the Primary Laws of Elastic Fluids. 283 
of height. It is thus obvious that the equivalent work would be 
completely transferred to W in raising it through (Gd) = °°,dths 
of the unit. But the density then, instead of being of the nor- 
mal amount corresponding to the ratio that subsists between the 
weight W and the transverse area of its cylinder GH, would 
exceed that by jth: hence to arrive at an equilibrium, the 
ascent of W would be continued a little further beyond the 
{5dth (viz. to a), and the work required to effect this must be 
derived from the conversion of some of the heat of the air con- 
tained in the ;°%dth of the unit of the height of the cylinder GH. 
A lowering of its temperature is the consequence, and equilibrium 
is attained before W has reached fully to the top of dH, the last 
zipdth of the unit. 
The proportion da to dH of the ~4,dth through which W is 
driven has been determined by the experiments above referred to, 
as detailed in the twelfth book of the Mécanique Céleste. It is 
nearly three-fourths; and it is such, that if the small amount of 
heat lost were exactly replaced from external sources, W would 
be carried through aH, the remaining fraction of the ;3,dth. It 
will be remarked, that the ratio of da to dH is the well-known 
ratio of the increments of heat required for the same incre- 
ment of temperature with volume constant and with pressure 
constant. 
In the above demonstration we must keep in view, that, to 
facilitate our reasoning, it is allowable to assume the plug to 
extend from the last or lower position of V to the first or lower 
position of W; also that the unit of height may represent an 
imcremental quantity, and thus the phenomena which, in order 
to fix our ideas, we consider as taking place in consecutive order, 
may be simultaneous. 
§ 7. Professor Thomson assumes that the cooling effect in his 
experiments with plugs is proof that the gas, on being com- 
pressed, evolves more heat than the amount mechanically equi- 
valent to the work of compression; that, in short, it does not 
alter its temperature in correspondence with the mechanical 
equivalent of the apparent work. It has not occurred to him 
that the depression of temperature may simply be caused by the 
conversion of heat into the mechanical force or work required to 
acquire against the atmospheric pressure that small augmenta- 
tion of volume which a deviation from Mariotte’s law demands. 
It is surely proper to take this first into consideration, yet the 
necessity of doing so seems never to have suggested itself. The 
experiments were originally proposed as a means of testing 
Mayer’s hypothesis only* (see Phil. Mag. vol. iv. pp. 482, 483, 
§§ 73, 78), and up to the present time this is supposed to have 
been successfully accomplished (see Phil. Trans. 1854*). 
* See Appendix (1) (2). 
