556 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XIII. 



to the number of unit tubes of induction cut perpendicularly 

 by the element in unit time. 



On the left of (A") appears the term 



A |^ + curl Vgu + v div g + 47r? 1 , 



consisting of, first, the ordinary conduction current q, as in 222 

 (2), second, the displacement current, as in equations (A), third, 

 a new term equal to the product of the velocity by the density of 

 electric charge. In other words a charge in motion produces the 

 same effect as a current. This is verified by Rowland's celebrated 

 experiment*. The corresponding quantity in equation (B") shows 

 the known electromotive forces produced by the motion of magnets, 

 and also explains the phenomena of unipolar induction. It is to 

 be noticed that the theory makes the magnets carry their lines of 

 force with them. 



The complete symmetry . between electrical and magnetic 

 phenomena may now be said to have been completely verified by 

 experiment, with the exception of the second term of equation (A") 

 which would show the existence of a magnetic field due to the 

 motion of insulating bodies in an electric field. The existence of 

 such magnetic fields is made probable by an experiment made by 

 Rontgenf. 



The method of deducing the equations (A") and (B") may be 

 applied even when our axes of coordinates are in motion, if a, /?, 7 

 be the velocities relative to the axes, and e, /*, X refer to the points 

 fixed with respect to the moving axes. Thus the mutual actions 

 of bodies depend only on their relative motion. Some simple 

 considerations of this nature elucidating the phenomena of uni- 

 polar induction are found in a paper by the author in the Electrical 

 World^, the statements there made being borne out by experi- 

 ments by Lecher. 



* Helmholtz, "Bericht betreffend Versuche iiber die elektromagnetische 

 Wirkung elektrischer Convection, ausgefiihrt von H. A. Eowland." Pogg. Ann. 

 148, p. 487, 1876 ; Wist. Abh. Bd. i. p. 791. 



t "Ueber die durch Bewegung eines im homogenen elektrischen Felde befind- 

 lichen Dielektricums hervorgerufene electrodynamische Kraft." Wied. Ann. 35, p. 

 264, 1888. 



J "Unipolar Induction and Current without difference of Potential." Elec. 

 World (N.Y.), 23, pp. 491, 523, Apr. 1421, 1894. 



"Eine Studie iiber unipolare Induction." Wied. Ann. 54, p. 276, 1895. 



