137] CYCLIC MOTION. 209 



and (,) = - ,? AT, 



dn&quot;&quot; } 



It is evident that K is the energy of the cyclic motion which 

 remains when the solids are maintained at rest in the configuration 

 (q ly q,, ...) We note that, by (3), (7), and (9), 



dK dK 



.................. (11). 



If we add to (5) the kinetic energy of the solids themselves, we 

 obtain for the total kinetic energy of the system an expression of 

 the form 



T=1S, + K ........................... (12), 



where 2 = A u q, 2 + A?&amp;gt;q&amp;lt;? + ... + ZA^q, + ......... (13), 



the coefficients being in general functions of q lt q 2) ....... 



To obtain the equations of motion we have recourse as before 

 to the formula 



2 Xb+ FAT + A dt 



......... (14). 



The only new feature is in the treatment of the expression on 

 the right-hand side. By the usual method of partial integration 

 we find 



dxdydz 



+ p f |(JAf + mAri + Af ) dff+pK I |( 



............... (15), 



where /, m, ?? are the direction-cosines of the normal to any 



element 8S of a bounding surface, drawn towards the fluid, or 



L. 14 



