Dispersion in Relation to the Electron Theory. 477 



Although the values used were simply deduced from 

 four reference substances, a very fair agreement is shown 

 throughout. A much better agreement may be expected if 

 average values are worked out from a larger number of data, 

 and for some given temperature. Unfortunately, most of 

 the refraction data available have reference to the a line 

 of hydrogen, and the magnetic rotations have reference to 

 the I) line. The values of the molecular refraction P iu the 

 above table are those of Conrady *, and in many cases were 

 obtained by interpolation. 



I hope to deal later with the application of the method to 

 unsaturated and aromatic compounds, and with the recalcu- 

 lation of some of the values given above. If the electrons 

 of class IV. are inoperative, the refractive value of the 

 hydrogen atom in the ultraviolet should be zero. The value 

 •087 is so small that a better collection of data may prove 

 this to be the case, but the values for the carbon and oxygen 

 atoms can at present only be ascribed to the influence of a 

 large number of electrons of class IV. 



Note 1. — Prom a well-known theorem in inequalities we have 

 for n positive quantities a, b, c, .... Jc, 



( a + 6 + c+ . . . 4-£) 2 <"(> 2 + & 2 + c 2 + . . .Jc 2 ). 



If now N^ of the quantities each equal unity, N 2 equal a, &c.,. 

 we have at once, 



(N 1 +*.« + *V+ • ..) 2 <(N 3 +N 2 +tf 3 + . ..)(N 1 + ^ 2 a 2 + ^ 2 + • ••) 

 Hence, if a. /3, &c. are all positive, 



X'< 3s\ + N a + ]sr3+...+ff P . 



JjfoU 2. — In the explanation of the experimental results we have 

 assumed a coefficient -q effective in the absence of the magnetic 

 field as well as in its presence, £ being put zero for simplicity. If, 

 however, the electronic coupling only occurs in the presence of the 

 field, we must write rj=l and retain £. The ratio e/m will then 

 retain its normal value in natural dispersion but not in the 

 magnetic field, and the values of p given in Table II. will hold good. 



Note 3. — This result also indicates that the periods of the 

 electrons giving rise to a are approximately the same in the 

 different substances considered, and are therefore little affected by 

 the polarization. 



Note 4- — A polarization formula which has only come to my 

 notice since the above has been at press, and which contains the 

 factor n/(n 2 + 2y, has been deduced by Sir J. Larmor, with whom 



* Zeits. Phys. Chem. (3) p. 210 (1899). 



