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HI8T0EY OF PHYSICAL ASTKONOMY.

ticity. The fourth datum was the equation of the centre of the thirdsatellite, depending on the position of the perijove of the fourth. Thefifth was the motion of the apsides of the fourth satellite.

By comparing these data with his analytical formulae, Laplace determined ithe masses of the satellites and the ratio between the equatorial and polar iaxes of their primary. It appeared from his results that the third satellite >contained the greatest quantity of matter, and the first satellite the least *. !The mass of the third satellite was found to be about double the moon’s *mass, and that of the fourth satellite was equal to it. By assuming theequatorial axis of Jupiter to be equal to unity, he found that the polar axis jwas equal to .9280. It hence followed that the lengths of the polar andequatorial axes were very nearly as 13 to 14; a result which almostcoincides with that derived from micrometric measurements of the twoaxes. Laplace , indeed, considers that in this case theory conducts to a jmore accurate result than direct observation. It is assuredly one of the jgreatest triumphs that the human mind can boast of, to have been enabled ’to determine the precise shape of the planet, by merely observing theeclipses of the small bodies which circulate round him. j

Delambre determined the thirty-one elements of Laplace ’s theory by jcomparing together a vast number of eclipses observed by astronomers at idifferent periods. Having executed this important task, he then com- jputed the numerical values of all the equations, and employed them in the 1construction of ecliptic tables of the satellites. These tables were in- ,serted in the third edition of Lalande’s Astronomy , which was published jin the year 1792, and were found to surpass greatly in accuracy the tables iof Wargentin, and those of all preceding astronomers. '

The eclipses of the first satellite originally led to the discovery of thesuccessive propagation of light, and this important doctrine was afterwardsestablished upon an indisputable basis by Bradley’s discovery of aberra-tion. Laplace , however, conceived that the order of the inquiry might beinverted, by deriving the maximum value of aberration from the velocityof light, as indicated by the eclipses of the satellite. Having suggestedthis view of the question to Delambre, that indefatigable astronomerundertook the laborious task of computing the velocity of light by thediscussion of a great number of eclipses ; and from the result obtained byhim, he concluded that the maximum value of aberration is equal to |20".2o. This value agrees precisely with that which Bradley derived jfrom direct observations on a great number of stars. It is interesting to Itrace so close an agreement between two methods so widely different. This jcoincidence shews that the motion of light is uniform within the earth’s ;orbit, for the aberration is derived, in the one case from the velocity of Jlight in the earth’s orbit, and, in the other case, from the time which it <takes in traversing the diameter of the orbit. Its motion is also uniform jwithin the orbit of Jupiter , for the variations of the radius vector of theplanet are very sensible, and the differences in tlie times of eclipses whichthese occasion are found to correspond exactly with the supposition of theuniform motion of light.

* The following are the values of the masses of the satellites as given by Laplace in theMecanique Celeste, liv. viii. chap, viii., Jupiter ’s mass being supposed equal to unity.

Mass.

1st satellite 0.00001732812nd „ 0.0000232355

3rd „ 0.0000884972

4th „ 0.0000426591