43] WHICH OCCUR IN DYNAMICAL PROBLEMS. 281 
where for greater clearness an additional letter of the series ©, <f> ... has been introduced, 
and where 
a = 
b = 
(d<& y /d<&V 
\dx) \dy) 
ffîî+(Tï+-’ 
\dxj \dy) 
fd® d$? d% d!<I>\ 
V dx dx dy dy ) 
Hence differentiating with respect to x', 
d© d\ 7 d/i dv 
28 ~chc + a ~dx' + 1 dx / + 9 № 
2 $ < *®+h ( ^ } + b^,+ f dv 
dx 
dx ' dx' ' " dx' 1 J dx'" 
^ dfy dX , dii dv 
yh dx +9 M + f dF +C dF"‘ 
dx' 
= 0, 
= 0, 
= 0; 
or representing by K the determinant formed with the quantities a, h, g, ... h, b, f,... 
g, f, c, ... and by A, H, G, ... H, B, F, ... G, F, C, ... the inverse system of coefficients, 
we have 
dx dx dx 
+ K 
dX 
dx' 
0, 
Vgsr.