Central Forces. / 4843 
dQ ¢ e oe ‘ 
S=—u-7~> by substituting these values of P and S, and for T its val- 
al hci curs 
eV MeN) 3 
sieee()ti-()-H(2)_ tt 
dQ . 
ue u7> in (A), (B), (C) they become dt= 
4: (22) (29) sen. () 
w. (eons Zl <2) 
tions “ given at p. 151, Vol. I. of the Mécanique Celeste. 
._ ,{dQ\ d dv? 
(A’) is easily changed to h? of(2) = aa =0, whose dif- 
‘ : s dQ\ dv_ d?tdv?_ 2dv?du 
ferential, regarding dv as constant, gives (Fe) get aegis + dé 
_. d?t  Qdudt (22). dts 
=0, (C’); which are the equa- 
Sear dae ® \ da} Gee ee hence, and by reducing 
(B’), (C’) to a common denominator, rejecting the denominator and 
d*t  2dudt 
dividing by A? also dividing (C’) by u®, there results 5-5-+}—g-+ 
dQ ~ i dQ dv i- 
(2) a= 0, (a”),(S2 pu (45° S (Fe) ; =) hz 
((i) rae (ae) wae) =0, 9, (0) C4 
Jes) aa) tear (Ge (ae)—™ (Ge) 04) =o 
”), which agree oe ee 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, }= 
a d. 
the angle at which the radius vector (7) cuts s, F —=V = a= the ve- 
; d 
locity, ‘b= R= half the chord of the equicurve circle with s, at 
