SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 291 

 From the equations (4) and (5) we get, by help of TAYLOR'S theorem, 



* 3r 2 8r 



and 



[ 





From (2), (6), and (7) can be found except for a constant, which can be determined 

 by the condition 



f2ir ra + f f2.r 



rdrd$=\ ^(a + WdS- = ira* ....... (8) 



Jo Ju Jo 



First Approximation. 



(Solution of the problem neglecting all terms of higher order than the first.) 

 From (G) and (7) we get 



and 



M _ T 



a a 

 Eliminating from (9) and (10), we get 



+F(I)-0 ....... (11) 



Putting F() = 0, (11) will be satisfied by 



T 

 $ = A? 1 " cos n3 sin gi when q 2 = s (n 8 n) ..... (12) 



DC' 



Introducing this in (9), we get 



P = -wcT^A cos n sin o, C = - o-^A cos nS cosg<+/(^). . . (13) 

 ct q 



From (10) we get, using (12) and (13), 



" (.) = const, 



which is satisfied by 



/() - C- 

 From (8) we get in this case 



= 0. 



2 P 2 



