408 The Inverfe Method, 
centre be required, it will immediately be 
found by making P=o in the three firft of 
‘he above theerems. 
PROPOSITION Itt. 
it a body be acted upon by two forces tending 
to the fame centre, which vary as the nth. 
and the gth. powers of the diftance reciprocally ; 
it is required to determine the equation of the 
orbit it will defcribe, &c. 
Suppofe the whole force acting upon the 
body, at the diftance y from the centre, to be 
Ants Bar 
——— 
—— 
; hence, by proceeding as in 
bi o 
: P*v v 
the firft Propofition, we fhall have ee 
Are ytd yt Bre 
—— OO —— 
g—1 Kr * h aah g—i . rt 
qt yf om Bot salt 
Co Bea (“Let = vy", then 
EEN qa) . rt 
¢ a xt yt 
there arifes —-— 1 = ——_—=—- + 
P ih ae 
a ae reshape 
Hence by reduction it will ap- 
1m 
‘ pear 
