968 DR JOHN DOUGALL ON AN ANALYTICAL THEORY OF THE 



For brevity we write 



and 



/92m; dho\ 

 V8f2+8^J 



3?< . dv\ _ 3m ) 



^T),{^o), 



(4) 



3m dv 



£ fdu dv\ I , /3« 3w\ -. dv ) „ , 

 H3^ + 37) + ^lH3l + 3-J + '%} "^^^^'^)' 



= hi^")- 



^%+ V ' 



Then the equations of equilibrium (2) and (3) may be arranged as follows :— 



.a-{D,K,.„) + (XH-,)|^ + ,^^2} 



^ = 0, 



+ 



+ a-*D2(M_2 , W-2) 



+ «-3{D2(^._,,._,) + (X + ;.)|^J^^ 



+ «-2{d2(«o, .o) + (^ + /^)9-/-^ + /.'^^ 



+ 



1 = 0, 





.<.-{D>_,).(X..>i(?|..^)} 



3A 3| 3^ 

 + . . . 



= 0, 



Uo, 



(6) 



(7) 



(8) 



(9) 



