December 9, 1898.] 



SCIENCE. 



805 



If Maxwell's theory was true, then ex- 

 perimenters should discover the magnetic 

 effect of the displacement current. We 

 may well imagine that for many years in- 

 vestigators were devising means to accom- 

 plish this result ; but if this was so, they 

 were not rewarded by success. However, 

 a crucial question had been agitated, for, 

 according to Maxwell, electrical and mag- 

 netic disturbances must be propagated with 

 a finite velocity, and the theory of action at 

 a distance must be doomed. 



Before passing to the post- Max wellian, or, 

 as we may call it, the modern era, it may 

 be convenient to state Maxwell's theory as 

 he left it. 



Electrical changes are related, not to 

 the so-called field intensity, whose com- 

 ponents are X, Y, Z, derivable from a poten- 

 tial r, 



(1) 



ay- 



92, "^ 33 ' 



but to a new vector, called the electric dis- 

 placement, and denoting the state of polar- 

 ization discovered by Faraday. The com- 

 ponents of this, /, g, h, are proportional to 

 the components of the field, 



(2) 



/= 



^3f X, 



471- 



^ y,A = ^ z, 



of the medium, 

 ever 



(6) 



47r ' iw 



where K measures a physical property of 

 the medium, Faraday's specific inductive 

 capacity. 



The density of the charge then is derived 

 from the displacement by the equation 



(3) 



dx 



3(7 . 37j 



Similarly in magnetism we are to con- 

 sider two vectors, the field a, /3, y, derivable 

 from a potential i2, 



_ 9" rt_ 3^ ,_ 3" 

 ^x' dy' dz' 



(4) 



and the induction, proportional to it, 



(5) a^fia, Izzz |U^, c = fiy, 



where /t measures another physical property 



Maxwell here puts how- 



3a . 3i , 3e 



dx ' dy dz 



SO that the analogy with the electrical equa- 

 tion (3) is not quite perfect. 



To the equations previously accepted giv- 

 ing the relations between the current den- 

 sity M, V, w, and the magnetic field produced 

 by it, 



32'_3^ 

 '3y 3a' 



da 3y 



dz dx ' 



(7) 



4 TTM = — - 



4 7rD = 



3/3 da 



Attv] = - — , 



dx dy 



Maxwell adds the effect of the displace- 

 ment currents, so that he has 



dy 3/3 



(8) 



\dt / dz dx 



^1- 

 dx 



The induced electromotive-forces due to 

 changes in the magnetic field are represented 

 by Maxwell in a somewhat peculiar manner, 

 as the negative derivatives of a new vector 

 called the vector -potential, so that 



(9) 



dF 

 ' dt' 



dG 

 dt' 



= — ~~, B = - 



dH 

 'dt' 



The vector-potential is related to the mag- 

 netic induction by the equations 

 dH dG 



dy dz 



(1«) *=3T-3:r' 



_3g dF 



dx dy 



Thus the vector- potential itself does not 

 appear, but only its time-derivatives. 



The vector-potential was introduced by 

 Maxwell to denote what Farraday termed 

 the electro- tonic state of a body undergoing 

 induction of current by magnetic changes. 



Strangely, as it now seems, the ideas of 



