve in a retrogade direction, as is the case with the nodes of the lunar orbit; the period for the IInd is 30o, for the IIIrd 140, and for the IVth 520." It occasionally, but very rarely, happens that all 4 satellites are for a short time invisible, being either directly in front of, or a Laplace demonstrated by the theory of Gravitation that if this relation be once approximately begun, it will always last. Acta Soc. Upsal., p. 41. 1743 s Ast. Nach., vol. lviii. No. 1377. Aug. 25, 1862. t Sol. Syst., p. 98. behind, the planet. Such was the case, according to Molyneux", on Nov. 2, 1681 (o. s.) The same thing was noticed by Sir W. Herschel on May 23, 1802; by Wallis on April 15, 1826; by Dawes and W. Griesbach on Sept. 27, 1843. Dawes published in 1862 an account of his observations". Jupiter's (apparent) deprivation of its satellites lasted about 35m. A repetition of this phenomenon occurred on Aug. 21, 1867, when the planet was for 13h apparently without satellites projected on the sky. The satellites appear to vary in brilliancy in a way wholly inexplicable. I have already stated that III is commonly the brightest; but Maraldi and Bond have seen the contrary. On the whole, perhaps, we are justified in saying that the faintest is IV; but the lustre of this is irregular: in 1711 Bianchini and another, and on June 13, 1849, Lassell, saw it so feeble as to be almost invisible, whilst Webb repeatedly saw it surpass III. This observer wrote-" Spots... may easily cause this variable light; but a stranger anomaly has been perceived,—the discs themselves do not always appear of the same size or form. W. Herschel noticed the former fact, and inferred the latter; and both have been since confirmed by others. Beer and Mädler, Lassell, Secchi and Buffham have sometimes seen the disc of II larger than I; and Lassell, and Secchi and his assistant, and Burton have distinctly seen that of III irregular and elliptical; and according to the Roman observers the ellipse does not always lie the same way: Mitchell also, with an 11-inch achromatic, has observed this disc irregular and hazy. Buffham has often found IV the smallest of all, and irregular-looking. Phenomena so minute hardly find a suitable place in these pages, but they seem too singular to be omitted; and in some cases, possibly small instruments [?] may indicate them; at least, with an inferior fluid achromatic reduced to 3 inches aperture I have sometimes noticed differences in the size of the discs which I thought were not imaginary.' Sir W. Herschel, by attentive and prolonged observation, was u Opticks, p. 271. w Month. Not., vol. xxii. p. 292. June 1862. * Celest. Objects, 4th ed., p. 162. led to infer that each of the satellites rotated on its axis in the same time that it made a sidereal revolution round its primary thus presenting an analogy to the case of our Moon. The immediate reason which led to this conclusion was a belief that the variation in their brilliancy always recurred in nearly the same positions of the satellites with respect to Jupiter and the Sun, which supposition had previously presented itself to the mind of Cassini'. But modern observations do not harmonise with these statements; that is to say, we are not entitled to affirm now that peculiarities in the appearances of the satellites correspond with definite orbital positions. On the contrary, the peculiarities observed are not governed by any known law of time or place. Arago thus summed up Sir W. Herschel's photometric deductions. "The Ist satellite is at its maximum brightness when it attains the point of its orbit which is almost midway between the greatest Eastern Elongation and its Conjunction. The brightest side of the IInd satellite is also turned towards the Earth when that body is between the greatest Eastern Elongation and Conjunction. The brightness of the IIIrd satellite attains 2 maxima in the course of a revolution, namely at the 2 Elongations. The IVth shines with a bright light only a little before and a little after Opposition"." Various observers have assigned colours, or rather tinges of colour, to the different satellites, but the results are not sufficiently of accord to be worth citing. Eclipses as viewed on Jupiter take place on a grand scale; for in consequence of the small inclinations of the orbits of the satellites to the planet's equator and the small inclination of the latter to the ecliptic, all the satellites, the IVth excepted, are eclipsed some time in every revolution; so that a spectator on Jupiter might witness during the Jovian year 4500 eclipses of the Moon (Moons) and about the same number of the