244, 245] EQUATIONS OF ELECTROMAGNETIC FIELD. 509 



induction this will generally be true. We are now, however, about 

 to consider a new class of phenomena, and it will be convenient to 

 use the Gaussian system, that is, to measure all electrical quantities 

 in electrostatic units, and all magnetic ones in magnetic units. 

 We shall therefore be obliged to reintroduce the factor A, 210, 

 which will multiply the electric currents, and divide the electrical 

 forces, according to 212, equations (6) and (9). Equations (14) and 

 (5) thus become* 



. a* dN dM . as dz 97 



A ^T + QtTrAu = -= -- ir- , A^- = ^ -- -r , 



dt dy dz dt dy dz 



.eg) dL dN . m dx dz 



(A) A ^ + 4i7rAv = -^ ---- , (B) -.4 = - -- ^-, 



dt dz dx dt dz dx 



, 93 dM dL . 99t dY dX 



A ~ 



~ -^ -- 5- , ^r- - - . 



dt dx dy dt dx dy 



These are the equations of cross-connection between the elec- 

 tric and magnetic fields and thus show that in non-conductors the 

 curl of the force of either field determines, or is determined by, 

 the time-variation of the induction of the other. If we know the 

 state of the field at any instant we may accordingly find it at any 

 subsequent instant. For we have the three sets of equations 

 expressing the Fourier-Ohm laws, 



= eX, 8 = /juL, u = \X, 



(C) g) = eF, (D) W = pM, (E) v=\Y, 



The letter e denotes the electric inductivity, which in Chapter IX, 

 where we did not distinguish electric and magnetic quantities, was 

 denoted by ^. It will be noticed that equations (A) and (B), 

 which are the fundamental equations of the theory, contain no 

 quantities that are intrinsic to the media, but only those quantities 

 which completely specify the electric and magnetic state of the 

 fields. The equations (C), (D), and (E), on the contrary, contain 

 the quantities e, //, and X, which denote properties of the media. 

 These latter equations are not fundamental to the theory, as they 

 may under certain circumstances be replaced by others. In addition 



* In Hertz's papers the right-hand members appear with the opposite sign, since 

 Hertz employs the left-handed arrangement of axes. (Cf. Fig. 1.) 



