2 R. F. GWYTHER, Specification of the elements of stress. 



stress quadric to be drawn. These two quadrics will be 

 coaxial. 



We have three dynamical equations which give the 

 whole dynannical relation between the stresses, and to 

 which there is nothing to add. It is regarded, and the 

 truth will appear from the paper, that these relations fix 

 the characteristics of a stress quadric from the essentially 

 dynamical basis, but that they do not determine its 

 orientation. To complete the dynamical specification, I 

 make the further hypothesis that this quadric shall be so 

 oriented as to be coaxial with the strain and the elastic 

 stress quadrics, and be drawn on the same scale as the 

 latter. The strain quadric has now served its purpose 

 and may be ignored. We remain with two coaxial stress 

 quadrics, one the " elastic " stress quadric, the other the 

 " dynamical " stress quadric. 



Each is definite, and they are not identical except as 

 the result of three further conditions of equality. 



If we call the elements of the elastic stress 



p:qiris[t:u: 



each is defined by Hooke's Law. 



If the elements of the dynamical stress are 



P, Q, R, S, T, U, 



we have 



dF dU dT ^ 



— + ^- + ^ = 0, 

 cix vy ds 



dU dQ dS ^ 



ox oy cs 



dr ds dj? ^^ 



dx oy oz 

 or p__?^>_^3 



^ ~ dz' dx' ' 



