183, 184.] UNIFORM MOTION OF SPHERE. 227 



ducts of u, v, w, -,- , &c. may be neglected, we obtain by elimina- 

 dx 



tion of p from (15), 



If, as in Art. 140, we write 



rj = a) sin ^, = w cos ^-, 



we find on transformation of co-ordinates that the equations (32) 

 reduce to the one equation 



cPo) d? co 1 dco _ w __ ~ 



d^ + d^* + vd^~^~ 



2 d z 1 dl 

 or -T 2 + -v- a -7- \^o) = 0, 



whence, substituting the value of co from (31), we obtain 



2 J2 -I 7 T2 



CL . LI/ 



If we write 



x r co& 0, 



this becomes 



r^ 



|&amp;gt; 2 



or 



If R, denote the component velocities at any point of the fluid 

 along r, and perpendicular to r in the plane of 6, respectively, we 

 have, from the definition of -v/r, 



_ 

 ~~rwn0rd0 rsiut) dr 



The conditions to be satisfied at infinity are 



J^-Fcosfl, e=Fsin&amp;lt;9 ............... (35). 



If we assume 



we find that (34) is satisfied provided 



152 



