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



For Fahrenheit's scale C=494°-28. ■ 



In the sequel I shall represent temperatures measured from 

 that of melting ice by T=t — C. • 



We have now to consider the absolute quantity of heat, or of 

 molecular i^is viva, which corresponds to a given temperature in 

 a given substance. It is obvious that 



.^ . . . 



represents, in terms of gravity, the portion of vis viva, in one 

 atom, due to the molecular vortices; but besides the vortical 

 motion, there may be oscillations of expansion and contraction, 

 or of rectilinear vibration about a position of equilibrium. The 

 velocity with which these additional motions are performed will 

 be in a permanent condition when the mean value of its square, 

 independent of small periodic changes, is equal throughout the 

 atomic atmosphere. We may therefore represent by 



27-^^ ...... (X.) 



the total vis viva of the atomic atmosphere. To this we have to 

 add that of the nucleus, raising the quantity of heat in one 

 atom to ]y/[j;2 



while the quantity of heat in unity of weight is > . . (XI.) 



— = Q. 



. ^^ 

 The coefficient k (which enters into the value of specific heat) 



being the ratio of the vis viva of the entire motion impressed on 



the atomic atmospheres by the action of their nuclei, to the vis 



viva of a peculiar kind of motion, may be conjectured to have 



a specific value for each substance depending in a manner yet 



unknown on some circumstance in the constitution of its atoms. 



Although it varies in some cases for the same substance in the 



solid, hquid and gaseous states, there is no experimental evidence 



that it varies for the same substance in the same condition. In 



the investigation which follows, therefore, I have treated it as 



sensibly constant. 



The following, then, are the expressions for quantity of heat 



in terms of temperature. In one atom : — 



v^ ,, 3AM , „ ,, 



In unity of weight : — 



Q= TT = or^~ {r — Cnfxb}. 



y . . . (XII.) 



