98 
Proceedings of Royal Society of Edinburgh. [sess. 
triangular faces BCD, CDA, DAB, ABC respectively, so that 
we have p — a/3, q = f3y, r = ya, p = yS, f = aS, r' = f3§. Consider 
now, in advance, the amounts of work done by the six pairs of 
balancing forces constituting the six stress-components described in 
§ 2, when the strain-components vary ; for example, the balancing 
pulls P, parallel to AB, when a/3 increases from p to p + dp, all 
the other five lengths q, r, p, q, r remaining constant. For the 
reckoning of work we may suppose the opposite forces, P, to he 
applied at a and (3, instead of being equably distributed over the 
faces ADC, BDC. Hence the work which they do is P dp ; and 
other five pairs of balancing pulls, Q, R, P', Q', R', do no work. 
§ 2. Parallel to the edge AB apply to the faces ADC, BDC 
equal and opposite pulls, P, equally distributed over them. These 
two balancing pulls we shall call a stress or a stress-component. 
Similarly, parallel to each of the five other edges apply balancing 
pulls on the pair of faces cutting it. Thus we have in all six stress- 
components parallel to the six edges of the tetrahedron, denoted 
as follows : — 
(P,F) (Q,Q’) (B, B’) .... (3); 
and we suppose that these forces, applied as they are to the four 
faces of the solid, are balanced in virtue of the mutual forces 
between its particles, when its edges are of the lengths specified as 
in (1). Let _p 0 , pf , g 0 , gf , r 0 , rf be the values of the specifying 
elements when no forces are applied to the faces. Thus the 
differences from these values, of the six lengths shown in formula 
(2), represent the strain of the substance when under the stress 
represented by (3). 
§ 3. Let w be the work done when pulls upon the faces, each 
commencing at zero, are gradually increased to the values shown 
in (3). In the course of this process we have 
dw = Ydp + Ydp + Qdq + (fdq + Rcfo* 4 - R'dr' . . (4). 
Hence if we suppose w expressed as a function of p, p , q, q', r, r , 
we have 
dw -p. die , dw _ dw dw „ dw T> , 
^ =p> #' =p> dj =q ’ s? =Q ’ d/ =R • (4) - 
This completes the foundation of the molar dynamics of an 
