348 The Followers of Maxwell. 



the same way as dynamical energy is carried by water flowing 

 in a pipe; whereas in Maxwell's theory, the storehouse and 

 vehicle of energy is the dielectric medium surrounding the wire. 

 What Poynting achieved was to show that the flux of energy at 

 any place might be expressed by a simple formula in terms of 

 the electric and magnetic forces at the place. 



Denoting as usual by E the electric force, by D the electric 

 displacement, by H the magnetic force, and by B the magnetic 

 induction, the energy stored in unit volume of the medium is* 

 l ED + (1/8*) BH ; 



so the increase of this in unit time is (since in isotropic media 

 D is proportional to E, and B is proportional to H) 



ED + (1/4*) HB 



or E (S - i) + (1/4*) HB, 



where S denotes the total current, and i the current of 



conduction ; or (in virtue of the fundamental electromagnetic 



equations) 



- (E . i) 4. (1/4*) (E . curl H) - (1/4*) (H . curl E}, 

 or - (E . i) - (1/4*) div [E . H]. 



Now (E . i) is the amount of electric energy transformed into 

 heat per unit volume per second; and therefore the quantity 

 - (1/4*) div [E . H] must represent the deposit of energy in unit 

 volume per second due to the streaming of energy; which 

 shows that the flux of energy is represented by the vector 

 (1/4*) [E.HJ.f This is Poynting's theorem: that the flux of 

 energy at any place is represented by the vector-product of the 

 electric and magnetic forces, divided by 4*.* 



* Cf. pp. 248, 250, 282. 



t Of course any circuital vector may be added. II. M. Macdonald, Electric Waves, 

 p. 72, propounded a form which differs from Poynting's by a non-circuital vector. 



J The analogue of Poynting's theorem in the theory of the vibrations of an 

 isotropic elastic solid may be easily obtained ; for from the equation of motion of 

 an elastic solid, 



p& = - (k + 4/3) gnid div e n curl curl e, 

 it follows that 



tot* + i (* + $) (div e) + in (curl e)'} = - div W, 



