154 The Rev. S. Haucuton on the Equilibrium and 
This value of the function v contains all solid and fluid bodies, together with 
the class of bodies which cannot be said to be either solid or perfectly fluid, and 
which are generally called “viscous” fluids. If we knew sufficiently well the 
difference of molecular structure of these different classes of bodies, we should 
be able to determine the proper v for each of them; but in the absence of accu- 
rate knowledge on this point, we must only give the best definition we can of 
solids and fluids, and the agreement of the secondary laws deduced from the defi- 
nition, with the observed laws of these bodies, will be sufficient proof of the cor- 
rectness of the definition founded on their molecular structure. fs 
I define a solid body to be of such a nature that the part of the molecular force 
depending on F, does not exist, so that in a solid body, Fr, and, consequently, v,, 
is zero. In all other bodies, liquid, gaseous, and viscous, the function v will 
contain a part v,, which does not enter into the function peculiar to solid bodies. 
The definition of a solid by means of the assumption that r, and v, are zero, is the 
same thing as supposing that in a solid body the molecular forces equilibrate each 
other, without the aid of external forces; while in fluid bodies the molecular 
forces do not equilibrate themselves without the aid of external forces and pres- 
sures; and this notion of a solid seems to be correct from the nature of the mole- 
cular forces themselves, which appear to be attractive up to a certain distance ; 
but if the distance be still further diminished, the force becomes repulsive. The 
condition v, = 0, may then arise from the molecules of a solid body being placed 
at such distances from each other that they are held in equilibrium by the action 
of powerful, attractive, and repulsive forces acting in opposite directions. How- 
ever, our ignorance of the internal structure of bodies is so great, that such 
considerations as these would be, by themselves, an unsafe foundation for a theory 
of solids and fluids; and the best course is, to use them only as indications of 
the correct definitions, which must themselves be ascertained by the agreement 
of the results they lead to, with the known laws of solid and fluid bodies. 
In following this method in the present paper, I hope to show that the 
presence of v, will produce the equations of hydrostatics and hydrodynamics, 
while the term vy, will give all the laws of solid bodies; so that we have the fol- 
lowing functions ;—for solids, VW = Ke 
for perfect fluids, == TAA 
for viscous fluids, V=v,+YV; 
