Researches in physical astronomy

Abstract

The first part of this paper relates to the theory of the moon. The method of solution pursued by Clairaut consisted in the inte­gration of differential equations, in which the true longitude of the moon is the independent variable: the time is then obtained in terms of the true longitude; and by the reversion of series, the lon­gitude afterwards obtained in terms of the time. This method is the one adopted by Mayer, Laplace, and Damoiseau. The au­thor has been led, by reflecting on the difficulties of this problem, to believe that the integration of the differential equations in which the time is the independent variable would be at least as easy as the former process; and it would possess the advantage of employing the same system of equations for the moon as for the planets. The lunar theory proposed by the author, and developed in this paper, is an extension of the equations given in his former Researches in Physical Astronomy, already published in the Philosophical Trans­actions; by including those terms, which, in consequence of the great eccentricity of the moon’s orbit, are sensible; and by sup­pressing those which are insensible from the great distance of the sun, the disturbing body. He has not yet attempted to obtain numerical results, but proposes at some future time to engage in their computation. In the second part of the paper, he investigates the precession of the equinoxes, on the supposition that the earth revolves in a re­sisting medium; an investigation which may also be considered as a sequel to the author’s last paper on Physical Astronomy. The effects of the resistance of such a medium is to increase the latitude of the axis of rotation (reckoned from the equator of the figure) till it reaches 90°. Such is now the condition of the axis of the earth: but as the chances are infinitely great against this having been its original position, may not its attainment of this position be ascribed to the resistance of a medium of small density acting for a great length of time, —a supposition which may account for many geological indications of changes having taken place in the climates of the earth ? The operation of such a cause would be also sen­sible in the case of comets: and the accuracy with which the ec­centricity of the Halleian comet of 1759 is known, would appear to afford a favourable opportunity of verifying this hypothesis.