124 LOUIS VESSOT KING 
of which the complete primitive is 
U=Art=, (1) 
A and B being constants to be determined from the specified bound- 
ary conditions. Longitudinal stress superimposed upon the radial 
stresses can be taken into account by taking the displacement w in 
the direction of the axis to be w=ez, e being a constant representing 
a uniform longitudinal extension. 
If we denote by 77 the stress-component along the radius 7, by 
66 the component at right angles to r and by 2 that along the 
axis, we find from the stress-equations of equilibrium, 
) 
rr = (A+ 2p) ee 
66 = (at an) pre a (2) 
on id ry) 
sncureian(4tt 
According to Lamé’s notation is the modulus of rigidity and » 
one of the moduli of elasticity such that «= (A+2,z) is the modulus 
Xu 
of compression. Poisson’s ratio, 7, is denoted by «= ———... 
In terms of A and B of equation (1) we have for the principal 
stresses. and the hydrostatic pressure p 
p= 2(A+n)A —SB+e 
G0=2(\+n)A +S B+ (3) 
23 = 2AA+(A+2p)e 
—3(7 +6042) = —«(A +e) 
If accented letters refer to corresponding quantities in the 
coaxial nickel-steel jacket, we have for the principal stresses a set 
of equations analogous to (1) and (3), 
