FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
433 
c __ 4 % ~ c 23 I i C 13 ~ C 31 
2 J 2 
c 12 
(31) 
The important characteristic of a self-conjugate operator is 
Ei Do — E 2 Di, | 
1 " 2 1 >.(32) 
or E 1 c 0 E 2 = EsjCoEj, J 
where E 1 and E 3 are any two E’s, and D 1} D 3 the corresponding D’s. But when 
there is not symmetry, the corresponding property is 
E,D, = EJ>\, j 
12 >.(33) 
or E l cE 2 = Eoc'E^ J 
Of these operators we have three or four in electromagnetism connecting forces and 
fluxes, and three more connected with the stresses and strains concerned. As it 
seems impossible to avoid the consideration of rotational stresses in electromagnetism, 
and these are not usually considered in works on elasticity, it will be desirable to 
briefly note their peculiarities here, rather than later on. 
On Stresses, irrotational and rotational, and their Activities. 
§ 10. Let P N be the vector stress on the N plane, or the plane whose unit normal 
is N. It is a linear function of N. This will fully specify the stress on any plane. 
Thus, if P l5 P 3 , P 3 are the stresses on the i, j, k planes, we shall have 
P x = iP n + jP 12 +kP 13 ,'| 
Po = ip 21 + jP 2 o + kP 23 , l.(34) 
= f?31 + JP 32 + k P 33- J 
Let, also, Q N be the conjugate stress; then, similarly, 
Q-i = iPn + jP 2 i + kP 31 ,'| 
a 2 = iP 12 +jP 22 + kP 32 , l.(35) 
^3 — fPl3 + JP23 + ^ I> 33-' 
Half the. sum of the stresses P N and is an ordinary irrotational stress ; so that 
where (j> 0 is self-conjugate, and 
MDCCCXCir.— A. 
P N = 0,N + V€N ] 
a N = 0 o N-Y€N,J 
3 K 
(36) 
