218 Prof. W. J. M. Rankine on the Thermal Energy 

 by experiment, 



*= J x - 



3 



£-) 



This method is applicable only to substances that are nearly 

 in the perfectly gaseous state. 



There is another method, applicable to the same class of sub- 

 stances, which is expressed as follows : — 



k =*pgjc m ...... (16) 



This second method may be applied to liquids and solids also, 



under the following conditions : the quantity -— istobecalcu- 



■ Po^o 

 lated as for the perfectly gaseous state ; and the specific heat c 

 must be nearly constant. 



The ratio which the energy of periodical disturbances in a 

 unit of volume bears to the centrifugal pressure may be inter- 

 esting in connexion with hypothetical views of the constitution 

 of matter. It is expressed as follows : — 



3 -M (17) 



A 



The following are some examples of the results of calculations 



by formulae (15) and (17) : — 



c' 3 



Substance. -. Jc. ^(^~~1)- 



c 2 



Atmospheric air 

 Nitrogen 

 Oxygen . 

 Hydrogen . 

 Steam-gas . 



1-408 1*634 0-951 



1-409 1*630 0945 



1-400 1-667 1-000 



1-4J3 1-614 0-921 



1-297 2-242 1-863 



§11. General Equation of Thermodynamics. — In the paper of 

 1849-50, pp. 158-164, the general equation of thermodynamics 

 (equation 6 of that paper, p. 161) is deduced from the hypo- 

 thesis of molecular vortices, on the supposition of a special form 

 and arrangement of the vortices. In a subsequent paper, " On 

 the Centrifugal Theory of Elasticity," read to the Royal Society 

 of Edinburgh in December 1851 (Transactions, vol. xx. pp. 433- 

 436), the same general equation (being equation 25 of the 

 latter paper, p. 436) is deduced from the hypothesis of molecular 

 vortices, without any special supposition as to the form and 

 arrangement of the vortices, but with certain assumptions as to 

 the laws of the elasticity of the matter which moves in them. In 



