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



where, for example, 



day 



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 defined 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 pK,pK,pic&quot;... 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 l3 %, f 1} 

 X ls fa, Vi 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 



(1). 



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 the axis of a?, 



= X, - p jj (&amp;lt;/&amp;gt; + &amp;lt;/, ) (ny - mz) dS 



