1901 - 2 .] 
Lord Kelvin on Stress and Strain . 
101 
And solving for a, b, c, e , /, g, in terms of p, q, r, p', q\ r, 
we have 
a=p-p; b = q~q'; c = r-r' : 
e = s-p-p+ 2 ; /= s-g-^' + 2;^ = s-r-/ + 2:J ' 
§ 8. The work required to produce an infinitesimal strain 
e, /, g, a, b } c, in a homogeneous solid of cubic crystalline sym- 
metry is expressed by the following formula : — 
2 w = H(e 2 +/ 2 + g 2 ) 4- ’2$$(fg + ge + ef) 4- n{a? + b 2 + c 2 ) (8). 
This may be conveniently modified by putting 
* = J(H + 2»); ^ = • . • . (9), 
where & denotes the bulk modulus and n v n the two" rigidity- 
moduluses. With this notation (8) becomes 
2w = k(e +f + gf + § n^_(f - gf + {g- ef + (e -ff] + n(a 2 + b 2 4- c 2 ) . . . (1 0). 
The rigidity relative to shearings parallel to the pairs of planes 
of the cube, or, which is the same thing, changes of the angles of 
the corners of the square faces from right angles to acute or obtuse 
angles, is n Y The rigidity relative to changes of the angles be- 
tween the diagonals of the faces from right angles to acute or 
obtuse angles is n. The compressibility modulus is k. Using now 
(7) in (10) we have 
2 w = ks 2 + ^n x [{q + q - r - r'f -1- (r + r -p -pf -\-(p+p -q- qff] 
+ n[{p-p')‘ 2 + {q-qf + {r-r'f) (11). 
(. Issued separately April 1 , 1902 .) 
