MOTIVE POWER OF HEAT. 81 



page 68, that the quantities of heat consumed by 

 each are the same, that is, that there passes from 

 the body A to the body B the same quantity of 

 heat in both cases. 



The heat abstracted from the body A and com- 

 municated to the body B, is simply the heat ab- 

 sorbed during the rarefaction of the gas, and after- 

 wards liberated by its compression. We are therefore 

 led to establish the following theorem : 



When an elastic fluid passes without change of 

 temperature from the volume U to the volume V, 

 and when a similar ponderable quantity of the 

 same gas passes at the same temperature from the 

 volume V to the volume V, if the ratio of U' to 

 V is found to be the same as the ratio of U to V, 

 the quantities of heat absorbed or disengaged in 

 the two cases will be equal. 



This theorem might also be expressed as follows : 



When a gas varies in volume without change of 

 temperature, the quantities of heat absorbed or 

 liberated by this gas are in arithmetical progres- 

 sion, if the increments or the decrements of volume 

 are found to be in geometrical progression. 



When a litre of air maintained at a temperature 

 of ten degrees is compressed, and when it is re- 

 duced to one half a litre, a certain quantity of 

 heat is set free. This quantity will be found always 



