218 Dr. L. Silberstein on Dispersion and the Size of 

 iurements by Class* 



1-008 e/c e/c 



direct measurements by Classen, Wolz, and others *, we 

 find 



3tt b m sjkrr mR s / ^ 



=■=0-107. 1*77. 10 7 . 9650 



cm. 



= 183. 10 8 — . . (10) 

 gr. 



This is the numerical value to be substituted in (9). The 

 assumption (9) can be put in words by saying that each 

 atomic resonator consists of a certain number k o£ electrons. 

 In fact, provided that the distance of these electrons apart is 

 large as compared with their radii f, the mutual mass will 

 be negligible, so that their total mass will be k times the 

 mass, and their total charge tc times the charge of a single 

 electron. Thus ejm will retain its value and e/m R will be 

 k times greater. We need not enter into the mutual action 

 of these k electrons, but can treat them summarily by attri- 

 buting to the whole system a single relevant free frequency 

 Vyo? which may already be the outcome of their co-operation 

 together with the usual restitutive force. 



But it seems safer to abstain from any such interpretation 

 and to take our assumption as it is written down in (9). 

 Merely for the sake of convenient language, this can be read 

 as " atomic resonator consisting of a; electrons," or "atom 

 containing /c dispersive electrons/' The clause that/e should 

 be the smallest integer compatible with the special condi- 

 tions of the problem will be made clear presently. 



Equations (8) with (9) are now sufficient for the determin- 

 ation of the two attributes b , g of the atoms and of their 

 mutual distance in the molecule. This will be done con- 

 veniently, in each of the concrete cases, in the following 

 manner. To abbreviate, write 



b 2 , ' . h 



k=-, and £ -^ (11) 



9 </o 



Then k is known from experience, and k = fce. Dividing 

 the square of the first by the second of (8), we have 



whence 



2k —k±* /k(k -ik) (V2) 



° b °-~ fa-h " • • • • M 



Now, k is essentially positive ; thus the smallest value of 



* Cf. Zeeman's ' Kesearches in Magneto-optics' (1913), p. 68 and 

 passim. 



t I. e. large compared with 10 "~ 13 cm., which, however, may still be 

 a very small distance in comparison with atomic dimensions, 10 - cm. 



