161 
discussing such problems. We are led to consider the fluids as 
consisting of congeries of heavy very small nuclei surrounded 
each by imponderable existences, as caloric, electricity, &c., 
and the volume of each molecule depending chiefly, if not 
entirely, on the calorific atmosphere. When the whole volume 
of a fluid body is made up of such molecules we must attribute 
a cube of space to each molecule, since the cube is the only 
regular figure which will fill all space symmetrically without 
vacancies, and the faces of this cube are the areas on which the 
pressures are to be taken which are transmitted to the nucleus 
through the means of its elastic atmosphere. These cubes will 
be of the same volume throughout surfaces of equal pressure 
and temperature, but will continually vary in volume along 
directions of variable pressure and temperature. An imaginary 
vertical cylindrical column of the atmosphere supposed of homo- 
geneous constitution will form an illustration of this; the at- 
tributed cubes of the molecules being of equal volume in hori- 
zontal strata, but varying imperceptibly in the vertical direction. 
If at any point in a fluid és is the perpendicular distance of 
the center from the faces of the cube, and therefore 25s is the 
length of the edges, and the distance of the centers of contiguous 
nuclei; then 46s” is the area of each face of the cube, and 88s° is 
the volume of the cube. If m is the mass of the nucleus and 
also of the cube, and p the density of the fluid at this point and 
also the average density of the cube, we have m=p.86s*. Let 
p be the pressure on a unit of area at the given point, and 
therefore the pressure on each face of the cube is p. 46s? in 
equilibrium. When s is the space measured from any fixed 
point along the line of variable pressure at right angles to the 
surface of equal pressure where the pressure is p; then if p be- 
comes p’ in surfaces of equal pressure similarly situated at a 
distance s + 26s, we have, by Taylor’s theorem, 
ra 26s d’p 46s? d’p 86s? 
Soe oe tae Tae Tat a Tas 
+ &e, 
