220] 
IN RELATION TO THE PROBLEM OF THREE BODIES. 
521 
C. III. 
66 
M. de Pontecoulant, in his Lunar Theory (1846), where the solar eccentricity is 
neglected, writes (p. 91), 
I d'R = fi + mJ d j?dt, 
(n' = mn = m, since n is there 
(p. 43), 
put equal to unity); and combining this with the equation 
r 2 dv 
(1 + s 2 ) dt 
we have 
(d'R = R-mh + 7 ^ d * 
J (1 +s 2 )dt 
and substituting this value of I d'R in the integral of Vis Viva (p. 41), 
'dr\ 2 Vdv- r 2 ds 2 2 1_ f ,, 
Vt) (1 4- s 2 ) dt 2 (1 + s 2 ) 2 dt 2 r^ a J ’ 
we have what is, in fact, Jacobi’s equation.