528 Mr. Hellins’s improved Solution of 
an ocular demonstration of the attraction of that mountain, and 
a strong argument for the general attraction of matter, a sub- 
ject 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. 
The diffidence with which I entered on a speculation which 
had engaged the attention of such learned men as Simpson, 
Euler, and De la Grange, is well known to you. Consi- 
dering the great abilities of these men, and the length of time 
which Euler, in particular, appears to have employed on the 
subject, all that I at first expected to effect was, to facilitate 
the summation of the slowly converging series by means of 
which they had computed the perturbations of the motions of 
the planets in their orbits, which arise from their actions on 
one another, by the force of gravity ; and that this might be 
done by a metjhod which I had some time before discovered, 
was evident, pn inspecting their series. Here, it is probable, I 
should have stopped, had not you been pleased to put into my 
hands a sheet of paper, written by the late Mr. Simpson, which, 
though very ingenious, was, by mistakes, which seem to have 
entered in transcribing it, rendered unintelligible to some emi- 
nent mathematicians who had perused it; in which state it 
had remained thirty-six years. On perusing this paper, the 
first thing that occurred to me was, a different method of find- 
ing the fluent, from that which had been used by Mr. Simpson; 
by which means, series converging by the powers of p were 
obtained, while the series brought out the common way lost all 
eonvergency by a geometrical progression, and a computation 
by it was more difficult than the computation of the length of 
