Littell's Living Age/Volume 127/Issue 1646/Miscellany

The Theory of Saturn. — M. Le Verrier has given in the Comptes Rendus the comparison between his tables of this planet's motion and the observations made at Greenwich for the last hundred and twenty years, and at Paris for the last thirty years. There are peculiar difficulties in the analytical theory arising from the circumstance that numberless small terms of the second order in the expression for the perturbations, instead of destroying each other on the average, as is usually the case, are added together and thus produce by their combination a sensible effect, so that M. Le Verrier has had to carry his approximations to the seventh degree. Not satisfied with this, he has, by considering this solution as merely a first approximation, obtained a rigorous theory, in which the complete expression of each of the terms is obtained, instead of an infinite series, of which only a limited number of terms can be calculated by successive approximations. But, notwithstanding all the pains that M. Le Verrier has taken, there remain discordances between theory and observation which were not found in the case of Jupiter, and, though these are not very large, the result is anything but satisfactory, especially as the Paris observations agree well with those made at Greenwich. In the ancient observations from 1750 to 1827 especially, there are very large outstanding errors, but the most remarkable discordance is shown about 1840, the error of longitude having changed from plus 5s. in 1839 to minus 5s. in 1843, an interval of only four years; whilst the difference between the Paris and Greenwich results nowhere exceeds 2s. The only explanation that M. Le Verrier can suggest is that the presence of the ring may have influenced the observation of the ball of the planet; but so many observers took part in these observations, and the circumstances were so exactly similar during the period in question, that the explanation cannot be considered very satisfactory, especially as the ring was not in a position to interfere materially with the observation. At the same time the theory of this planet's motion is complicated from the effect of the attraction of its neighbour, Jupiter, giving rise to the wellknown inequality of about 49m. either way in the longitude of Saturn in the space of about 918 years, besides oscillations in the eccentricity and node in a period of 70,000 years, and a host of minor inequalities.

But, though the influence of Jupiter on the motion of Saturn is so great, M. Le Verrier has come to the conclusion that the observations at present available are insufficient to determine the mass of the disturbing planet, owing to a peculiar compensation in its effect on the four elements affected by it, this compensation having operated to a great extent throughout the period under consideration, so that the longitude is only slightly affected by an alteration in the mass of Jupiter. M. Le Verrier considers, therefore, that Bouvard's determination of this mass was an instance of reasoning in a vicious circle, and that the close agreement between his result and that deduced from observations of the satellites was simply a consequence of his having used the latter value in his theory, and, that he must of necessity have been led round to the same value again. But though nothing can at present be concluded with regard to this point, circumstances will change in course of time, and instead of the effect of Jupiter's mass disappearing it will enter with its full weight, and can then be accurately determined by means of the theory of Saturn. For the present, however, M. Le Verrier considers that the value found by Sir George Airy from measures of Jupiter's fourth satellite is that which should be adopted.

END OF VOLUME CXXVII.

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