APPLICABLE TO THE MOTION OF FLUIDS. 383 



Hence by substitution, 



Again, on the above limitation respecting the variation from one 

 point to another of space, 



ss^e-yg*. 



The foregoing equation consequently becomes, 



rdV V* 

 Fit) + P-Q + J-^ds + — = (14), 



which is precisely the same in form as equation (7), and differs only in 

 being limited as to the direction of variation of the co-ordinates. The 

 same equation subject to the same limitation may be obtained directly 

 from equation (2) as follows. 



If F be the sum of the impressed forces and f the effective acce- 

 lerative force in the direction of an arbitrary line s drawn in the mass 

 of fluid in motion, then by D'Alembert's Principle and Hydrostatics, 



dp = P {F-f)ds. 



But Fds = (X.?£ + F.gf + Z.jgj ds = Xdx + Ydy + Zd%. 



Hence, by integration, 



P - Q + ifds = F(f). 



If V be the velocity in the direction of s, 



J " \dt J " dt + dt : 



indicating by (dV) as before, 



dV , ^dV, ^dV, 

 -j-dx + 1¥ d ! , + —dz 



UU 2 



