of Molecular Vortices. 217 



The part of the specific heat which depends on periodical dis- 

 turbances is expressed as follows : — 



rf/ (*-l)Q \ = 3(*-l)/> Sp r_dk 

 dr^L k J " 2p r 2p r Q dr 



It is only by experiment that it can be ascertained whether 

 this part of the specific heat is constant or variable. Experi- 

 ment has proved that it is constant for the perfectly gaseous 

 state, and nearly, if not exactly, constant for other conditions, 

 but that its values for the same substance in the solid, liquid, 

 and gaseous conditions are often different*. 



The apparent specific heat contains other terms, depending on 

 the expenditure of energy in performing external and internal 

 work, according to principles of thermodynamics which are now 

 well known. 



§ 10. Examples of the Proportion in which the Total Energy 

 of the Thermal Motions exceeds the Energy of the Steady Circu- 

 lation. — In the perfectly gaseous state, the coefficient given in 

 equation (9) is the specific heat at constant volume; and as that 

 quantity is known to be constant at all temperatures, the second 

 term of the right-hand side of the equation disappears, and it is 

 reduced simply to the following, 



Jc=^ (12) 



The specific heat, in dynamical units per degree, of a perfect 

 gas under constant pressure, is expressed as follows, 



Jc '=J C+ ^=^.(?+l); . . . (13) 



and the ratio in which the latter coefficient is greater than the 

 former is therefore 



j- 1+ &i (14) 



whence we have the following formulae for deducing the propor- 

 tion k, borne by the total energy of the thermal motions to the 



c 

 energy of the steady circulation, from the ratio — as determined 



c 



* According to the nomenclature used by Clausius, the phrase "real 

 specific heat " is applied to that part only of the specific heat which is ne- 

 cessarily constant for a given substance in all conditions. Hence, if that 

 nomenclature were adapted to the hypothesis of molecular vortices, the 

 term real specific heat would be applied to the coefficient given in equa- 

 tion (10) only, and that given in equation (11) would be considered as part 

 of the apparent specific heat. 



