552] 
ON A DIFFERENTIAL FORMULA. 
557 
and thence 
h + J (a + b) + \!{H) = i If + V(f :3 - «)) {v + v'(»r - o)j, 
,.g + V(f-c) 
These also follow from the known differential formula 
that is, 
implying 
where a is a constant. 
4 (da^+df) = (h-k)(~ - ^ , 
4d%dr) _ cZ/t 2 rZA; 2 
V(! 2 -c) 
2acZ£ cZ/i eZA? 
V(f 5 - c) = V(F) + vTO ’ 
2eZ?7 _ eZ/i cZA; 
V(#) VW 
The foregoing integral formulae give at once 
cZ/i _ cZ£ cZ-?7 
Aff) = V(r lr Sj + VW-o)’ 
iZ& _ cZ| cZt? 
vW)“V(P-c) _ V(^-c)’ 
and substituting these values we find a = 1, and the differential formulae are then 
satisfied. 
We thence have 
const. = V{( a + h) (b + /¿)} + \/{{cl + k) (b + A;)}, 
as the integral of the differential equation 
dh dk _ 
7(H) 1 j(K)~