a = a' + V sin co. 



[138k"] 



On the y-axis and in the 2a;-plane q= \v\ and v = v' - V . 



On the ellipsoid itself, where ^ = ^g, q/- = and, using Equation [138w '] and Equa- 

 tions [138z, a '], 



?„ = 



,2x1/2 



fi cos O) 



2^^2„2n1/2 



[1381"] 



(l-e^)''^ (1-e-^ + eV ) 



?r„ = 



2e^h2V 

 (1-^2)1/2 



[138m"] 



The same remark concerning the variation of q applies here as in Case 3. Around the cir- 

 cumference of the ellipsoid in the 3a;-plane, q = \q \ and q is given by Equation [I38m "] 

 with sinw = 1. As e-»0, the coefficient 2e^h^/{l-e^)^''-^^3/2, as for a moving sphere. 



Case 5. Rotation of an Oblate Spheroid ot a Circular Disk about an Equatorial Axis. 

 Let the angular velocity be 12 about the y-axis. Then 



S6 = 4(^2^1)^/2 ^(i_^2)i/2 I 3 3<:cot-i C I sinoj, [138n"] 



C^ + l 



A ^ k^n 



3(2Co' + l)cot-i -Co- 6^0- 



^0 



[138o' 



At (^ = A this satisfies the boundary cond ition stated in Equation [137c "], which is easily 

 seen to hold for planetary coordinates as well. The axes are assumed to share in the rotation. 



At large distances from the ellipsoid where C is large, it is found, by expanding in 

 powers of 1/^ as in previous cases, using Equation [138g'], that approximately. 



1 ^ (l.^y/2^inc,=-e^c'A — 

 5 ^3 ' ' 5 ^5 



367 



