30 Mr Hides, On two pulsating spheres in a fluid. [Nov. 22, 



the term depending on the time variation of the potential. By 

 an oversight I treated the term depending on the square of the 

 velocity as if it had no effect on the resultant force. This is only 

 true if powers of the inverse distance higher than the second be 

 neglected (as was the case in the numerical examples). It is of 

 course not true in general, except in the case of the resultant- 

 force on the system regarded as rigidly connected. In the present 

 communication I propose to shew how the other terms may be 

 found. 



7. Using the same notation as in the former paper, the force 

 on B from A is 



x-fpQo&eas 



= - 2tt6 2 ["" & + i V 2 \ cos sin Odd. 



To find the general term in the series for X directly by means 

 of the infinite series for V would be extremely laborious, but this 

 may be avoided by means of the following proposition. 



Let <£ be the velocity-potential of any motion symmetrical 

 about a diameter of a sphere in the fluid, and such that the normal 

 motion at the surface of the sphere is constant over the sphere, 

 and equal to u. Then the force on the sphere is parallel to the 

 diameter and is equal to 



where P= \ " <J> sin 20 d6, 



Jo 



Q=rftsm26d0, 

 Jo 



provided the velocity, along the surface, is always finite. 



For consider the term irb 2 I V 2 sin 6 cos 9 dd. At every point 



of the surface of the sphere V 2 = u 2 + 1/b 2 (d(p/dd)\ Since u 2 is 

 constant the part of the force depending on it is zero, and the 

 integral becomes 



l ~ 2] o d0 Sm2d -d0 dd 



