( 350 ) 



nitiy bc rlecoiDposcd into these five t'mictious. Nuw we have the 

 o lowing solid harmonies 



'^'25 = ^h (- ^2 _ ^C _!_ 2 c2) , 



and, putting 



Va JT a~ /Jo = «o, ^/j n a~ B^ == /^g' 'Va n 11 a ^= to, , 

 the following values ut' the eoetticieuts : 



öj^ = «22 ^^ ":j3 ^^^ "44 ^^ ^ (f o- "j5 ^= 4 «j 

 i/j 1 = b... = h;^ = ^44 = 3 /?2, ^ i, = 4 /?2 



f j2 = + 2 fo, f21 = - 2 f2 



^31 = + fC' f4a = — f-z- 



All coefficients that have not been mentioned here have the 

 value 0. 



The equations of motion become 



3/V2^>i = -3«2/'i + 2f2/'c (10) 



3/^o>2 = -3«3po-2f2Al (11) 



3/^2/;3 = -3«2Ps + f2/'4 (12) 



3/'2i'4 = — 3 «2^)4 — fg/'a (13) 



ftih = — t^ 2 Po- 

 li appears that, in the absence of a magnetic force, ail vibrations 

 of the second order will have a common frequency n.^ , given by 



When the shell is placed in the magnetic field, it will be only 

 for the F-,-vibrations that this ficquency I'emains unchanged, and 

 there will be fonr motions with a slightly increased or diminished 

 frequency. 



