536 PROFESSOR KELLAND ON THE VIBRATIONS OF 



* '' 



IV. gives 



-rY r a= - cos 



.-. a(i r) 2 cos 2 - + az 2 0(7 Y) cos 2 <|> (1 *) sin 2 </>(z r) =0 



2 z 

 or a 3 i(i r)cos*(f) . a + t (z r) a (1 s) ('?) sin 2 = 



2(1-*) . 

 ^ - 1 2 



d> 



.. _ _ 



a 2 cos 4 (f> + 1 



Finally, I. gives to two dimensions 



o/-2 ^!\ /i ^/2 2% 

 2(z 2 -r 2 )-(l-*)(z 2 -/ 2 ) 



-r) f i 



. 

 ff 



_ 



2 a cos * 



i r 

 or . 



, 

 _ 2 (<_r) - (1-,) < = (1-.) 



2 



tan 



r = 



But if a be not equal to b, we have the following equations : 



-~ 



27-0 _ 2a 

 7 Y 



-'. CD 



