Mr. W. J. M. Rankine on the Mechanical Action of Heat. 5 



actions of all parts of the distinct atoms are forces acting along 

 the lines joining the nuclei or centres, then the body is a perfect 

 solid, having a tendency to preserve not only a certain bulk, but 

 a certain figure ; and the elasticity of figure, or rigidity, bears 

 cei-tain definite relations to the elasticity of volume. 



If the atmospheres are less condensed about their centres, so 

 that the mutual actions of distinct atoms are not reducible to a 

 system of forces acting along the lines joining the atomic centres, 

 but produce merely a cohesive force sufficient to balance the 

 superfcial-atomic elasticity, then the condition is that of a per- 

 fect liquid; and the intermediate conditions between this and 

 perfect solidity constitute the gelatinous, plastic, and viscous 

 states*. 



When the mutual actions of distinct atoms are very small as 

 compared with the superficial-atomic elasticity, the condition is 

 that of ffas or vapour ; and when the substance is so far rarefied 

 that the influence of the atomic nuclei or centres in modifying 

 the superficial elasticity of their atmospheres is insensible, it is 

 then in the state ai pjerfect gas. 



So far as our experimental knowledge goes, the elasticity of a 

 perfect gas at a given temperature varies simply in proportion to 

 its density. I have therefore assumed this to be the law of the 

 elasticity of the atomic atmospheres, ascribing a specific coeffi- 

 cient of elasticity to each substance. 



The second supposition, being that from which the hypothesis 

 of molecular vortices derives its name, is the following : — That 

 the elasticity due to heat arises from the centrifugal force of revo- 

 lutions or oscillations among the particles of the atomic atmospheres ; 

 so that quantity of heat is the vis viva of those revolutions or oscil- 

 lations. 



This supposition appears to have been first definitely stated 

 by Sir Humphry Davy. It has since been supported by Mr. 

 Joule, whose valuable experiments to establish the convertibility 

 of heat and mechanical power are well known. So far as I am 

 aware, however, its consequences have not hithei'to been mathe- 

 matically developed. 



To connect this hypothesis with the undulatory theory of 

 radiation, I have introduced a third supposition : — That the me- 

 dium which transmits light and radiant heat consists of the nuclei 

 of the atoms, vibrating independently, or almost independently, of 



* I Lave applied these ideas to the laws of the elasticity of solid bodies, 

 in a paper read to the Britisli Association for tlie Advaiiccmeut of Science 

 on the 1st of August l.S5(), and puhiished in the Cambridge and Dublin 

 Mathematical Journal for February \'t^-)\. Further developnienls of this 

 view of the theory of the elasticity of solids were published in tlic numbers 

 of the same journal for November IKijl and Ntivend)cr W>'2. 



