56 TOE DYNAMICAL THEORY OF OASES. 



uderation, then by the ordinary investigation of the increase or diminution 

 or matter in an element of volume as contained in treatises on Hydrodynamics, 



(72), 



where the last three terms are derived from equation (59) and two similar 

 equations, and denote the quantity of Q which flows out of an element of volume, 

 that element moving with the velocities u', v' t w'. If we perform the differen- 

 tiations and then make u' = , v' = v, and w' = w, then the variation will be that 

 in an element which moves with the actual mean velocity of the system of 

 molecules, and the equation becomes 



Equation of Continuity. 



Put Q = M the mass of a molecule ; M is unalterable, and we have, 

 putting MN=p, 



(du dv dw\ 



< 74 >> 



which is the ordinary equation of continuity in hydrodynamics, the element 

 being supposed to move with the velocity of the fluid. Combining this equa- 

 tion wih that from which it was obtained, we find 



a more convenient form of the general equation. 



Equations of Motion (a). 



To obtain the Equation of Motion in the direction of x, put Q = M J (u l + ( l ), 

 the momentum of a molecule in the direction of x. 



80 

 We obtain the value of ^ from equation (51), and the equation may be 



written 



~ dz (P = ^V-P. K ~ + Xfr. -(76). 



