L 63 3 
u neceffarily arife two different values of the diftance 
“ x, for the fame attra&ive force. 3 ’ 
Sufpedting therefore, that fome error muff have 
llipt into Mr. Clairaufs reafonings (as he himfelf 
afterwards found there had) I refolved to try, whe- 
ther, by an arithmetical calculation, from Sir Ifaac 
Newton’s propofitions only, the motion in queftion 
might not be accounted for. 
The refult of this inquiry I ffiould have taken the ' 
liberty to fend you before now, but that, other things 
intervening, I did not think of revifing and tran- 
fcribing it, till lately; that Mr. Walmefley having 
made me a prefent of his ingenious treatife on the 
fame fubjedt, it appears, that, however Mr. Clairaut’s 
hypothecs is given up, yet a notion ff ill prevails, as if 
Sir Ifaac Newton’s propofitions, concerning the mo- 
tion of apfids , were mere mathematical fictions, not 
applicable to nature. 
How far I have fucceeded in fhewing the contrary, 
is now fubmitted to your judgment. . And I, at the 
fame time, embrace, with pleafure, an opportunity 
of profeffing myfelf, with the higheft refpedt, 
Sradifhall, 6 April, 
1750 . 
Reverend Sir, 
Your moft obliged, and 
moff obedient humble fervant, 
Pat. Murdocke. 
Of 
