430 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, 
k(@—9!) 
[[fezay azar fe Vago. 
yy 
a a (f—4,) k (9-91) 
WUVE h Yardy dz=kMV fe odd 
w! 
k being a specific constant, and y and 4 functions of ¢, and of the nature and 
density of the substance. 
The lower limit of integration of @ must be made—-, that it may include 
orbits of indefinitely small magnitude described round the atomic centre. 
The nature of the function ¥ is limited by the following condition, 
o, '@-o) 
1=uf ''s Ee Pe oie toe ane 
29 4k 
6) 
Then these transformations give the following result for the pressure at the bound- 
ing surface of an atom :— 
he , kd akg) 
pH=he= uve foe @ meee 
e's (8.) 

w',, &c. being the successive differential coefficients of w with respect to 4, when 
p=>i- 
(4.) The following transformation will be found useful in the sequel. 
Let A be the indefinite value of log. V, and A, its actual value in the case 
under consideration. Let G be the same function of A which w is of & , and let 
G’, G”, &c. be its successive differential coefficients with respect to A. 
Let ON 
Then 
_ ApG ; 
DME re Pen ae . oy 
The function H has the following properties, which will be afterwards referred 
to :— 

dH, 
a ee j i : ; ; : ; | 
10.) 
Ay dH ( 
HdA=- — 
ee a0 | 

ee 
