Prof. Potter on Hydrodynamics. 207 



Let 28« be the distance of contiguous atoms at M, so that Bs 

 is the distance of the nucleus or centre of an atom to the face of 

 its attributed cube, of which the area is ^hs^, and therefore 

 4<hp.hs^ is the moving force acting on the atom. 



By D'Alembert's principle, the forces in the directions parallel 

 to the axes which would make equihbrium, are respectively 



and by the principle of vii'tual velocities, we have 



(mX + 4Sp.as^J-m^)^.r+(mY + 4Sp.Ss^^-»n^)rfy 



+ (wZ + 48/j.Ss^ ^ -/«^)rf^ = 0, 

 or 

 (X&+Y., + Zi)+4|. &'.*- (4 +4 +w J)*=0. 



We have also by Boyle's law, jj = «/j for elastic fluids ; and by 

 Canton's law for liquids, p, = /d(1—9)), where c measures the 

 compression under a unit of pressure ; and Zp being formed from 

 the conditions existing in any given case, these equations suffice 

 for the solution of eveiy problem, without any auxiliaiy equations 

 like the equation of continuity. 



If R be the impressed accelerating force acting in the direction 

 of the motion, we have 



^ds^lLdx + Ydy + Zdz; 



also 



du dv dw Idhr + v^ + w^) 

 ''li-^''di-^''lt='2 dt 



i<§y. 



3 ,// 

 and integrating, the above general equation becomes 



./k*H-4/|a..*-i(|)'=0. 



To apply this to particular cases, let s be vertical, and R=^ 

 = the force of gravity ; also let the pressure be a simple func- 



