24 



and 



Making the substitution [33], we have 



Mj = S M^ii) 



M/i; = r,xF/t; + j pr-|-(q-q)(Rxn)-(q. n) (R x q)' 



\(i)-\ p{q-n)(Rxq)da 



J c 



r.. X F, 



since R x n •= 0. Again using polar coordinates, 



I,2TT j%7T 



/Wj^(i) = (^ X F^fi;. i) - pR^^^^^sinedOdk 



o o 



f (i) = (r. xF/i;.j)+ pR2[(t.^(D„sin 0sinA 



•'o ■^ o 



+ $^ $^ cos 6 cos X'\ddd\ 



/'27T r n 

 ^iz(^) = (''i ^ FiCiJ- k) + p R2[- <I)^<I)^ sin 61 cos \ 



+ $v O^cos sin X]c? <f X 



[56] 



[57] 



[58a] 



[58b] 



[58c] 



The same procedure used in obtaining FJi) is followed. The integrals in the above expres- 

 sions then become 



i'2tt rn °° n 



x| (2n + I) s (P'^)^ d ^ 

 *' -1 



[59a] 



