of the Hall Effect and Allied Phenomena. 527 



electromotive force directed at right angles to the current 

 and to the magnetic force. Thus, if a metal bar, along 

 which a current is flowing, be placed in a magnetic field 

 perpendicular to the direction of the current, the current 

 will tend to be deflected from its course and to move towards 

 the one or the other of the edges of the bar. This cross flux 

 of electricity will in fact initially exist, but it cannot be 

 permanent since it will give rise to a slight accumulation of 

 charge on the outer edges of the bar, the additional electric 

 field thus set up tending to oppose the transverse current. 

 A final steady state of equilibrium will be attained in which 

 there is no cross flow of electricity, the additional electric 

 field being just sufficient to balance the transverse electro- 

 motive force arising from the magnetic field. The additional 

 electric field thus created is capable of precise determination 

 by connecting the opposite edges of the bar to the terminals 

 ot: an electrometer. It is in fact this potential difference 

 which was actually measured by Hall and subsequent workers 

 in this subject*. 



In 1886 Nernst and von Ettingshausen found that a similar 

 potential difference can be measured when the electric current 

 is replaced by a current of heat in the same direction along 

 the bar, and then in 1887 von Ettingshausen found that in 

 the arrangement adopted by Hall a temperature difference 

 analogous to the potential difference in Hall's experiments 

 can be obtained. Finally, and also in the year 1887, Rigbi 

 and Leduc found a similar temperature difference if the 

 electric current is replaced as in Nernst's experiments by a 

 current of heat. 



A simple explanation of these phenomena was soon forth- 

 coming as soon as the electron theory of metallic conduction 

 began to be developed, and was, in fact, provided by Riecke f , 

 Drude J, and J. J. Thomson §. An electric conduction 

 current consists essentially in a flux of negative electrons 

 which possess, as the result of the action of the electric 

 driving field, a finite average velocity in the direction opposite 

 to that of the electric force If we suppose this average 

 velocity of drift of the electrons to be represented bv the 

 vector r, then the action of a magnetic field of force of 

 intensity H would be such that each electron will on the 

 average be acted on by a force specified in magnitude and 



* See K. Baedeker, ' Die elektrische Eischeinrmgen in metallischen 

 Leifcern ' (Braunschweig, 1911), Ch. IV. 

 t Wied. Ann. lxvi. (1898). 

 1 Ann. der Phj/sik, i. p. 566 ; iii. p. 369 (1900). 

 § Itapp. Congr. Physique, iii. p. 143 (Paris, 1900). 



