PROFESSOR KELLAND ON THE VIBRATIONS OF 



('i r cos a) cos 6 r sm a sin . 



t = > -H 73 r^ sin 



sin (0 4-) 



i cos 6 r cos (a 6) . 



_ i ^ Cl 



sin(0 



sin <p 



4* \ 



T I 



sn 



= sn 



-y 



v), 



omitting the product (ir) (& ty 2 of three dimensions. 

 Similarly we obtain 



cos 4/ r cos (a 4/) . 

 P = - ^ TO n - sm 

 r sin (a -v]/) 



= sm 



2 sil 



a 



]_ _ __ 



= s- sin (2 a r + f r . + 4>) 



p ^ 2 sin (i y) g + (e r) r . a 2 a 



'' ' " 



to no dimensions, 



r = COS 

 <y = COS 



^6 '6 



1 ,. 



3 ra Y 3 ) + (* Y ra 



7-Y! 



7-Y 



(7-Y) 2 } 



to no dimensions . cos 



) r _ 2tf = _ _r_ 



r-<r ' r-tf 



= 2 - (1 -) 



to one dimension. 



