174 General Analytical Theorems [CH. vn 



Thus if P XX) Pay, etc. have the values given by equations (118) and (119), 

 we have 



E' = K, etc. 



This shews that the mechanical force 5, H, Z reversed would just be 

 in equilibrium with the system of stresses P xx , P xy , etc. given by equations 

 (118) and (119). In other words, the mechanical forces which have been 

 found to act on a dielectric can exactly be accounted for by a system of 

 stresses in the medium, these stresses being given by equations (118) and 

 (119). 



199. The system of stresses given by equations (118) and (119) can be 

 regarded as the superposition of two systems : 



I. A system in which 



II. A system in which 



r>2 377- 



P -p -p -L T ^ 



xx * yy * zz o ' ^ > 



07T OT 



The first system is exactly K times the system which has been found to 

 occur in free ether, while the second system represents a hydrostatic pressure 

 of amount 



_^! *K 



STT T dr ' 



(In general -^ will be positive, so that this pressure will be negative, and 

 must be interpreted as a tension.) 



Hence, as in 165, the system of stresses may be supposed to consist of: 



TT D2 



(i) a tension -- - per unit area in the direction of the lines of force ; 



O7T 



(ii) a pressure - - per unit area perpendicular to the lines of force ; 



O7T 



D2 ^ 7" 



(iii) a hydrostatic pressure of amount ^ T -^ in all directions. 



The system of stresses we have obtained is that given by Helmholtz. The system 



7?2 7\ JT 



differs from that given by Maxwell by including the pressure r ^ . The neglect of 



O7T 07" 



this pressure by Maxwell, and by other writers who have followed him, does not appear to 

 be defensible. 



