Tait — P)'Oof of Hamilton,'' s Principle of Varying Action. 69 



IX. — Proof of Hamilton's Principle of Varying Action, By Pro- 

 fessor Tait ; Communicated by Dr. Ball. 



[Eead, April 9, 1877.] 

 We have as usual, 



A = 2\Tdt, 

 8A=j{8T+8II-SVy(U 



= 2 



^se + ^sdy-80]dt + t8ir 



<^^ dO dO 



5 \{~] se\ + tSR 



uld J ) 



+ 2 J (terms disappeaiing in consequence of Lagrange's 

 Equations of Motion) 80dt, 



whence of course 



dA dT ^ 

 — = — , &c., 



d8 dO 



dA 



which is the essence of Hamilton's varying action. 



