Magnetic Properties of Corpuscles descrlhi/uj Orbits. 073 



by Mr. Poeklinotoii. For oiven electrical i'orce on tlie wire 

 the vibrations become more persistent as tlie wire becomes 

 thinner, the energy of" tlie wave system increasing i-apidly 

 while the radiation is not mnch altered ; but it was a mistake 

 to ex|)ress the result, which is sensibly though not rigorously 

 true for thin wire rings, as if it were true for rings of large 

 cross-section. The other corrections pointed out by Prof. Orr 

 deserve my best thanks and atford gratifying evidence of 

 the kindly interest he has taken in my work.] 



LXXXIV. The Mof/netic Properties of Systems of Corpuscles 

 describing Circular Orbits. By J. J. Thomson, M.A., 

 F.P.S., Cavendish Professor of Experimental Physics, 

 Cambridge"^, 



ri IHE problems discussed in this paper are : — (1) The 

 X magnetic field due to a number of negatively electrified 

 corpuscles situated at equal intervals round the circumference 

 of a circle and rotating in one plane wdth uniform velocity 

 round its centre ; and (2) The efi^'ect of an external magnetic 

 field on the motion and periods of vibration of such a system. 

 These problems are met with ^vhen we attempt to develop the 

 theory that the atoms of the chemical elements are built up 

 of large numbers of „negatively electrified corpuscles revolving 

 around the centre of a sphere filled with uniform positive 

 electrification. 



If an electrified particle is moving uniformly with a velocity 

 small compared with that of lights it produces a magnetic 

 field whose components a, yS, 7 at a distance r from the particle 

 are given by the equations 



/ d d\l r, { d d\l ( d d\l ,^. 



where e is the charge on the particle and u, v, w the com- 

 ponents of its velocity. These expressions will not give the 

 magnetic force when the motion is variable ; when, however, 

 tlie velocity is periodic^ proportional say to e'^^, the equations 

 for the components of the magnetic force can be derived at 



once from equations (1) by writing e 'V / r for l/r in those 

 equations : Y being the velocity of light through the medium. 

 \\'e can see this at once by noticing that the modified 

 equations satisfy dift'erential equations of the type 



d^ cP^ (P^ 1 ^ "^ 



du^'^df'^ d^'^^Y'd?' 

 * I'ommunic-ated hv the Author, 



