resulting from Hamilton's Theory of Motion, 291 



the result is 



and from this the integral 



W= f X /2gl* + 2l*E-gl a 2 dd. . . (12) 



If we now form out of (11) and (12) the differential quotients 



__ ay _ eu/gi e h/gi 



tanx/^t sm a/ 9- 1 



dW 



= \/2gl 3 + 2m-gl 3 6*, 



dW 



= -*s/ZgP + 2l*&-gl*ei> 



and introduce them into the action-equation, we get 



Wgl[ 



-'o% + eM 



(It 



dt ■ 





It 



=s/2gl 3 + 2PE-ffl< > d 2 M 



d9, 



V2gP + 2PE-gl»0l-3f 



(13) 



Indeed it can be readily shown that the individual derivata 

 are/? andjp respectively. Tor if the quantity p be eliminated 

 from the second of the integral equations for example by aid of 

 the first, we get immediately 



r ^_ 6ls/~gl_ __0 9 l>/gl = _^ 



tan a/ 9. t sin a/2 t 



~de 



and if we put this value of p in the expression of the energy, it 

 changes into 



E = 



gl s 0*co S *^t~2gim o cos^Zt+gm> 



— ~~9\ 



2/ 2 sin 



and hence 



iVjf, 



\ 



■be 



V 



glW cos 8 a/2 *~-2pZ'W cos aA t+gl^l 



sin 

 U2 



«M 



-=p. 



