NEWTON S PRINCIPIA. 345 



that in which the body is a single particle. It then leads 

 us to the three laws of motion. When Newton said that 

 a particle acted on by no external force will remain at 

 rest or move in a straight line with a uniform velocity, he 

 implied that there was no internal tendency in the particle 

 to affect its state of rest or motion. D Alembert ex 

 tended this to any system of particles, and his principle 

 asserts that the internal forces of a dynamical system are 

 in equilibrium among themselves during the whole mo 

 tion. It follows from this that the effective moving 

 forces upon the molecules of a dynamical system, if their 

 directions be reversed, will balance the external impressed 

 forces. Let us apply this to the state of any fluid. 



Let a small element be taken in any fluid in motion 

 whose coordinates are x, y, z. Let p be the density at this 

 point and p the pressure referred to a unit of area. And 

 let X, Y, Z be the external impressed forces on the element. 

 The effective accelerating forces will be 



d 2 x d 2 ?/ d 2 z 



Hence the forces 



d 2 x d z d* z 



acting on the element dxdydz, will, when all the elements 

 are considered, balance each other. Hence from the equa 

 tions of fluid equilibrium, we have 



X 



d x = &quot; d t* 



= 

 pdy dt 1 



