295-296] MOTION OF AN ELLIPSOID. 535 



and they evidently make w = u, v = 0, w = Q at infinity. Again, they make 



so that the equations (1) of Art. 294 are satisfied by 



-+ const ............................... (x). 



It remains to shew by a proper choice of A, B we can make u, v, w = at 

 the surface (i). The conditions = 0, w = require 



+S &amp;lt;^] =0) 

 dAj*=o 



or 27r^/a 2 + = ................................. (xi). 



With the help of this relation, the condition u = reduces to 



2ir4ao-#xo-Hl = .............................. (xii), 



where the suffix denotes that the lower limit in the integrals (vi) and (vii) is 

 to be replaced by zero. Hence 



u 



( xiii )- 



At a great distance r from the origin we have 



Q = A Trabcjr, ^ = 2a6c/r, 



whence it appears, on comparison with the equations (iv) of the preceding Art., 

 that the disturbance is the same as would be produced by a sphere of radius 

 a, determined by 



(xiv), 



&quot;*i* .............................. (xv) &quot; 



The resistance experienced by the ellipsoid will therefore be 



(xvi). 



In the case of a circular disk moving broadside-on, we have a=0, 6 = c; 

 whence o = 2, ^ O =TTOC, so that 



a = ^-c=-85c. 



O7T 



We must not delay longer over problems which, for reasons 

 already given, have hardly any real application except to fluids of 

 extremely great viscosity. We can therefore only advert to the 

 mathematically very elegant investigations which have been 

 given of the steady rotation of an ellipsoid*, and of the flow 



* Edwardes, Quart. Journ. Math., t. xxvi., pp. 70, 157 (1892). 



