SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 293 



Putting 



F (t) = qn (4n+ 3) a 2 "- 2 A a sin 2qt, 



(19) will be satisfied by 



4> = Ar" cos nS sin at *-, , ' \ n i A.V 2 " cos 2nS sin 2qt, (20) 



R i V'/) -t- 1 \ fiff 



when, as by first approximation, 



<7 2 / 3 ti^ /91\ 



w ~ i it it i, (^ A / 



pci 



Introducing this in (17), we get 



3 . A2 n 2 2n 3 -7n 2 -2n + 4 2n _ 3 



= na A cos n.9 sin ot+A - a cos 2%^ sin 2qt 



dt 4o 2w a +l 



- - (22) 

 * 

 from (22) we get 



=- Aa"- 1 cos n& cos at- A 2 - n \ 2n * 7n ' a 2 "- 3 cos 2A cos Iqt 



q 8r/ 2w J 



. (23) 

 U 1 



Introducing in (18) the values found for </>, q, , and F' (i), we get 



= -A 2 ^ 



2 



which is satisfied by 



(24) 



By (8) we get in this case 



rj ^ A 2 ^2n-3 (25^ 



From (23), (24), and (25) we get 



-1 cos n& cos at A 2 ~ 3 a 2 "" 3 cos 2n9- cos 



8q* 2rt J +l 



+ A 2 / M ~ a 2 "" 3 cos 2n^-A 2 - 2 a 2 "" 3 cos 2 g ^-A 2 - a 2 "- 3 . . (26) 

 S^ 2 2w 1 8q 3 8q* 



Third Approximation. 

 From (6) and (7) we get 



._. 



8r 2 2 3r 3 r 3 95 8S r 2 Brfo 



