274 Maxwell. 



he connexion between the strength i of a current and the 

 magnetic field H, to which it gives rise, may be represented by 

 the equation 



4?ri = curl H ; 



this equation is equivalent to the statement that " the entire 

 magnetic intensity round the boundary of any surface measures 

 the quantity of electric current which passes through that 

 surface." 



In the same year (1856) in which Maxwell's investigation 

 was published, Thomson* put forward an alternative inter- 

 pretation of magnetism. He had now come to the conclusion, 

 from a study of the magnetic rotation of the plane of polariza- 

 tion of light, that magnetism possesses a rotatory character; 

 and suggested that the resultant angular momentum of the 

 thermal motions of a bodyf might be taken as the measure of 

 the magnetic moment. " The explanation," he wrote, " of all 

 phenomena of electromagnetic attraction or repulsion, or of 

 electromagnetic induction, is to be looked for simply in the 

 inertia or pressure of the matter of which the motions 

 constitute heat. Whether this matter is or is not electricity, 

 whether it is a continuous fluid interpermeating the spaces 

 between molecular nuclei, or is itself molecularly grouped : or 

 whether all matter is continuous, and molecular heterogeneous- 

 ness consists in finite vortical or other relative motions of 

 contiguous parts of a body: it is impossible to decide, and, 

 perhaps, in vain to speculate, in the present state of science." 



The two interpretations of magnetism, in which the linear 

 and rotatory characters respectively are attributed to it, occur 

 frequently in the subsequent history of the subject. The 

 former was amplified in 1858, when Helmholtz published his 

 researches^ on vortex motion ; for Helmholtz showed that if a 



*Proc. Roy. Soc. viii (1856), p. 150 ; xi (1861), p. 327, foot-note: Phil. Mag. 

 xiii (1857), p. 198; Baltimore Lectures, Appendix F. 



t This was written shortly before the kinetic theory of gases was developed 

 by Clausius and Maxwell. 



+ Journal fur Math. Iv (1858), p. 25; Helmholtz's Wiss. Abh. i, p. 101; 

 translated Phil. Mag. xxxiii (1867), p. 485. 



