XXII. An improved solution of a problem in physical astronomy; by which, swiftly converging series are obtained, which are useful in computing the perturbations of the motions of the Earth, Mars, and Venus, by their mutual attraction. To which is added an appendix, containing an easy method of obtaining the sums of many slowly converging series which arise in taking

Abstract

Reverend Sir, Such is the subject of the inclosed paper, and such the repu­tation for skill and industry, which the many valuable papers you have communicated to the Royal Society, and your other learned works, have justly procured to you, that it could not with more propriety be submitted to the judgment of any other person than yourself, even if the writer of it were a stranger to you. But there are circumstances which render my presenting it to you, in some measure, a duty. I had the advantage of being, for some years, your Assistant in the Royal Observatory at Greenwich; during which time, you made the important observations on the mountain Schehallien , in Scotland, which afford an ocular demonstration of the attraction of that mountain, and a strong argument for the general attraction of matter, a subject nearly connected with that of the following pages; and it was from you that I received the problem of which you will here find an improved solution.