176 



MOTION OF SOLIDS THROUGH A LIQUID. [CHAP. VI 



Hence the remaining terms, involving T, must represent the 

 system of impulsive pressures exerted by the surface of the solid on 

 the fluid, in the supposed instantaneous generation of the motion 

 from rest. 



This is easily verified. For example, the ^-component of the 

 above system of impulsive pressures is 



= Au + G'v + "B'w + L> + I*'q -f I/V 



du 



(6), 



by the formulae of Arts. 115, 118. In the same way, the moment 

 of the impulsive pressures about Ox is 



(ny - 





dS 



-f Nw + Pp + JL'q + QV 



dp 



.(7). 



121. The equations of motion may now be written 

 d dT dT dT 



} (1)*. 



* See KirchhoflF, I.e. ante p. 167 ; also Sir W. Thomson, "Hydrokinetic Solutions 

 and Observations," Phil. Mag., Nov. 1871, 



