Theory of X-Ray Reflexion.* 327 



refractive index, we get the Selmeyer dispersion formula. 

 Since it is quite possible that k should be greater than k for 

 all the electrons, the refractive index may quite well be less 

 than unity. 



12. Mutual Action of the Electrons in an Atom. 



For the electrons which contribute the light spectrum k 

 is very much smaller than k and may be neglected. Sir 

 J. J. Thomson* assumes this for all the electrons. The 

 imaginary term is very much smaller than the real, so he 



e 



puts f= ^2 for each electron, and uses this expression to 



m(J 



estimate the number of electrons in the atom, from the known 

 scattering of an amorphous substance. 



But without further discussion this is not legitimate, even 

 assuming that all the & 's are negligible. For some of the 

 electrons are crowded very close together, probably within a 

 distance of about 5 x 10~ 10 cm.t, which is fairly small com- 

 pared with the wave-length of the radiation. Now it is well 

 known that a small body scatters light of short wave-length 

 much more completely than long. We must make certain 

 that this will not be the case here. Suppose we have v elec- 

 trons crowded together at points x 1 y l Z\ &c, the scale of 

 their distances being measured by a length p. Let the 

 external radiation be ~K=e ikCt . This sets all the electrons 

 in vibration, and the motion of each influences the others. 

 Let f : be the displacement of the first electron. Then ^ is 



A 



of the form — exp ihCt. At a near point this electron 



exerts a force 



Zx — xt 2 — r 2 . ., r . 



1 a e tkCt . 



r b 



Similarly for the others. The whole electric force on the 

 first electron then is 



V 2 r ls 5 / e e 2 



<We are neglecting the restraining forces on the electrons, 



* J. J. Thomson, * Conduction of Electricity in Gases/ p. 326. 

 t Calculated on Bohr's theory for a ring of -A electrons in a sodium 

 atom. 



