1879.J the Capillary Phenomena of Jets. 97 



If T be the cohesive tension, the potential energy is 



P=29rT2(»-l)'(»+2)(2»+l)- 1 a» a . . (36). 



We have now to calculate the kinetic energy of the motion. The 

 velocity-potential may be expanded in the series 



0=/3 o +/VPiOO+ • • +fttf*P*G0 + • (37); 

 and thus for K we get 



K=y [ L ikd&=ip . 2^ [ +1 W dfjL=i P . W . 2 (272- + 1) -% o?»-- w. 

 JJ J-i ar 



But by comparison of the value of ^ from (37) with (33), we find 



at 



and thus 



K=2^ P a^(2n+l)-hi-^(^J . . . (38). 



Since the products of the quantities a n and do not occur in the 



etc 



expressions for P and K, the motions represented by the various terms 

 occur independently of one another. The equation for a u is .by 

 Lagrange's method 



^+<»-l)(*+2)-2^==0 . . (39); 



air pa 6 



so that, if a n oc cos (pt + e), 



_p»=»(»-l)(»+2)-? r (40). 



The periodic time t given in the text (equation (10) ) follows from 

 (40) by putting T=2irp- 1 , n=2, Y==f Tret 3 , 



To find the radius of the sphere of water which vibrates seconds, 

 put p = 27r, T = 81, /> = 1, n=2. Thus <x=2*54 centims., or one inch 

 almost exactly. 



The Society adjourned over Ascension Day to Thursday, May 29. 



VOL. XXIX. 



H 



