Abstract
THE MASS OF JUPITER.—M. Leverrier has made a special communication to the Paris Academy of Sciences with reference to the bearing of his researches on the motion of Saturn, in a period of 120 years, on the value of Jupiter's mass. Laplace, in the Mécauique Céleste, had fixed 1/1067.09 making use of the elongation of the fourth satellite as determined by the observations of Pound, the contemporary of Newton, observations of which it appears we have no knowledge, except from the reference to them in the “Principia;”subsequently Bouvard, comparing Laplace's formulæ with a great number of observations, discussed with particular care, constructed new Tables of Jupiter, Saturn, and Uranus, in which important work he formed equations of condition, wherein the masses of the planets entered as indeterminates, and by the solution of which their values adopted in the Tables were obtained. The denominator for Jupiter's mass, expressed as a fraction of the sun's taken as unity, is 1070.0, and Laplace stated that on applying his theory of probabilities to Bouvard's equations it appeared to be nearly a million to one against the error of the mass thus deduced, amounting to one-hundredth part of the whole. M. Leverrier then refers generally to the discussion of the observations of several of the minor planets with the view to correcting the mass of Jupiter, and to the observations of elongations of the fourth satellite by the present Astronomer Royal at Cambridge, which last assigned for the denominator of the fraction 1046.77. He then remarks upon the circumstance of Bouvard having deduced from his comparison of the theory of Saturn with seventy-four years' observations a mass so nearly identical with that of the Mécanique Céleste; Bouvard left no details of his work behind him; it is only known that he adopted at the outset the value of Jupiter's mass admitted at the time, that-of Laplace, and M. Leverrier explains that on the method of procedure adopted, Bouvard could not do otherwise than reproduce at the termination of his calculations the value he had assumed at starting. This is illustrated by the result of Leverrier's solution of his own equations of condition, founded upon the much longer period of 120 years, which proved wholly insufficient for the correction of Jupiter's mass. He remarks, with respect to Bouvard's work, that any value of the mass taken arbitrarily within certain limits will allow of a tolerable representation of the observations of Saturn, on the condition that this same arbitrary value is introduced throughout in the functions representing the mean longitude, mean motion, excentricity and longitude of perihelion; the elements obtained by Bouvard are therefore found represented by these functions of his arbitrary quantity, and he reverts to the mass assumed at the commencement of his work.
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Our Astronomical Column . Nature 12, 455–456 (1875). https://doi.org/10.1038/012455c0
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DOI: https://doi.org/10.1038/012455c0