302 Maxwell. 



the resultant force per unit area along the outward normal is 

 therefore 



- IDE . t . (l//t>i + I//*), 

 and so we have 



T = - IDE . t ; 



or the pressure at right angles to the lines of force is |DE per 

 unit area that is, it is numerically equal to the tension along 

 the lines of force. 



The principal stresses in the medium being thus determined, 

 it readily follows that the stress across any plane, to which the 

 unit vector N is normal, is 



(D.N)E-i( D - E ) N - 



Maxwell obtained* a similar formula for the case of magnetic 

 fields ; the ponderornotive forces on magnetized matter and on 

 conductors carrying currents may be accounted for by assuming 

 a stress in the medium, the stress across the plane N" being 

 represented by the vector 



1(B.K).H-1( B .H).N. ;j 



This, like the corresponding electrostatic formula, represents a 

 tension across planes perpendicular to the lines of force, and a 

 pressure across planes parallel to them. 



It may be remarked that Maxwell made no distinction 

 between stress in the material dielectric and stress in the 

 aether : indeed, so long as it was supposed that material bodies 

 when displaced carry the contained aether along with them, 

 no distinction was possible. In the modifications of Maxwell's 

 theory which were developed many years afterwards by his 

 followers, stresses corresponding to those introduced by Maxwell 

 were assigned to the aether, as distinct from ponderable matter ; 

 and it was assumed that the only stresses set up in material 

 bodies by the electromagnetic field are produced indirectly: 

 they may be calculated by the methods of the theory of 

 elasticity, from a knowledge of the ponderomotive forces 

 exerted on the electric charges connected with the bodies. 



* Maxwell's Treatise on Electricity and Magnetism, 643. 



