SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 297 



Considering the fluids as inviscid, we can suppose the existence of a velocity- 

 potential <f). Putting 



we get 



9r 2 r 3r r 2 * 

 which gives 



/(*) - 



As the velocity, as well inside as outside the cylinder-surface, must not be infinitely 

 great, the potential inside the surface must be 



and outside 



< 2 = Br-V B 



Let the surface be expressed by 



r-a = = C 

 For r = a the following conditions must be satisfied : 



From (1) we get 



B =^ Act 2 " and 



from (2) we get 



Introducing in (3) the values found for < 1; < 2 , and , we get 



T n a -n 



In the above we have investigated the influence on the phenomenon in question of 

 the viscosity of the liquid, the magnitude of the wave-amplitudes, and the inertia of 

 the air.* Collecting the results found, we get the following formula for determination 

 of the surface-tension, setting n = 2, as will be the case in the experiments : 



..iat) I" /2t_r + 3 / ^ V] L + 37 V 

 ' (3 + 2 F) ia* J' a (tai) [ \pca 8 V Vca^/ J \ 24 a 2 ' 



* The corrections are to be considered as additive, since it can be shown that the wave-length also in 

 the case of viscosity will be an even function of b/a. 

 VOL. CCIX. A. 2 Q 



