3.0. < Mr. Pickering’s Eulogy on 
himself (though now not much used), and sanctioned by his com- 
mentators. 
The immediate occasion of examining this subject, was an at- 
tempt made by a celebrated English mathematician, the late Mr. 
Emerson (in the notes to a new edition of La Motte’s Translation 
of the Principia), to prove the accuracy of two equations used in 
the case; this had also been before attempted by other commenta- 
tors on the Principia, as Gregory, Le Seur, and Jacquier ; “and in 
none of the editions (that Dr. Bowditch had seen), not even that 
published by Bishop Horsley, is any doubt of their accuracy ex- 
pressed or even insinuated.” Yet, the method sanctioned by these 
high authorities, would, as Dr. Bowditch states, always make the 
corrections in question “double of what they ought to be.” The 
method of La Place, which is also examined by Dr. Bowditch, 
though simple and elegant when used with a small number of ob- 
servations, becomes objectionable and inconvenient when the num- 
ber of observations is large.* 
In the same volume we have a concise but interesting paper on 
the great question of the permanency of the Solar System, which 
I shall notice more particularly hereafter. 
This was followed by an important paper on Doctor Matthew 
Stewart’s formula for computing the motion of the Moon’s apsides. 
It presents a curious case, in astronomical science, where a for- 
mula, apparently general, happened to be true only in the particular 
instance in which it was accidentally first used by its author. 
In the year 1763 Dr. Matthew Stewart, of Edinburgh, published 
his computation of the Sun’s distance from the earth by means of 
the motion of the Moon’s apsides ; and four years afterwards Bishop 
Horsley made a communication to the Royal Society of London in 
* Mem. Amer. Acad. Vol. IV. p. 62. 
