682 Dr. J. R. Wilton on Figures of 



In these equations we have put a = l, as may be done 

 without loss of generality. • 



The moment of inertia is proportional to 



Jo 

 i. e., as far as 2 , to 



f 1 1 — x 2 f 5 5 r 



' + %3^3 + t (3«i 2 + 10%o«iiRi + 14tz 10 a 12 R 2 + 7a n 2 R^ 

 + 18a 11 a 12 R 1 R 2 + lla 12 2 R 2 2 )] 1 . 

 Also w, the angular velocity, is proportional to 



l+ 8 -+|(K -K)-^±||(K -K'/+ .... 



■2°"> 



2wp 



<£{ 



The angular velocity will be stationary for = 0, so that 

 (from equation (13)), 



a n ( K — 1 P 2 Ri^ | = a 12 1 P 2 R 2 rf e i\ 



This value of a u makes the moment of inertia, and there- 

 fore also the angular momentum, stationary for = ; for 

 equation (16) may be written 



« 10 — o shi 2 » «n + -r sin 4 a a 12 = ; 



i) 



and the coefficient of in the expression for the moment of 

 inertia is proportional to 



dx 



J. 



J (l + *V)f 



i. e. to 



(aio + «nRi + «i2R2), 



cos a ( 1 — 75 sin 2 a j a 10 — — cos a sin 2 a (4 -f 3 cos 2 ct) a n 



+ 77^ cos a sin* a (6 4- 5 cos 2 a) a 12> 



i. £. to 6 



an— =- sin* a a i2. 



7 



2 

 where we have divided out by 1 — .j sin 2 a and by cos a sin 2 a. 



