248 Intelligence and Miscellaneous Articles. 



bodies in circulating streams with a velocity either constant or fluctua- 

 ting periodically. This, of course, implies that the forces acting 

 amongst those particles are capable of transmitting that motion. 



The principal conclusions arrived at are the following : — 



(1) In a substance in which the action of the vortices is isotropic, 

 the inteusity of the centrifugal pressure per unit of area is two-thirds 

 of the energy due to the steady circulation in a unit of volume. 

 The centrifugal pressure is the pressure exerted by the substance in 

 the perfectly gaseous state. 



(2*) If there be substances in which the action of the vortices is 

 not isotropic, then in such substances the proportion already stated 

 applies to the mean of the intensities of the centrifugal pressures in 

 any three orthogonal directions. 



(3*) The proportion which the whole energy of the vortices, in- 

 cluding that of the periodic disturbances, bears to the energy of the 

 steady circulation alone may be constant or variable. 



(4) Absolute temperature is proportional to the energy of the 

 steady circulation in unity of mass, and to the specific volume in the 

 perfectly gaseous state. 



(5) In substances which are nearly in the perfectly gaseous state, 

 experiment shows the proportion in which the whole energy exceeds 

 that of the steady circulation to be sensibly constant ; and its value 

 may be found by computing in what proportion the dynamical value 

 of the specific heat at constant volume exceeds once and a half the 

 quotient found by dividing the product of the pressure and volume by 

 the absolute temperature. *The following are examples : — air, 1*634 ; 

 nitrogen, 1*630; oxygen, 1*667; hydrogen, 1*614; steam-gas, 2*242. 



(6) The known general equation of thermodynamics is deduced 

 from the hypothesis of molecular vortices*, freed from the special 

 suppositions made in the paper of 1849-50. 



The new conclusions obtained in the present paper are marked *, 

 Those not so marked were arrived at in the paper of 1849-50. 



[The general equation of thermodynamics is here stated for con- 

 venience : — Let dQ be the thermal energy which must be given to 

 unity of mass of a given substance in order to produce a given inde- 

 finitely small change in its temperature and dimensions ; then 



dQt=-d .<j>; 



in which r is the absolute temperature, and (j> the thermodynamic 

 function. The value of that function is 



= Jchyp.logr + x(O+ -j-* 



Jc being the dynamical value of the real specific heat, U the potential 

 energy of the elasticity of the body at constant temperature, and 

 x( T ) a function of the absolute temperature, which is null or inap- 

 preciable in a substance capable, at that temperature, of approxi- 

 mating indefinitely to the perfectly gaseous state, and is included in 

 the formula in order to provide for the possibility, suggested by 

 Clausius, that there may be substances which have not that property 

 at all temperatures.] 



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