J 



G66 Mr. J. Rice on the Form assumed 



Now apply the method o£ the Calculus of Variations taking 

 s as the independent variable, of which x and y are functions, 

 whose differential coefficients x and y are connected by the 

 relation 



x 2 + f = l (1) 



We have to find the condition for a minimum value of 



A x.T.ds, (2) 



B 



subject to the condition of constant volume, i. e. 



x . y . x . ds = constant (3) 



B 



Introduce an arbitrary constant c (whose value can after- 

 wards be determined from the known volume of the drop), 

 and we have to find the condition for a minimum value of 



•a 



(x . T -f- c xy . x) ds 



B 



subject to condition (1). This latter condition we can take 

 account of in the usual way by introducing an undetermined 

 function (^(5), and then seeking for a minimum solution of 



1 \x.T+cxy.x + (f>(s)[x 2 + y 2 -l] } ds. . (4) 



Call the function inside the brackets {} in (4) V, and let 

 hx and 8y stand for the variations of x and y due to the 

 changing forms of the functions connecting these quantities 

 with 5; also let Ax, Ay, As stand for the total variations 

 of x, y, s due to a movement of the point along the curve 

 combined with a change due to a deformation of the curve. 



Then by the usual methods of the calculus of variations 

 we obtain 



r 



♦[(~£-'SH 



alue 



A Vds=0 3 



.In 



Ldx " "by. 

 Now for a minimum value 



'A 



