132 Mr. 0. Heaviside on Electromagnetic Waves, and the 



2. Plane Sheets of Impressed Force in a Nonconducting 

 Dielectric. — We need only refer to impressed electric force e, 

 as solutions relating to h are quite similar. Let an infinitely 

 extended nonconducting dielectric be divided into two regions 

 by an infinitely extended plane (x, y), on one side of which, 

 say the left, or that of —z, is a field of e of uniform intensity e, 

 but varying with the time. If it be perpendicular to the 

 boundary, it produces no flux. Only the tangential compo- 

 nent can be operative. Hence we may suppose that e is 

 parallel to the plane, and choose it parallel to x. Then E, the 

 force of the flux, is parallel to x, of intensity E say, and the 

 magnetic force, of intensity H, is parallel to ?/. Let e=f(t) ; 

 the complete solutions due to the impressed force are then 



E = ^H=-i/(*-*/i;j (9) 



on the right side of the plane, where z is + , and 



-E=tivTL=-if{t + z/v) (10) 



on the left side of the plane, where z is — . In the latter case 

 we must deduct the impressed force from E to obtain the 

 force of the field, say F, which is therefore 



F: 



-A0+if(t+i) (ii) 



The results are most easily followed thus. At the plane 

 itself, where the vortex-lines of e are situated, we, by varying 

 e, produce simultaneous changes in H, thus, 



H =^. W 



at the plane. This disturbance is then propagated both ways 

 undistorted at the speed v= (fic)~K 



On the other hand, the corresponding electric displacements 

 are oppositely directed on the two sides of the plane. 



Since the line-integral of H is electric current, and the 

 line-integral of e is electromotive force, the ratio of e to H is 

 the resistance-operator of an infinitely long tube of unit area ; 

 a constant, measurable in ohms, being 60 ohms in vacuum, 

 or 30 ohms on each side. Why it is a constant is simply 



they may be added on), and allows us to work without change of nota- 

 tion, especially when the -vectors are in special type, as they should be, 

 being entities of widely different nature from scalars. I denote a vector 

 by (say) E, its tensor by E, and its x, y, z components, when wanted, by 

 E„ E 2 , E 3 . The perpetually occurring scalar product of two vectors 

 requires no prefix. The prefix V of a vector product should be a special 

 symbol. 



