192 HOLTZMANN ON THB HEAT AND ELASTICITY 
The effect of the heat added to the gas is consequently either 
increase of temperature combined with increase of elasticity, or a 
mechanical action, or a combination of the two ; and a mechanical 
action is the equivalent of the increase of temperature. 
2. Heat can only be measured by its effects ; of the two effects 
mentioned the mechanical action is especially adapted for this 
purpose, and will be employed in the following pages. 
I term wnit of heat the heat which on its addition to any gas is 
capable of producing the mechanical action a, i. e. to use a defi- 
nite measure, which can raise a kilogrammes 1 metre. 
3. To render it more intelligible, I now imagine any gas in a 
vertical cylinder of 1”/* section, which is impermeable by heat, 
closed above by a moveable piston. This piston must be pressed 
down by a weight p kilogrammes, equal to the pressure of the 
gas, if the gas is to maintain its volume. Let the infinitely 
small quantity of heat dq be added to this gas, and by dimi- 
nishing the pressure let the gas expand until it has again ac- 
quired the former temperature. Let this expansion be dv; it 
is attained by the gas forcing up the piston, and the pressure rest- 
ing on it, dv in height. The effect of the heat dg is conse- 
quently the mechanical action (p—dyp) kilogrammes raised to 
dv metres, or (p—dp).dv kilogrammes to 1 metre. 
dp expresses the necessary diminution of the pressure ; it is 
infinitely small, and therefore disappears in comparison to p. 
The mechanical action of the heat dq is then p.dv, and the 
action of the unit of heat, 
p.dv 
dq’ 
which according to No. 2 is equal to a. 
If ¢ be the density of the gas, i. e, the weight of the unit of 
volume, the volume of m kil. gas is 
and gigi ane de 
therefore the above equation 
_mp.de aus 1 
errs PGE 
4, The quantity of heat g in 1 kil. gas depends on the pres- 
sure p to which the gas is subjected, the density e and the tem- 
* 1mq@ denoting one square metre. 
