Cd 
Central Forces. ° ; 343 
d' _ ’ 
Ss — by substituting these values of P and §, and for T its val- 
Bf, \n) ae 
d 
ae a in (A), (B), (C) they become dt= 
po Seen "ee 
), wae | 
mt Te) 
ds dQ dQ = dQ * 
tea a ) cet z 2) 1G = ds | ee 
tions (K) given at p. 151, Vol. I. of the Mécanique Celeste. 
z dQ\ d dv? : 
(A’) is easily changed to h? +INF f 2) oe a =0, whose dif- 
dv d?tdv? 2dv?du 
ferential, regarding dv as constant, gives (32) wt wide + wate 
d2t 2d ae dt* - ; 
=0, *. +g = ue (@) * pi = 03 hence, and by reducing 
(B9, (C) to a common denominator, rejecting the denominator and 
d*t  2dudt 
dividing by A? also dividing (C’) by u*, there results 7 +7 qa 
= (G2) 5 T= (A, (Gate) - (45 ga (a): a) + i 
(2): 3.-(B)-3(2)) =. @. (t+) 
nes me): ) +a (Ze dv (2) -w(F =) - -40)(@))=o 
(C”), which agree with the equations (L) given at the place cited . 
above 
Again, supposing the disturbing force to be situated in the plane of 
the curve described by the particle around the first centre ; let s de- 
note the length of the curve described in any time, p= the perpen- 
dicular from the first centre to the tangent at the extremity of s, )= 
the oe at which the radius vector (7) cuts s, i” ae= the ve- 
locity, FF = R= half the chord.of the equicurve circle with s, at 
