containing 4, 5, 6, 7, and 8 corpuscles, etc. 41 



/ m 

 Pi + q-i + n with a period 2ir a/ ^t 5 



Pi — °2, Pi~ r-i with two periods 27r a / -r- - . 



Thus there are four different periods the squares of which are 

 in the proportion of 1, 2, 3, 4. 



Effect of a magnetic field on the vibrations of the tetrahedron. 

 If a, /3, 7 are the components of the external magnetic field, there 



will be terms in the expression for m —^ , equal to eB -~ —ey ~, 



in addition to the terms independent of the magnetic field, and 



corresponding terms in the expressions for -rrf , ~nf- 



Hence instead of the equations 



m -£ = ~ k P> eta > 



we have 



nt 



-^=-kp + e8j t (£ + £ 2 + f s + £») - ey ^ fa + % + % + V*), 



d-p j r, dr da 



m a4 = - kp+e ^drt- e ^df 



Similarly 



d 2 q 7 dp dr 



d 2 r , da n dp 



m -rr, — — fcr + ea -+ — en -£ , 



dt- dt dt 





or if p, q, r vary as e'^, we have 





(m/x 2 - k) 3 - (nifi 2 - k) /j, 2 e 2 (a 2 + B 2 + y 2 ) = 



= 0. 



The roots of this are 





Ik 



^~\l m' 





. He 

 Pi = ^o + £ — , 

 m 





. He 



p* = Ho - i — > 

 m 





where H = Va 2 + B 2 + y 2 . 





