which we call Heat. 117 
greater than before, if it recedes less. By means of special ma- 
thematical considerations, it may without difficulty be proved 
that the increase or decrease of the vis viva thereby produced 
must exactly correspond to the external work done by the expan- 
sive force of the gas; nevertheless it is not even necessary to give 
a special proof of this theorem, since the same is an immediate 
consequence of the general law of equivalence between vis viva 
and work. 
If the side moves so slowly that the pressure of the gas against 
the moving side is just as great as against a stationary one, then, 
in determining the work, the velocity of the side no longer enters 
into consideration, but merely the whole path described by the 
same. On the contrary, if the velocity of the side is so great 
that in the vicinity of the same a sensible compression or rare- 
faction of the gas thereby ensues, then the pressure actually ex- 
ercised by the gas during the motion must always be brought 
into calculation. 
When an overflow takes place between two vessels filled with 
gases of different densities, or between a full and an empty ves- 
sel, on the whole no work will be performed, and therefore no 
change in the total quantity of heat can occur. It is not here 
asserted that no change in the quantity of heat takes place in 
either of the two vessels considered separately, for a mass of gas 
whose molecules move principally in a definite direction deports 
itself towards adjoining gaseous masses in the same manner as a 
moved side; and when the moved gaseous mass strikes against 
stationary walls, just as much motion of heat makes its appear- 
ance as vis viva is lost by the common translatory motion of the 
whole mass. 
Just as in the changes of volume of gaseous bodies, so also in 
other cases the external work must be taken into consideration ; 
as, for instance, the work which during the evaporation is em- 
ployed to overcome external resistance, and thus to make room for 
the vapour as it is generated. In solid and liquid bodies which 
only suffer small changes of volume, the external work is also for 
the most part only small; nevertheless here also cases occur in 
which its influence becomes considerable. 
11. Lastly, I must mention a phenomenon the explanation 
of which appears to me to be of great importance, viz. when two 
gases combine with each other, or when a gas combines with another 
body, and the combination is also gaseous, the volume of the com- 
pound gas bears a simple ratio to the volumes of the single consti- 
tuents, at least when the latter are gaseous. 
Kroénig has already proved that the pressure exerted by a gas 
on the unit of its enclosing surface must be proportional to the 
number of molecules contained in the unit of volume, and to the 
