1901—2.] 
Lord Kelvin on Stress and Strain. 
97 
A New Specifying Method for Stress and Strain in an 
Elastic Solid. By Lord Kelvin. 
(Read January 20, 1902.) 
The method for specifying stress and strain hitherto followed 
by all writers on elasticity has the great disadvantage that it essen- 
tially requires the strain to be infinitely small. As a notational 
method it has the inconvenience that the specifying elements are 
of two essentially different kinds (in the notation of Thomson and 
Tait e, /, g, simple elongations ; a, b, c , shearings). Both these 
faults are avoided if we take the six lengths of the six edges of a 
tetrahedron of the solid, or, what amounts to the same, though less 
simple, the three pairs of face-diagonals of a hexahedron,'" as the 
specifying elements. This I have thought of for the last thirty 
years, but not till a few weeks ago have I seen how to make it 
conveniently practicable, especially for application to the generalised 
dynamics of a crystal. 
§ 1. We shall suppose the solid to be a homogeneous crystal of 
any possible character. Cut from it a tetrahedron ABCD of any 
shape and orientation. Let the three non-intersecting pairs (AB, 
CD), (BC, AD), (CA, BD) of its six edges be denoted by 
(%, Sp-), (32. 3gO, (Sr, 30 . . . (1). 
This notation gives 
(p, p')> fo 2')» (r, r') (2) 
for the six edges of a tetrahedron, similar to ABCD, formed by 
taking for its corners (a, /3, y, S) the centres of gravity f of the four 
* This name, signifying a figure bounded by three pairs of parallel planes, 
is admitted in crystallography ; but the longer and less expressive ‘ £ parallele- 
piped” is too frequently used instead of it by mathematical writers and 
teachers. A hexahedron, with its angles acute and obtuse, is what is commonly 
called, both in pure mathematics and crystallography, a rhombohedron. A 
right-angled hexahedron is a brick, for which no Greek or other learned name 
is hitherto to the front in usage. A rectangular equilateral hexahedron is a 
cube. 
t For brevity I shall henceforth call the centre of gravity of a triangle, or 
of a tetrahedron, simply its centre. 
PROC. ROY. SOC. EDIN. — VOL. XXIV. 7 
