422 The Rev. J. M. Heath on Thermodynamics. 



densing energy was identical with the deductive dynamical law, 

 and the whole question would be definitively settled. 



In two articles previously communicated to this Magazine, I 

 have shown that the assumption that the heat developed in a 

 compression is proportional to the whole force externally applied 

 to the surface of the gas, multiplied by the compression, is erro- 

 neous, because the externally applied force necessarily includes 

 a part, called in D'Aleinbert's Principle "the lost force," which 

 has been already included in the value of the internal forces of 

 the gas, and that it is the remainder only of the applied forces, 

 commonly called the " effective forces," which can produce any 

 such effect as heat or vis viva affecting the temperature or total 

 energy of the gas. I shall now complete what I have to say 

 upon this subject, by showing that the same assumption (the 

 proportionality of the heat to the whole impressed force) is 

 equally at variance with the laws of dynamics, which show that 

 the vis viva produced is proportional only to the action of the 

 effective forces. 



Let M be the mass of the gas, and let it be contained in a 

 cylinder the area of whose section is unity, in which a piston 

 moves vertically, loaded with a weight P pounds. Let v be the 

 depth of gas between the piston and the bottom of the cylinder, 

 and Q the upward pressure upon the lower surface of the piston, 

 resulting from the expansive force of the gas. 



The forces P and Q may be considered to be distributively ap- 

 plied to every separate particle in the gas. The force, therefore, 



which acts upon one such particle (m) will be ^P acting verti- 

 cally downwards, and — =■= Q acting upwards; or the whole 



force will be ^ (P — Q). Let r be the distance between two ad- 

 jacent molecules situated on the same vertical line; then + dr 

 will be the distance by which such particles will approach or re- 

 cede from each other in consequence of any condensation or 

 expansion which may take place in the vertical direction ; but 

 v } the depth of the gas, =%r, the sum of all the distances of 

 adjacent particles situated in one line; .*. dv = 1 t dr. Now dv is 

 the quantity by which the piston descends or ascends during 

 condensation or expansion of the gas ; it is equal, therefore, to 

 the sum of all the extensions or contractions of the constant dis- 

 tance r between all the particles upon the same vertical line. 



The equation for determining the vis viva generated by any 

 system of forces is ^mv' 2 = feVdp— \ l^Qdq, where P and Q are 

 respectively the forces which aid and those which resist any par- 



