[ 62 ] 
XI. A Letter from the Rev. Patrick Mur- 
docke, F. R . S. concerning the mean Motion 
of the MoonV Apogee, to the Rev. Dr. 
Robert Smith, M after of Trinity College 
Cambridge. 
Reverend Sir, 
Head Jan. 31. ‘ »r AST fummer, when I was to pay 
17S °' 1 J my refpe&s to you at Trinity Col- 
lege, I gave you fome account of the warm difpute, 
then lately arifen between Mr. de BufFon and Mr. 
Clairaut, two eminent academicians at Paris j the 
latter pretending, that the Newtonian law of attrac- 
tion is inconfiflent with the motion of the moon’s 
apogee; and that its quantity ought not to be ex- 
preffed by ~ of the difiance, but by two, or perhaps 
more, terms of a feries, as — + -7. Which new doc- 
7 x x* 
trine Mr. Clairaut had got inferted in the memoirs 
of the academy, and Mr. de BufFon had followed him 
dole with another memoir, confuting it. 
When I firfl heard of this controverfy, it was im- 
poffible to judge of the validity of Mr. Clairaut’s rea- 
sons, becaufe he kept his calculus a profound fecret. 
But an abfurd confequence of his new law of attrac- 
tion occurred to me, as foon as Mr. de BufFon men- 
tion’d the thing, that, “ if we fhould put the at- 
“ tradiion, exprefs’d by his two terms, of an afFumed 
u quantity G f and refolve the equation, there would 
4 u necefFarily 
