104 MR JAMES CLERK MAXWELL ON THE 
by external and internal normal pressures /, and /., it is required to determine 
the equilibrium of the elastic solid. 
The pressures at any point in the solid are :— 
1. A pressure p in the direction of the radius ; 
2. A pressure g in the perpendicular plane. 
These pressures depend on the distance from the centre, which is denoted by 7. 
The compressions at any point are a in the radial direction, and es in the 
tangent plane, the values of these compressions are :— 
dor 1 1 1 
ore = (s3-gq) P+ 29)+—p- . . (84) 
ore i 
an =l-== — 35) (+2 Qt - » + (35.) 
Multiplying the last equation by 7, differentiating with respect to r, and 
equating the result with that of the first equation, we find 
i 1 dp LO /aag 
. Ga sa) (F +20!) 4 (rhe ge ») =e 
Since the forces which act on the particle in Ws direction of the radius must 

balance one another, or 2¢gdrd0+p(rd0=(p — dr)(r+d7r)0 
r dp 
ies 5 dr 
Substituting this value of g—p in the preceding equation, and reducing, 
dp dq 
ceeds 
(36.) 
Sl 
Integrating, p+2q=¢, 
rd 
But I1=5 576 +p, and the equation becomes 
apg & 5 
a 3° +2 =0 
i rae 
Urs oa 3 
Since p=h, when r=a,, and p=’, when r=a,, the value of p at any time is 
found to be 


a2h,—a eh, a a,2h,—h 
Pt aae Vice ee ee 
a h,—a,*h, a> a? h—h, 
a ae ra ape - (38.) 
Dro Ore ee =4,5 hy dy oct (ae h,—h, 1 

ay 3 
V r a~—a,> pp 2 7 a3—a,> m 
