Sijsfi'ms of Corpuscles (Jescrih'uuj Ci/'CJihir OrJnts. 085 

 .so that 



CO 



2 — .V = a-{cos '201 (siir -v^cos- — cos'^-v/r) — slu '26i 81112-^008 ^}, 



Tims each particle produces the same effect as a magnet 

 maoiietized ])arallel to the direction o£ H and having a 

 moment equal to 



- a- {cos 2^i(sin- -v/r cos^ ^ — cos- i/r) — sin 2^i sin 2'v/rcos </>}. 

 bin 



The coefficient of magnetization of any substance is the 

 sum of these moments for the unit of volume when the 

 external force H is unity. We see from the preceding 

 expression for the magnetic moment due to a single orbit 

 that if the particles and their orbits are uniformly distributed 

 this sum must be zero. For consider orbits whose planes 

 are all in any given direction : for such orbits -^ and (j) will 

 have constant values ; the phase 0^ at the time ^ = will, 

 however, vary from orbit to orbit, and if these phases are 

 equally distributed the mean values of cos 2^^ and sin 2^i will 

 be zero. Thus the coefficient of magnetization o£ the system 

 will be zero ; so that we cannot explain the magnetic or dia- 

 magnetic properties of bodies by the supposition that the 

 atoms consist of charged particles describing closed yieriodic 

 orbits under the action of a force proportional to the distance 

 from a fixed point. I find that Professor Voigt has already 

 come to this conclusion by a different method. 



11. I find that the same absence of diamagnetic or 

 magnetic properties will persist whatever be the law of 

 force, provided the force is central and there is no dissipation 

 of energy. 



To prove this, let oc, y, z be the coordinates of the particle ; 

 then a, the a:-component of the magnetic force at the point 

 {x' ^ y', z!)y is given by the equation 



___ f dz _d^ 1^ _dy d^ l\ 

 "'~ ^Xdtdy'V dtdz'r'y 



where ?-' is the distance between the points [x, y, z) and 

 (.L^j y' ^ z). If T is the distance of [x' ^ tj\ z'^ from the centre 

 of the orbit taken as the origin, then 



1 \ ( d d d\\ 



riul Mag. S. 0. Vol. 6. No. 36. Dec. 1903. 2 Z 



