the Dynamical Theory of Heat. 197 



the piston under atmospheric pressure is allowed to rise while 

 the absolute temperature is being doubled, 142 of heat are 

 required. The additional 42 represents the amount of heat 

 consumed in mechanical work in raising the load. When a 

 quantity of heat equal to that which had been applied (142) is 

 withdrawn from the air, the piston then falls to its original posi- 

 tion ; and in doing so, according to the received opinion among 

 physicists, performs an amount of work equal to that expended 

 in raising it. Mr. Gill disputes this point, and asserts that the 

 piston in descending under the pressure of the atmosphere 

 performs only one-fourth part of the above amount of work. 



Now if the work that we are in search of were mechanical 

 work, such as raising a weight or driving an engine, it is per- 

 fectly true that the descent of the piston will not perform as 

 much work of this sort as is equivalent to the raising of the 

 piston one foot under atmospheric pressure, because there are 

 other effects to be produced by the descending piston besides 

 mechanical work. First. The air has to be compressed into 

 one half its present volume against its elasticity. Here we have 

 work analogous to bending a spring, or winding up a w^atch. 

 A portion of the vis viva of the descending weight is converted 

 into the potential energy of elasticity. Secondly. The piston, 

 in compressing the air, raises its temperature. Hence a portion 

 of the vis viva of the descending piston becomes converted into 

 that form of molecular motion called heat. Now if Mr. Gill 

 will add the three effects together, he will find that their sum is 

 exactly equal to 2116*4 foot-pounds, the amount of energy 

 required to raise the piston when under the pressure of the 

 atmosphere, — the air being, of course, assumed to be a per- 

 fect gas. 



1. Mechanical work performed by the>. 



descending piston, =21 16*4 foot-pounds, 



2. Work performed in compressing > the amount expended 

 the air, in raising the piston. 



3. Work performed in heating the air,-' 



It is more than probable, however, for reasons into the consi- 

 deration of which we need not at present enter, that the elasti- 

 city is entirely due to heat. But nevertheless this does not 

 alter the fact that we must draw a distinction between the vis 

 viva which is consumed in work, against that form of heat 

 called elasticity, and that form called rise of temperature. 



When the piston is at the top of the cylinder, each particle of 

 the air, by virtue of the vibratory motion which it possesses in 

 the form of heat, strikes against the bottom of the piston with a 

 force proportional to its temperature. When the piston descends 



