of the Motion of Fluids, SjC. 397 



Here the pressure p is equal to a'p, p being the density. 

 Also as before 



dF = Xdx + Ydy + Zdz, and d<p = udx + vdi/ + wdz. 



If we put r =x- +y + Z-, and suppose ^ to be a function of 

 r and t, we shall find that the equation (w) will reduce itself to 



_ „ dr(p d"(p d(p d'(j> d(p- d-(p 

 dr- df dr'drdt dr" ' dr" 



, /2«- Xx Yy , Ssx dfb , , 



V r r r r / dr 



This equation does not accord in giving a function of r and t, 



unless 



Xx , Yy Zz 

 r r r 



which is the part of the impressed force resolved in the direc- 

 tion of r, be a function of r and t. In consequence of the 

 supposition respecting ^, and the equation 



d(^ = udx + vdy + wdz, 



this direction is that of the motion. As, however, this resolved 

 force may be considered a function of r and t, the form of 

 which is constant for an indefinitely small portion of the fluid, 

 the equation (p) shews that for every elementary portion, ^ is 

 a function of r and t, and consequently that the motion at every 

 point is directed to a fixed or moveable centre, and varies 

 according to a law to be determined by the integration of this 

 equation. This law is not, as in incompressible fluids, in- 

 dejiendent of the impressed forces. 



5. Let us suppose the force to act in the direction of r and 

 to be P, and r to be infinitely great. Then (;>) becomes, 



dr de dr " drdt dr" ' dr '^ dr ' 



