r 7.1- ] 
XII. A Letter from Mr. John Robcrtfon, 
Lib. R. S. to James Weft, Pr eft- 
dent of the Royal Society ; containing the 
Demonflration of a Law of Motion^ in 
the Cafe of a Body defleSied by two Forces 
tending confantly to two fixed Points. 
S I R, 
Read April 6, H E late Mr. Machin (who was, 
1/69. many years, fecretary to the 
Royal Society, and Grediam profelTor of agronomy) 
gave to the editor of the Englilh edition of Sir Ifaac 
Newton’s Principia, publidied in the year 1729, a 
tradt entitled, “ The Laws of the Moon’s Motion 
“ according to Gravity,” which was annexed to that 
impreffion : Mr, Machin, in the Poftfeript to that 
tract, after apologizing for not mentioning the funda- 
mental principles of the demonflration of the propo- 
fitions relating to the Moon’s motions, fays, “ Some 
cf which, I am apt to think, cannot eafily be 
“ proved to be either true or falfe, by any methods 
“ which are now in common ufe.” 
One of thefe principles he gives In the following 
words : 
“ There is a law of motion which holds in the 
“ cafe where a body is defledled by two forces, 
tending conflantly to two fixed points. 
“ Which 
