
STRESSES DUE TO COMPOUND STRAINS. 487 
The application of (/) to J*_, produces the stress-group 


(Bb + Ce—Dd,..... , De + dE — Cf— Fe). 
Theorem (h). If we choose J = V =|uv w| we obtain the force-group 
apy fy 
(yo — Bw, ... Bu — av); while if we choose J’= V* and put a? = a, 
w=A.., oB =f, w= F, we reproduce the stress-group last 
found 
‘fj one ad d d : 
_By putting w= 7. v= dy? = qi We arrive at the force - group 
dv dw GB dC a?) 
ie apelet ) and the stress-group ye ale dyde °° ) 
Theorem (i). J = (wa + vB + wy) (ax + By + yz) and J'= (ux + ry + wz) 
(az + By + yz) generate respectively the force- and stress-groups 
| 5 ee cr 
(uA + oF + wE,...), (ua, ....,5 UB + a). 
: : dA dF dk 
These include as particular cases the groups (= oF Ae De 3s) and 
da 1,dB. da 
dtd Eta): 
Theorem (j). J = V . (wa + vB + wy) generates the force-group (6 — eD 
—dB—C+/fE—eF,...); while J'‘= V . (av + By + yz) generates 
the stress-group (vE — wF,... ; .wA —B—uE — 2F). 
! : e F : d d? 
These include as particular cases those in which a= 7, a=73.../ 
@ 
— dx dy’ 
