19 

 PRELIMINARY NOTES ON ME. HALL'S RECENT DISCOVERY * 



[Philosophical Magazine [5], IX, 432-434, 1880 ; Proceedings of the Physical Society, IV, 

 10-13, 1880; American Journal of Mathematics, II, 354-356, 1879] 



The recent discovery by Mr. Hall 3 of a new action of magnetism on 

 electric currents opens a wide field for the mathematician, seeing that 

 we must now regard most of the equations which we have hitherto used 

 in electromagnetism as only approximate, and as applying only to some 

 ideal substance which may or may not exist in nature, but which cer- 

 tainly does not include the ordinary metals. But as the effect is very 

 small, probably it will always be treated as a correction to the ordinary 

 equations. 



The facts of the case seem to be as follows, as nearly as they have 

 yet been determined: Whenever a substance transmitting an electric 

 current is placed in a magnetic field, besides the ordinary electromotive 

 force in the medium, we now have another acting at right angles to the 

 current and to the magnetic lines of force. Whether there may not be 

 also an electromotive force in the direction of the current has not yet 

 been determined with accuracy; but it has been proved, within the limits 

 of accuracy of the experiment, that no electromotive force exists in the 

 direction of the lines of magnetic force. This electromotive force in a 

 given medium is proportional to the strength of the current and to 

 the magnetic intensity, and is reversed when either the primary current 

 or the magnetism is reversed. It has also been lately found that the 

 direction is different in iron from what it is in gold or silver. 



To analyze the phenomenon in gold, let us suppose that the line A B 

 represents the original current at the point A, and that B C is the new 

 effect. The magnetic pole is supposed to be either above or below the 

 paper, as the case may be. The line A C will represent the final 

 resultant electromotive force at the point A. The circle with arrow 

 represents the direction in which the current is rotated by the mag- 

 netism. 



1 From the American Journal of Mathematics. Communicated by the Physical 

 Society. 



* Phil. Mag. [5], vol. ix, p. 225. 



