294 PROFESSOR WILLIAM THOMSON ON THE 
this:—The total external thermal effect is determined when air is allowed to 
expand, through a small orifice, from one vessel into another previously ex- 
hausted by anair-pump. Here the first mechanical effect produced by the expand- 
ing gas, is vis viva generated in the rushing of the air. By the time equilibrium 
is established, all this mechanical effect has been lost in fluid friction (there being 
no appreciable mechanical effect produced externally in sound, which is the only 
external mechanical effect, other than heat, that can be produced by the motions 
of a fluid within a fixed rigid vessel) ; and no truth in physical science can be 
more certain than that by the time thermal as well as mechanical equilibrium 
is established at the primitive temperature, the contents of the two vessels must 
have parted with just as much more heat than they would have parted with, had 
the air in expanding pushed out a piston against an external resisting force, as is 
equivalent to the mechanical effect thus produced externally. Hence, if the two 
vessels and the tube connecting them be immersed (as they are in Jouue’s first | 
set of experiments with this apparatus) in one vessel of water, and if, after time 
is allowed for the pressure and temperature of the air to become the same in the 
two vessels, the water be found to have neither gained nor lost heat (it being un- 
derstood, of course, that the air and all other matter external to the water are at 
an absolutely constant temperature during the experiment), then, for the tempera- 
ture of the experiment, Mayer’s hypothesis is perfectly confirmed; but any final 
elevation or depression of temperature in the water, would show that the work 
due to the expansion is either greater than or less than the absolute equivalent of 
the heat absorbed. 
12. Mr Joute’s second experiment on the same apparatus, in which he exa- 
mined separately the external thermal effects round each of the two vessels, and 
round a portion of the tube containing the small orifice (a stop-cock) has sug- 
gested to me a method which appears still simpler, and more suitable for obtain- 
ing an excessively delicate test of Mavrr’s hypothesis for any temperature. It 
consists merely in dispensing with the two vessels in JouLn’s apparatus, and sub- 
stituting for them two long spirals of tube (instead of doing this for only one of the 
vessels, as JouLE does in his third experiment with the same apparatus); and in 
forcing air continuously through the whole. The first spiral portion of the tube, 
up to ashort distance from the orifice, ought to be kept as nearly as possible at the 
temperature of the atmosphere surrounding the portion containing the orifice, 
and serves merely to fix the temperature of the entering air. The following 
investigation shows what conclusions might be drawn by experimenting on the 
thermal phenomena of any fluid whatever treated in this manner. 
13. Let p be the uniform pressure of the fluid in the first spiral, up to a short 
distance from the orifice, and let p’ be the pressure a short distance from the 
orifice on the other side, which will be uniform through the second spiral. Let ¢ 
be the constant external temperature, and let the air in both spirals be kept as 

