Bailly's earliest researches on Jupiter's satellites began in 1763.
The subject was happily chosen. Studying it in all its generalities, he showed himself both an indefatigable computer, a clear-sighted geometer, and an industrious and able observer. Bailly's researches on the satellites of Jupiter, will always be his first and chief claim to scientific glory. Before him, the Maraldis, the Bradleys, the Wargentins had discovered empirically some of the principal perturbations that those bodies undergo, in their revolving motions around the powerful planet that rules them; but they had not been traced up to the principles of universal attraction. The initiative honour in this respect belongs to Bailly. Nor is this honour decreased by the ulterior and considerable improvements that the science has since received; even the discoveries of Lagrange and of Laplace have left this honour intact.
The knowledge of the satellitic motions rests almost entirely on the observation of the precise moment when each of those bodies disappears, by entering into the conical shadow, which the immense opaque globe of Jupiter projects on the opposite side from the sun. In the course of discussing a multitude of these eclipses, Bailly was not long in perceiving that the computers of the Satellitic Tables worked on numerical data that were not at all comparable with each other. This seemed of little consequence previous to the birth of the theory; but, after the analytical discovery of the perturbations, it became desirable to estimate the possible errors of observation, and to suggest means for remedying them. This was the object of the very considerable work that Bailly presented to the Academy in 1771.
In this beautiful memoir, the illustrious astronomer developes the series of experiments, by the aid of which each observation may give the instant of the real disappearance of a satellite, distinguished from the instant of the apparent disappearance, whatever be the power of the telescope used, whatever be the altitude of the eclipsed body above the horizon, and consequently, whatever be the transparency of the atmospheric strata through which the phenomenon is observed, also whatever be the distance from that body to the sun, or to the planet; finally, whatever be the sensibility of the observer's sight, all which circumstances considerably influence the time of apparent disappearance. The same series of ingenious and delicate observations led the author, very curiously, to the determination of the true diameters of the satellites, that is to say, of small luminous points, which, with the telescopes then in use, showed no perceptible diameter.
I will rest contented with these general considerations; only remarking, in addition, that the diaphragms used by Bailly were not intended only to diminish the quantity of light contributing to the formation of the images, but that they considerably increase the diameter, and in a variable way, at least in the instance of stars.
Under this new aspect, it will be requisite to submit the question to a new examination.
Any geometers and astronomers who wish to know all the extent of Bailly's labours, must not content themselves with consulting the collections in the Academy of Sciences; for he published, at the beginning of 1766, a separate work under the modest title of Essay on the Theory of Jupiter's Satellites.
The author commences with the Astronomical History of the Satellites. This history contains an almost complete analysis of the discoveries by Maraldi, by Bradley, by Wargentin. The labours of Galileo and his contemporaries are given with less detail and exactness. I have thought that I ought to fill up the lacunæ, by availing myself of some very precious documents published a few years since, and which were unknown to Bailly.
But this I will do in a separate notice, free from all preconceived ideas, and free from all party spirit; I will not forget that an honest man ought not to calumniate any one, not even the agents of the Inquisition.