512 Prof. De la Rive on the Action of Magnetism upon 



the fluid velocity along the axis through the centre of the ring, when 



the section is so small that log — ^ is large in comparison with 2?r. 



a 



But the velocity of translation is always small in comparison with 



the velocity of the fluid at the surface of the core, and the more so 



the smaller is the diameter of the section in comparison with the 



diameter of the ring. 



" These results remove completely the difficulty which has hitherto 

 been felt with reference to the translation of infinitely thin vortex- 

 filaments. I have only succeeded in obtaining them since the com- 

 munication of my mathematical paper (April 29, 1867) to the Royal 

 Society of Edinburgh, but hope to be allowed to add a proof of them 

 to that paper should it be accepted for the Transactions." 



"May 17, 1867." 



LXIV. On the Action of Magnetism upon the Electric Discharge 

 in highly Rarefied Gaseous Media*. By Professor A. de la 

 RiVE-j-. 



IN the memoir which I recently published " On the Propaga- 

 tion of Electricity in Elastic Eluids/' I reserved for a subse- 

 quent publication the investigation of the manner in which this 

 propagation is -modified by the action of magnetism. I demon- 

 strated the existence of this action as early as 1849, by showing 

 that a magnetic pole causes jets of electricity which escape from 

 it radially to rotate. M. Pliicker subsequently proved by seve- 

 ral remarkable experiments that this action is general. The 

 luminous veins which show themselves in rarefied gases traversed 

 by the discharges of a Ruhmkorft's apparatus are in fact attracted 

 and repelled in the same way as electric currents passing along 

 metallic wires would be. In a word, this action is subject to 

 the laws of electrodynamics, with the difference, however, that, 

 all the parts of the moveable conductor being independent of 

 each other instead of being connected together as they are in a 

 rigid wire, they obey perfectly the forces by which they are soli- 

 cited, and take up positions of equilibrium determined by these 

 forces. It follows that each luminous vein assumes the form of 

 a magnetic curve, the only condition under which equilibrium 

 can be produced, since the action of the magnet upon an element 

 of the current is then nothing, the direction of this action be- 



* Translated from the Archives des Sciences Physiques et Naturelles, 

 vol. xxvii. p. 289 (December 1866). 



t This paper forms a continuation of the one which I published, on the 

 propagation of electricity in highly rarefied elasticjfluids, in the Number of 

 the Archives des Sciences Physiques et Naturelles for July 1866 (vol. xxvi. 

 p. 177)- [A translation of the paper here referred to will be found at p. 241 

 of the present volume of the Philosophical Magazine.] 



