of Attractive Forces. 333 



the factor q being, bj' the previous reasoning, a very small quan- 

 tity. In fact, since -jr is of the order — -, that the second term 

 clt A 



of the value of V may not be very large, q must be of the order 



of — . Let, therefore, p be the pressure at any point of the first 



half of the surface, andy that at any point of the other half. 

 Then the total resulting pressure on the former 



=2Trc^^p sin 6 cos 6 d9 from ^=0 to ^= |, 



and that on the latter 



=27rc^ ry sin 6 cos dO from 0=^ to 6=7r. 



Now, omitting periodic terms and terms involving q", it has been 

 found that 



/W2 c2 dVf^\ „. 



and 



-(S 



W^ _cl_ dW^_cqW (FW\ ^ 

 ' '^"^S/tV" dt^ 2aK^' ^^2; cos- 1 



Hence it will be seen, by executing the integi'ations indicated 

 above, that the resultant pressure on the whole sphere, estimated 

 in the direction of the incidence of the waves, is 



TTfq d^V 



(27rKat \ 

 — ^- \-cj, wc shall have 



W . -^^^,- = -, sm^ (-^ + c), 



and the non-periodic part of the pressure is 



2kX ' 



the negative sign indicating that it takes effect in the direction 

 contrary to that of the propagation of the waves. This is the 

 main result to which the investigation has been directed. It 

 remains to clear up one point of the reasoning, to which allusion 

 has already been made. 



It has been asserted that the partial differential equation, of 

 which V is the principal variable, embraces only those parts of 

 the velocity which are accompanied by condensation. This 

 assertion admits of being supported as follows. As the fluid is 

 compelled to move along the surface of the sphere, we may regard 



