162 
When there is not equilibrium, the internal moving force 
arising from variation of pressure on the opposite faces of any 
cube will be + 8p.46s. If Ris the resultant external accele- 
rating force acting on the nucleus, mR is the moving force ; 
and if v is the velocity relative to the neighbouring particles 
of the fluid, we have m a pa a the effective force acting on 
the molecule. Then by D’Alembert’s principle we have 
mR + dp . 46s” — mF = = 0, 
and m= 8p8s° ; 
sp 1 _ de 
i 2p "ds 
When R=0 and the problem is such that we may stop at 
therefore R+ =0. 
the first term in the expansion of 6p, as in the problem of resist- 
ances, by substituting and reducing we have 
ldp du 
to Er LT 0, 
2 
where we must put p=— for the gases, and p= i 
Pp _ for the 
liquids by Canton’s law. This expression differs from that found 
by the ordinary method only in having the double sign, which 
has never been hitherto found on the methods of Kuler, Laplace, 
Lagrange, or of all those who following them more or less im- 
plicitly have considered fluids as continuous homogeneous 
bodies; so that they have never been able to find more than the 
front resistance which bodies experience whilst moving through 
fluids. This consideration leads us to conclude that such 
methods are essentially defective and erroneous, and that the 
science of hydrodynamics requires the recognition of the 
atomic or molecular constitution of fluids. 
Let p, be the pressure on a unit of area when the relative 
velocity v is nothing, then for gases p = = and integrating we find 
