126 ON THE MOTION OF SOLIDS THROUGH A LIQUID. [CHAP. V. 



motion at any instant generated impulsively from rest, and cal 

 culating the effect of the impulsive fluid pressures on the surface 

 of the solid. For instance, the resultant impulsive force parallel 

 to x due to this cause is 



or 



i i * 



i.e. by (2) and (22), 



- (Au + C v + B w + Lp + L q + L&quot;r), 



(if A, B } C, &c. be supposed for a moment to refer to the fluid 

 only), or -y- . Hence 



-7 = momentum of solid parallel to x, (by ordinary Dynamics) 

 = total impulse in same direction 



du 

 so that 



du ~ du 

 and in the same way the rest of the formulae (23) may be verified. 



113. The equations of motion (20) may now be written in 

 the form 



d^dT =r dT_ dT + , 



dt du dv dw 



&c., &c., , 



d_dT_ dT__ dT^ ^dT _ dT 



dt dp dv dw dq ^ dr 



&c., &c. 



We can at once derive some interesting conclusions from these 

 equations, in the case where no external forces act. In the first 

 place Kirchhoff has pointed out that (24) are then satisfied by 

 p } q } r = 0, and u, v, w constant, provided we have 



dT dT dT 



-j~ u = -j- : v ~ ~J~ : w &amp;gt; 

 du dv dw 



