INVKSTKlATKP I!V TIIK MKTIIOD OF JET VIBRATION. 345 



It will be conveuient to set out together the meaning of the symliols employed: 



V = velocity of the jet (cm./sec.). 

 A = cross-section of tin- j-t (cm.*). 

 p = density of liquid (gm./om.*). 

 T = surface-tension (dynr/i-Mi.). 

 Q = VA = discharge of the jet (cm. 3 /8ec.). 



X. = 'iTTJk = wave-length corresponding to the vibration determined by for- 

 mula (I) (cm.). 



Let us suppose that the jx>lar equation of the surface of the jet is 



r = a + b, cos < . cos kz ......... ( 1 ). 



n is an integer greater than 1. The jet is here and in the sequel regarded as 

 horizontal and the plane </> = is also horizontal. According to Lord RAYKEIQH'S* 

 theory the surface-tension is determined by 



T _ y7T . _ 



"yFZJtt'SSRfia!}'*' x. P 



where 



, t f ,l\ - *S* l " ( ak ) 

 M " ( ~a'P + n'-rakl' n ak 



Vibrations corresponding to different values of n in (1) will lie independent of each 

 other. 



The development of Lord RAYLEIGH'S theory rests upon certain suppositions, 

 viz. : 



1. That the deviations from the circular-cylinder form are exceedingly small. 



2. That the vibrations are executed without any loss of energy. 



3. That the original velocity of the jet is the same over the whole cross-section. 



4. That the surface-tension is constant. 



Each of these hypotheses will now be viewed somewhat closer individually : 



1. This hypothesis is, in practice, impossible to carry out, as it is precisely on the 

 basis of the divergence from a cylindrical form that it is possible to determine the 

 \\ave-length, and the smaller the divergence the more difficult the determination 

 becomes. To reduce the uncertainty resulting from this, I have investigated a jet of 

 the same liquid partly with large, and partly with proportionally small deviation from 



* KAYI.KIGII, 'Roy. Soc Proc.,' 29, p. 71, 1879 ('Papers 1.,' p. 377). 

 VOL. ccvn. A. 2 Y 



