42 Mr. A. E. H. Love on the Motion of a 



Again, solving (1), the equation of the free surface, 



becomes 

 1 



Here 

 a 



Also 



IT/ dA^ dA^ dA\ 2 / BA^ dA^ BA\ 2 



A 4 L\^2 B^3 (3^2 (W \B^2 B-i"3 d«2 B«8/ 



+ /BA BA_BABA\ 2 "| 

 \d« 2 dya dy 8 cwJ 



3 W+ yi »+^) 



_ JL_ 



~A 2 

 so that 



Also A' = _L; 



A 2 

 thus 



-*+**KB)'+®)' + (g)r] ♦***>+/+<>+* oo 



and we have to substitute this in (6). 



By the principle of Least Action, the equations are to be 

 found by making the integral 



f Wi 9 +yi 9 + V+^ 2 +y 2 2 + ^+^ 2 +z/3 2 + ?3 9 )+x(* 



stationary, subject to the condition A = constant. 



Hence, taking a an arbitrary multiplier, the nine equations 

 of motion are of the type 



S 1= f*+4^ (8) 



