342 Mr. L. St. C. Broughall on the Frequency 



velocity about YY'^Wj. Angular velocity about XX' = o> 3 . 

 Angular velocity about ZZ' = &) 2 . 

 Using this notation we have : — 



e 2 



(1) Force due to <? 8 = — j^. 



e 2 I 



(2) Force due to e 6 = force due to e h — — 



4:S 2 ' s ' 



(3) Force due to e±= — —„ . . 



4c 2 c 



(4) Force due to nucleus = -f — s— .- 



<r c 



(5) Force due to e w = — 



e 2 



V(* 



r+Z 



* 2 



•+z) 2 + 5 2 



J 2 (r + Z) 



[(>-hZ) 2 + S 2 ]f 



r-l 



( r _/)2 + 5 2 



— _i 



'-l) 2 + S 2 



e\r-l) 



(6) Force due to e 9 — + 



\;r — ij--t-s- \[r- 



= + ^ r ^l ) 2 + s 2 ] i 



(7) Forces due to e 7 , e z , and e 2 = 0. 



(8) Force due to centrifugal force owing to rotation about 



axis YY' = — (o 2 s • -7n= — wJml. 

 s 



(9) Centrifugal force due to rotation about axis ZZ f 



= —coo 2 s • ~m = —<0 9 2 ml. 



s 



Since the sum of these forces must be zero, we obtain the 

 equation 



/t\ ^l l = ^ 4- 6 — -4- e '( r +Q 



W 4c 2 \i ti 2 + 2s 3i ~ [<> + /) 2 + s 2 ]f 



[.(*■— Z)^-t-s 2 _|! 



If we resolve along the line eie 7 and equate the total force 

 to zero we obtain the equation 



(ii.) 



»27 



39^ 2 



4c 2 



Z _ 

 c 



e 2 

 4Z* 



£ 2 Z <? 2 Z 



2s 3 [(r+Z)" + ^]* 



* 2 Z 

 + [(r-Z; 2 + 5 2 ]t 



