( 120 ) 



On the Belation between the Changes of Temperature and 

 Volume of Gases. By William Petrie, Esq., C.E, 

 Communicated by the Author. 



Several questions in art and science have lately required 

 for their solution the information referred to in the title. 

 In the absence of experiments, I endeavoured to obtain a 

 formula for it in the following manner : — 



1. Without taking up any theory of heat, we know as a 

 fact that heat is the cause of the apparently self-repulsive or 

 expansive power of gases, for that power varies with the 

 temperature. We may also, with tolerable certainty, con- 

 sider the mutual repulsions so caused between the particles, 

 to centre in the particles themselves. No matter how the 

 repulsive eifect is brought about, it must have relation to 

 the particles as centres, because they are the subjects of it. 



Therefore the repulsive effect must, almost necessarily, 

 follow the self-evident law of all central or radiating forces, 

 namely, that it varies as the inverse square of the distance ; 



that is, any two atoms of gas, placed at ^ th the distance, 



without any gain or loss of heat (the repelling cause), must 

 r.e.pel one another with \} x the force. 



Therefore, a mass of air compressed to ^rth of its lineal 



size, OP YT ^^ ^^® bulk, will have its particles L x as close to 



each other ; then (from the above) they should each repel the 

 other with L^ x the force, and there will be L^ times the 

 number of particles per square inch, so pressing on the sides 

 of the containing vessel ; therefore there will be L* x the 

 total force, per square inch, on the containing vessel. 



Or put N = L^, then, similarly, air compressed to ^th the 



bulk will have N^ x the expansive force per square inch. 



Now, it must be remembered that this is the expansive 

 force of air in the same condition (as to the possession of 

 heat) as it was before it was compressed ; and, as air begins 

 to part with heat directly it is compressed, it is evident that 



