of Molecular Vortices. 215 



is all actual ; at every other instant the energy is partly poten- 

 tial. Hence v 2 =kw 2 may be taken to denote, not the square of 

 an actual velocity common to all the particles, but the value to 

 which the square of the velocity of the particles would rise if all 

 the energy of the disturbances, actual and potential, were ex- 

 pended in increasing the velocity of steady circulation. 



§ 7. Total Energy of Thermal Motions. — The total energy of 

 the motion compounded of steady circulation and periodical dis- 

 turbances, in a unit of volume, is expressed, as in the paper of 

 1849-50, by the folio wing equation, which also shows its rela- 

 tion to the centrifugal pressure, 



kpw 1 3k fax 



2 =Y p - (6) 



in which (to recapitulate the notation) p is the mean density, 

 w the velocity of steady circulation ; the centrifugal pressure p 

 is expressed in absolute units of 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 ex- 

 periment. 



§ 8. Determination of Centrifugal Pressures. — The external 

 pressure exerted by any substance, as we find it in nature, is a 

 complex quantity, being compounded of the centrifugal pressure 

 already mentioned, and of forces which may be classed together 

 under the name of cohesion. To enable us to distinguish these 

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

 principle that the centrifugal pressure varies as the density sim- 

 ply; 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 sub- 

 stance 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 temperature 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 

 determining, to a close approximation, the centrifugal pressure 

 of a given substance at a given temperature and density ; the 



