(2) Rotation about the a-axis: 



r = — on ahc CO 

 15 



2(62-c2)+(62 + c2) (^o-Xo) 



15 ^ 



(b^-c^)^ (Yo-^o) 



2{b^~c') + {b^ + cY (/8o-yo) 



For the expression of a^, /3q, y^ in terms of elliptic integrals, see N.AoC.A, Report 210 

 by Tuckerman (235) or Volume I of Durand's Aerodynamic Theory (3). Some values of k and of 

 k\ distinguished by a subscript to denote the axis of the motion, were given by Zahm (174)o 

 35. Fluid inside ellipsoidal shell rotating about its o-axis, any relative magnitudes of a, b, c 

 (see last figure): 



2 {b^-cY 

 T= — on abc CO 



15 b^^c^ 



/'= — on abc (6^ + 0^), 

 15 



as in Equation [140f], 



k = 



b^ + C 



36o Solid of revolution formed by revolving about its axis of symmetry the limason defined by 

 T - b {s + cos d)/{s - 1) where b and s are constants. The curve for s = 1 is a cardioid. A 

 few values of k are given by Bateman in Reference (240): 



s = 1 1.1 1.2 2 3 



/t = 0.578 0.573 0.569 0.548 0,527 0.500. 



395 



