288 The Rev. J. M. Heath on the Variation of Temperature 



can have been attempted. Moreover, the question whether or 

 not hydrogen is a product of the action of sodium on acetic 

 ether is a plain question of fact; and I will content myself with 

 the simple statement, based on my experiments, that neither 

 acetic ether nor any analogous ether evolves hydrogen by action 

 on metallic sodium, and that every trace of that gas obtained by 

 Frankland and Duppa was derived from alcohol and not from 

 acetic ether. Sodium is now cheap, so is acetic ether ; let those 

 who desire other information make the experiment for themselves. 



XXXIX. On the Circumstances which determine the Variation of 

 Temperature in a Perfect Gas during Expansion and Condensa- 

 tion. By the Rev. J. M. Heath*. 



THE constancy of the total energy (potential energy + actual) 

 of a given weight of gas during any changes in its condi- 

 tion caused by the internal forces by which its particles act 

 upon one another, depends upon two conditions — that the in- 

 ternal forces or energies do all the internal work that is done, 

 and that they do no other. When these conditions do not 

 hold — that is to say, when either external forces do any part of 

 the internal work that is done, or when any part of the internal 

 forces (potential energy) is spent upon work external to the 

 system — then the total energy of the gas will be altered — by 

 augmentation in the one case, by diminution in the other. When 

 the denomination of the forces (external or internal) is the same 

 as that of the work they do, the total energy of the same name 

 is unaltered by their action. When the force is of a different 

 name from the work it does, the total energies of both names 

 are altered, but in opposite ways. 



The internal forces of a gas consist of pairs of equal and 

 opposite forces, by which each of two particles acts upon and is 

 acted upon by the other. And as the external surface of the 

 gas would consist of particles acted upon by the interior particles 

 but not reacting upon them in return, the reaction of the vessel 

 which bounds this surface in every part is necessarily included 

 in the calculation of the sum of all the internal forces acting 

 among the particles of the gas. 



^ A gas, then, confined in a vessel and reacted upon at the 

 surface of the vessel by a pressure equal and opposite to its 

 own pressure upon the vessel, is to be taken as acted upon by 

 internal forces and no other. 



If, now, internal work is done in this gas subject to the condi- 

 tion last mentioned, that the reaction of the containing vessel 



* Communicated by the Author. 