Sun. Soon after their discovery it suggested itself to the reflecting y Mém. Acad. des Sciences, vol. i. p. 266. mind of Galileo that eclipses of the satellites of Jupiter might be made useful for determining the longitude. Regarding eclipses as instantaneous phenomena visible at the same moment in every place which has the planet above its horizon, it is clear that a comparison of observations recorded in 2 local times would afford data for determining the difference of time (longitude) between the places to which the times belong. Eclipses accurately predicted for one meridian when observed under another one would afford a still more advanced means of ascertaining the difference of longitude between them. These eclipses could be predicted if sufficiently accurate tables of the satellites were in existence; but at sea, where the problem has chiefly to be solved, they cannot be observed with the most refined accuracy, and on land some difficulties present themselves; so that the method to some extent breaks down, and is only available where very rough approximations will suffice. It was to observations of one of the satellites of Jupiter, and Römer's discussion of them in 1675, that we owe the discovery that light is not propagated instantaneously through space". It was found that the calculated times of the eclipses did not correspond with the observed times, and that the difference was a quantity constantly affected by opposite signs of error according as Jupiter was in perigee or apogee. In the former case the eclipse always occurred before the calculated time; in the latter, always after it. The regularity with which these anomalies showed themselves led Römer to suspect that they had their origin in the variations which occurred in the distance of Jupiter from the Earth that as this distance increased or diminished so a longer or a shorter period was requisite for light to traverse the space between the 2 planets. Assuming from the data in his possession that light travelled at the rate of 192,000 miles per second, and required 16m to traverse the diameter of the Earth's orbit, and applying this (as yet hypothetical) conclusion to the eclipses in the form of a trial-correction, Römer promptly obtained proofs of the accuracy of his reasoning; but it was Bradley's discovery Opere di Galileo, vol. ii. p. 33. Padua ed., 1744. Л of aberration some half a century later which completely demonstrated the soundness of Römer's views and caused their general acceptance. The modern experiments of Fizeau have given for the velocity of light a result but slightly differing in amount from Römer's, namely, 194,000 miles per second. Like most new discoveries Römer's did not, when promulgated, find favour in the scientific world, and many years elapsed ere it was generally accepted. 53.7 The mass of Jupiter has never been a very doubtful quantity, all the values of it being much more in accord with one another than is usually the case. Laplace, from Pound's observations of the IVth satellite, placed it at 1087; Bouvard, from the perturbations of Saturn, at 170; Nicolai, from the perturbations of Juno, at 107; Encke, from the perturbations of Vesta, at 10s; and from perturbations of the Comet bearing his name, at 1; Santini at Too; Bessel at 1057; Airy, from motions of the satellites, at 10677; Krüger, from observations of Themis, at 10; Jacob, from the motions of the satellites, at 107; and Möller, from the motions of Faye's Comet, at 107; Schur, from heliometer measures of the satellites, at Toy. Any one of the 4 last values may be taken to be substantially exact. το 105 1 10509 7.87 047.7 47.23. 04754 "The most ancient observation of Jupiter which we are acquainted with is that reported by Ptolemy in Book X. chap. iii. of the Almagest, and considered by him free from all doubt. It is dated in the 83rd year after the death of Alexander the Great, on the 18th of the Egyptian month Epiphi, in the morning, when the planet eclipsed the star now known as d Cancri. This observation was made on Sept. 3, B.C. 240, about 18h on the meridian of Alexandria." This is a convenient place to mention the "Great Inequality in the motion of Jupiter and Saturn, so far as the fact of its b In consequence of the increase in the received value of the Sun's parallax a reduction in the velocity of light by several thousands of miles per second must be assumed, and singularly enough some experiments of Foucault's made before the parallax question came up for general discussion pointed to the same conclusion. The value for the velocity of light now generally accepted is about 186,660 miles per second. |