AND DEFORMATION <>i A THIN KLABTIC SHELL. 



.VJ7 



7. Vibrations of Spherical Sin //. 



15. Let us now apply the equations of Art. (13) to the discussion of the vibrations of 

 a spherical shell ; we have 



u*p . /)3H 3 / 2m ff, , m n <T| 



m + n kf m + n 



- 2 



2m 



m-n 



L - 



* T 



I -/-"> 



'^WV 



/ 5 p . -,3*1; _3/2m <r. , m n <7,\ 



sin _ := 2 ^ I " ? + 



n . ot* o<f> \m 4- n Aj m + n AI/ 



_ 2 3/IWJ^ 

 9^ \*i/ \ m + 



. /, 



- sm . , = 2 a on 



n 3r TO 



S\S 



3 T n 



m-n 



(45) 



In these we are to substitute for h lt h 2 their values 



h t I/a, ^ 2 = l/(a sin 



and for o-j, <r 2 , er their values from 



3u . 



a / \ . ./,s/f\ 



= 5- T^ -f Sin 53 1 T a 

 tty \Bu\ 6] off \3in 6] 



Let us take u, v, w as functions of < to be proportional to e*', then the period is 

 2ir/2> ; also take p*a?p = fl* 8 , where K is a number, then we have the three equations 



n 



| + w) 

 d& / 



<~ 



. '" 



(46) 



^(^+Mcot0 + 8 -^|+2M>). 



n 8 0) = 0, (47) 

 (48) 



