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XVIII. Light and Electrons. 

 By Sir Oliver Lodge *. 



REFERRING- to previous papers in April and June last, 

 Phil. Mag. vol. xli., especially to pages 557 and 943, 

 if it is ever possible to separate or tear asunder a positive and 

 a negative electron, bringing them into practical existence 

 from absolute neutrality or practical nonentity, by means o£ 

 light vibrations, it would seem likely that the uniting force 

 must at first follow the law of direct distance, in order that 

 the excited vibrations shall be isochronous whatever the 

 amplitude, and therefore cumulative in response to waves of 

 definite frequency. The opposite charges may be thought 

 of as initially united by an elastic thread of zero length 

 which is gradually elongated as the charges separate and 

 vibrate or revolve about one another till it snaps. Very 

 soon after this initial connexion is broken, the ordinary law 

 of inverse square must supervene, and thereafter hold for all 

 bigger distances. A law of force like Ar-f-Br -2 suggests 

 itself, with the second term imaginary for small values of r, 

 and with the first term only operating till discontinuity or 

 "snap" occurs, being then ready to connect up with an 

 inverse square law. 



There is no need to travel far afield for an example of a 

 direct-distance law inside a spherical boundary and an 

 inverse-square law outside : the earth is an example. There 

 is a discontinuity in the force, corresponding to the discon- 

 tinuous distribution of matter ; and the potential, though 

 continuous, has an abrupt reversal of curvature f. The 

 potential is 



3 M M 



V= -x T5g(R 2 — Jr 2 ) inside, and — out ; 



so this gives the intensity of force as 



, dV Mr ... , M 



r= -j- = — -™r inside, and ? out ; 



° dr R 6 r 2 



the inside and outside values being connected at the boundary, 

 but with discontinuity of gradient. 



* Communicated by the Author. 



t Thomson & Tait (§491 d, page 36, Part II, 1883 ed.) make a very 

 small slip here, by speaking of this as a point of inflexion ; but d 2 \ t dr 2 

 changes sign suddenly without passing through zero. The discontinuity is 

 like that felt by a railway traveller when the engineer of the line has made 

 an S curve by laying down two arcs of circles with a common tangent. 

 There is no abrupt change of direction but there is a sudden change of 

 curvature, and accordingly a necessary normal impact, which would have 

 been avoided by designing a curve with a real point o( Inflexion. 



Phil. Mag. S. 6. Vol. 42. No. 217. July 1921, N 



