591 
of Edinburgh, Session 18GS-69. 
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 ex- 
ceeds 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 ex- 
amples : — air, T634; 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 
indefinitely small change in its temperature and dimensions: 
then — 
dQ = t d * cf) ; 
in which r is the absolute temperature, and <£ the thermodynamic 
function. The value of that function is — 
JTT 
</> = Jc hyplog t + x( T ) + 
4 ir 
VOL. VI. 
