
, 
MECHANICAL ACTION OF HEAT. 159 
compressing a body appears in the form of heat. More or less power may be 
consumed or developed by changes of molecular arrangement, or of the internal 
distribution of the density of the atomic atmospheres; and changes of molecular 
arrangement or distribution may develope or consume heat, independently of 
changes of volume. 
(6.) We shall now investigate, according to the hypotneats of molecular 
vortices, the amount of heat produced by an indefinitely small compression of one 
atom of a body in that state of perfect fluidity which admits of the bounding 
surface of the atom being treated as if it were spherical: its radius being denoted 
by R, and the radius of any internal spherical layer of the atmosphere by multi- 
plying R by a fraction w. 
I shall denote by the ordinary symbol of differentiation d, such changes as 
depend on the various positions of portions of the atomic atmosphere relatively 
to each other, when changes of volume and temperature are not taken into con- 
sideration; while by the symbol 6 of the calculus of variations, I shall represent 
such changes as arise from the variations of volume and temperature. 
Let us consider the case of an indefinitely thin spherical layer of the atomic 
atmosphere, whose distance from the nucleus is Rw, its thickness Rdw, its area 
4 R?u?, and its density & D(u, D, 7). 
The weight, then, of this layer is 
An Rf Diy (uD, T) du. 
Its velocity of oscillation is 7, and having, in virtue of that velocity, a mean cen- 
trifugal force, as explained in the Introduction (Equation V.), equal to 
; : Ca 2Q 
its weight x a= i= ER =) 
it is kept in equilibrio by an equal and opposite centripetal force, arising from 
attraction and elastic pressure, which is consequently represented by 
2 
4a Re tp Dud (wD, 7) du 
=8rR? 7 QDud(uD,7) du. 
Let the mean density of the atom now be increased by the indefinitely small 
quantity 6D. Then the layer will approach the nucleus through the distance 
—d(Ruw)=—uvdR—RO uw, and being acted upon through that distance by the cen- 
tripetal force already stated, the vis viva of oscillation will be increased by a 
quantity correspcnding to the mechanical power (that is to say, the heat), repre- 
sented by the product of that distance by that force, or by 
—8rR? Fe yp etDu yD, 7) duxd (Ru) 
VOL. XX. PART I. 7410) 
