194 MOTION OF SOLIDS THROUGH A LIQUID. [CHAP. VI 



where, for example, 



do>' , dio 



The identity of the two forms of (K, K) follows from Art. 54 (4). 

 Hence the total energy of fluid and solid is given by 



T= + K ) ........................ (7), 



where is a homogeneous quadratic function of u, v, w, p, q, r 

 of the same form as Art. 118 (5), and K is denned by (5) and 

 (6) above. 



130. The 'impulse' of the motion now consists partly of 

 impulsive forces applied to the solid, and partly of impulsive 

 pressures p/c, p/c', pic" ... applied uniformly (as explained in Art. 54) 

 over the several membranes which are supposed for a moment to 

 occupy the positions of the barriers. Let us denote by f l5 77^ f l5 

 Xj, /AJ, i>! the components of the extraneous impulse applied to the 

 solid. Expressing that the ^-component of the momentum of the 

 solid is equal to the similar component of the total impulse acting 

 on it, we have 



where, as before, T x denotes the kinetic energy of the solid, and T 

 that part of the energy of the fluid which is independent of the 

 cyclic motion. Again, considering the angular momentum of the 

 solid about th,e axis of x, 



~ l = \ l -pfj(<f> + 4> a ) (ny - mz) dS 



