688 Prof. J. J. Thomson on the Magnetic Properties of 



the bracket will be n(lf-\-^^); if the number of particles 

 which at any time are situnted between two neighbouring 

 points P and Q on the orbit is proportional to the time taken 

 by the particle to pass through PQ, then the sum of y^-{-Zo 

 for the n orbits will be n[i/^ -\-~z^) , and thus the two terms 

 inside the bracket will balance each other and the resultant 

 magnetic moment of the system will be zero. V\'e thus see 

 that we cannot explain the magnetic properties of boaies by 

 means of charged particles describing without dissipation of 

 energy closed orbits. 



12. When there is dissipation of energy the collection of 

 moving charged particles may, I think, possess magnetic 

 properties. Let us represent the dissipation of energy by 

 supposing that the motion of the particles is resisted by a 

 force proportional to the velocity : the equations of motion 

 are 



ar tit dt 



where It-y. k~ represent the forces due to the viscous 

 at (It ^ 



resistance. Then, if the components Y and Z are those of a 



central force, we have 



d 



dt 



(4;-4)^'-tS-J) = iH,|(,.,, 



The solution of this equation is 



^- . / J^ J. s 1 TT, k . r*t k 



d^ Jy _ -£'/,. '^'0 rf.V«\ I'Re -it C'"-' d 



^ dt ~dt " ^ 



(-S-'.t)4!^'--'p'l,^--')- 



Thus, corresponding to the term ~-y(,/^^Jj\^ I 



^ V dt dt J dx' r 

 in the expression for a, the magnetic force parallel to x, 



we have as the coefficient of ^^_ ~, and therefore as the 



moment of the equivalent magnet, 



J / di/, dz^\ .^t iRe' -ItC' ^td , , ,, , 



The contribution of this particle to the coefficient of 

 magnetization is the mean value of the coefficient of H in 



