150 MR W. J. M. RANKINE ON THE 
any substance, / its coefficient of elasticity, and m the number of atoms which, in 
the state of perfect gas, occupy unity of volume under unity of pressure at the 
temperature of melting ice ;—then 
TA fa SAPNA Reh ek cei (IL) 
is a constant quantity for all substances. 
Secondly, The superficial elasticity of a vortex must not be a function of its 
diameter: to fulfil which condition, the linear velocity of revolution must be equal 
throughout all parts of each individual vortex. ‘ 
Thirdly, Yn all contiguous vortices of the same substance, the velocities of 
revolution must be equal; and in contiguous vortices of different substances, the 
squares of the velocities must be proportional to the coefficients of elasticity of 
the molecular atmospheres. 
The second and third conditions are those of equilibrium of heat, and are 
equivalent to this law :— 
TEMPERATURE ¢s a function of the square of the velocity of revolution in the mo- 
lecular vortices divided by the coeficient of elasticity of the atomic atmospheres ;—or 
we 
Temperature = $ (5) - aioe fei ACL) 
where w represents that velocity. 
The mean elasticity which a vortex exerts endways is not affected by its 
motion, being equal to 
tin cn oie oy Sel a ol CUES) 
where g is its mean density. The superficial elasticity at its lateral surfaces, 
however, is expressed by 
7” 0 
29 

RGR Lee We wees LV) 
The additional elasticity aR? being that which is due to the motion, is 
independent of the diameter. The divisor g (the force of gravity) is introduced, 
on the supposition of the density e being measured by weight. 
Supposing the atmosphere of an atom to be divided into concentric spherical 
layers, it may be shewn that the effect of the coexistence of a great number of 
small vortices in one of those layers whose radius is 7, and mean density e, is to 
give it a centrifugal force, expressed by 
Ww 
gr 
which tends to increase the density and elasticity of the atmosphere at the sur- 
face, which I have called the boundary of the atom. The layer is also acted upon 
by the difference between the mean elasticities at its two surfaces, and by the 
attraction towards the atomic centre; and these three forces must balance each 
other. 

v.) 4 

