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XC VIII. On the Energy of the Groups of j3 rays 

 from Radhnn. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



IN my paper entitled " The Origin of the /3 and 7 Rays 

 from Radioactive Substances " in the October number 

 of this Journal, the energy E of the electron has been calcu- 



/3 s 



lated from the formula E 



= 7>m Q c — j. — = — , 

 ~ ° V1-/3 2 

 of the electron at slow speeds, c the 

 3 the ratio of the .velocity of the 

 velocity of light. This is equivalent to 

 mass of the electron by 

 given by the Lorentz 



here 



m is 



th< 



mass 

 and 



" transverse 

 the velocit) 



velocity of light, 

 electron to the 

 multiplying the 

 half the square of 

 Einstein formula. 

 Mr. Moseley drew my attention to the fact, which I had 

 overlooked, that according to the Lorentz-Einstein theory 

 the total energy E of the electron is not given by the 



above formula but by 'E = m Q c 2 l t — 1 ). The latter 



: ■ \v/l-/3 2 _ / 



formula agrees nearly with the former for small values 



of /S, but departs widely from it when ft approaches unity. 



Calculating on the latter formula the energy of the electrons 



comprising the different groups of homogeneous rays given 



in the paper of Danysz, the difference between the energies 



of successive groups can still be expressed by a relation of 



the same form as that given in the paper, viz. pl$ 1 + q~E 2 , 



only E x and E 2 have new values. The values which fit in 



best with the data are E 1 =l*12 x 10 13 <? and E 2 ='356 x 10 13 ^; 



p has values between and 9 and q between and 2. All 



the twelve lines from Nos. 21 to 9 fit in with this relation 



except No. 11, which is nearly equal in energy to No. 10. 



It may be significant that all the lines Nos. 8 to 1, which 

 presumably belong to radium B, show an approximately 

 constant difference of energy E3 = *173x 10 13 £, which is very 

 nearly one half of E 2 . The observed and calculated energies 

 from Nos. 8 to 1 agree within the probable limit of experi- 

 mental error in the determination of the velocities. Line 

 No. 9 fits in equally well with the radium B or radium 

 series, and it is not known to which series it belongs. 



If the relation found by Whiddington (Proc. Roy. Soc. 

 lxxxv. p. 323, 1911) between the velocity required to excite 

 the characteristic radiations and the atomic weight depends 

 on the energy of the electron rather than on its velocity, the 

 energy of the electron to excite the characteristic radiation 



Phil. Mag. S. 6. Vol. 24. No. 141. Dec. 1912. 3 N 



