OF MOLECULAR VORTICES. 561 



force on the unit of area; and the proportion k, in which the total energy of 

 thermal motions exceeds the energy of steady circulation, is a quantity whose 

 values and laws are left to be deduced from the results of experiment. 



§ 8. Determination of Centrifugal Pressures. — The external pressure exerted 

 by any substance, as we find it in nature, is a complex quantity, being com- 

 pounded of the centrifugal pressure already mentioned, and of forces which may 

 be classed together under the name of cohesion. To enable us to distinguish 

 those components of the total pressure from each other, we have the principle, 

 that the centrifugal pressure varies as the density simply ; whereas pressure or 

 tension, or stress (to use a general term), arising from cohesive forces, must 

 vary as some function of the density of a higher order than the first power. 



The perfectly gaseous state is an ideal state in which the substance exerts 

 no external pressure except that which varies as the density simply ; that is, 

 centrifugal pressure. It is impossible to obtain a substance absolutely in the 

 state of perfect gas ; but the cohesive stress diminishes with increase of tempera- 

 ture and diminution of density in such a manner, that it is possible, as is well 

 known, to obtain substances approaching very nearly to the perfectly gaseous 

 state, such as atmospheric air and various other gases ; and the actual pressures 

 of such nearly perfect gases may be used, either as approximate values of the 

 pressures in the ideal state of perfect gas, or as data for calculating the latter 

 kind of pressures by the method of limits. We thus have the means of determin- 

 ing, to a close approximation, the centrifugal pressure of a given substance at a 

 given temperature and density; the well-known formula being 



p -=f-~ TO; 



p Po T o 



in which t is the absolute temperature of melting ice ; t the actual absolute 



temperature ; and — the value of the quotient - at the temperature of melting 



ice, for the particular substance in question. 



§ 9. Temperature and Specific Heat. — It is shown in the paper of 1849-50, 

 that temperature, according to the hypothesis of molecular vortices, is a function 

 of the quotient found by dividing the energy of the steady circulation in an unit of 

 mass by a constant depending on the nature of the substance ; which constant 

 may be defined, as the value which the energy of steady circulation in an unit 

 of mass of the given substance assumes at a standard temperature, such as that 

 of melting ice. The energy of the steady circulation in an unit of mass is 



w 2 3 p 



~2 = 2 ' p ' 



whence it appears, that the principle stated as to absolute temperature is 



VOL. XXV. PART II. 7 F 



