28 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, 
The suffix , being used to distinguish the value of quantities at those surfaces. 
Hence ®, isa maximum or minimum. Those surfaces are symmetrical in form 
round each nucleus, and equidistant between pairs of adjacent nuclei. Their 
equation is 
o—2,= O. 
Let M denote the total weight of an atom; » that of its atmospheric part, and 
M~—z that of its nucleus; then 
M V is the volume of the atom,— 
Ss the mean density of the atmospheric part, measured by weight, the 
nucleus being supposed to be of insensible magnitude ;— 
and we have the following equations 
WY Wf axay as 
(2.) 
pas LY 12 ay a2 fff, eazayaz b 
The suffix (,) denoting that the integration is to be extended to all points 
within the surface 
(6—®,=0). 
According to the hypothesis now under consideration, //eat consists in a re- 
volving motion of the particles of the atomic atmosphere, communicated to them 
by the nuclei. Let v be the common mean velocity possessed by the nucleus of 
an atom and the atmospheric particles, when the distribution of this motion has 
been equalised. I use the term mean velocity to denote, that the velocity of each 
particle may undergo small periodic changes, which it is unnecessary to consider 
in this investigation. 
Then the quantity of heat in unity of weight is 
Ye 
are 
being equal to the mechanical power of unity of weight falling through the height 
yy The quantity of heat in one atom is of course MQ, and in the atmospheric 
part of an atom, p Q. 
I shall leave the form of the paths described by the atmospheric particles in- 
determinate, except that they must be closed curves of permanent figure, and in- 
eluded within the surface (#-#,=0). Let the nucleus be taken as the origin of 
co-ordinates, and let a, 3, y, be the direction-cosines of the motion of the particles 
at any point (a, y, 2). Then the equations of a permanent condition of motion at 
that point, are 

