190 HENEY A. EOWLAND 



where d + l V2 7 . a d 



X*ar = sin - 



Y*dr = sin - I Y 2 dr, 

 diJL J_, 



tJ /*+' fi /+' 



C = - ~ I ZXYdr = sin 6 " I ZXYdr, 

 dv J -i a/jLj_, 



where I is half the length of the bar and cosd. 



= U*m0\ A]Q t Q' t + | A* ,#&]* + ^ A'Q.QP + A t A tll ( 



+ Q,Q'J P + A t A v (Q'& + Q& ) ^ + V- A UI J T (<?# 

 = U S in0\ A] (QW sin 2 - Q? cos 0) + A] tl ($&' sin 2 9 



- Q'L cos o) -jj- + ^ v (g; $;' sin 2 - c: cos o) .. + ^^ 



+ sn tf - ,,, cos ^ - + A,A, ((QW + Q'W sin' o 



-2QW cos^) + A tll A,((Q' tll <?,' + Q'^Q'^ sitf o 



C=+U\A* ((Qff + QV sin 2 e - Q& cos 9) + 3A' tl ((Q 



'^ sin 2 e - Q HI Qf HI cos *)-.+ 5 J 2 ((^ v ^,' - #; 2 ) sin 2 



- cos 



2 



cos 



sn e - 5, V + t J cos o) -. 

 + *Q'<& + 3 sin 2 - 



Where 



Q, =cos0, 



Q M = J (5 cos 3 e 3 cos 0) , 



Q, = i (63 cos 5 70 cos 3 + 15 cos 0) , 



^; =Y (21 cos 4 0-14 cos 2 + 1), 



<?'/ -o, 



cos 3 7cos0), 



fj. = COS 0. 



