- ; BOLTXMASN'8 THEOREM OS THB AVERAGE DISTRIBUTION 



the axes of * and y about tliat of z till A becomes a maximum, the condition 

 of which is 



We ahall abo reckon velocities with reference to the centre of mass of 

 the tyatem JA 



With these simplifications we find 



L'-L 



V 



_ ' 



m 



m 



1-a/iz 



" 



(82). 



We are now able to calculate the energy of rotation, J', of the minor 



a'F*+b'G' t +c'H' t -2l'G'H'-'2m'H'F'-2n f F'G' (83), 



-, jVa/iZ 5 - 2vpz (Fa - Hm) + /tz' (Fa - JHrn) 1 ] 



-iir)+pt*(Gi}-iny] 



(84). 



Combining these results and reducing we find for the energy of internal 

 motion of the system M' 

 /' - /- i/i (1 - fyu 1 )-' (u - Gb + in)'- - $n (1 - a^Y 1 (v - Fa + HI)" - ^w 1 . 



Hence 



the integration being extended to all values of u, v, and w which make /' 

 positive. 



D' 



Now (1 a/iO*) (1 fyi2*) = -yj, 



and this is an invariant. 



