ON PHYSICAL LINES OF FORCE. 503 



(2) If a, ft, y represent rotatory displacements in a uniform and continuous 

 substance, then p, q, r represent the relative linear displacement of a particle 

 with respect to those in its immediate neighbourhood. See a paper by Prof. W. 

 Thomson " On a Mechanical Representation of Electric, Magnetic, and Galvanic 

 Forces," Camb. and Dublin Math. Journal, Jan. 1847. 



(3) If a, fi, y represent the rotatory velocities of vortices whose centres 

 are fixed, then p, q, r represent the velocities with which loose particles placed 

 between them would be carried along. See the second part of this paper (Phil. 

 Mag. April, 1861) [p. 469]. 



It appears from all these instances that the connexion between magnetism 

 and electricity has the same mathematical form as that between certain 

 pairs of phenomena, of which one has a linear and the other a rotatory 

 character. Professor Challis* conceives magnetism to consist in currents of a 

 fluid whose direction corresponds with that of the lines of magnetic force ; and 

 electric currents, on this theory, are accompanied by, if not dependent on, a 

 rotatory motion of the fluid about the axis of the current. Professor Helmholtzf 

 has investigated the motion of an incompressible fluid, and has conceived lines 

 drawn so as to correspond at every point with the instantaneous axis of 

 rotation of the fluid there. He has pointed out that the lines of fluid motion 

 are arranged according to the same laws with respect to the lines of rotation, 

 as those by which the lines of magnetic force are arranged with respect to 

 electric currents. On the other hand, in this paper I have regarded magnetism 

 as a phenomenon of rotation, and electric currents as consisting of the actual 

 translation of particles, thus assuming the inverse of the relation between the 

 two sets of phenomena. 



Now it seems natural to suppose that all the direct effects of any cause 

 which is itself of a longitudinal character, must be themselves longitudinal, and 

 that the direct effects of a rotatory cause must be themselves rotatory. A 

 motion of translation along an axis cannot produce a rotation about that axis 

 unless it meets with some special mechanism, like that of a screw, which 

 connects a motion in a given direction along the axis with a rotation in a given 

 direction round it; and a motion of rotation, though it may produce tension 

 along the axis, cannot of itself produce a current in one direction along the axis 

 rather than the other. 



* Phil. Mag. December, 1860, January and February, 1861. 

 t Crelle, Journal, VoL LV. (1858), p. 25. 



