Dispersion in Relation to the Electron Theory. 467 



has already been referred to. When there are more dis- 

 persional periods than one, the shorter ones are more likely 

 to escape detection than the longer and the tendency is to 

 obtain too great a value for \ u with the result that a Y is 

 too small and a Q too great. The accuracy with which the 

 constants can be determined depends of course upon the 

 range of spectrum covered by the observations and upon 

 the accuracy with which the individual values of n have 

 been determined. Where both conditions have been ful- 

 filled, as in the case of quartz, rock-salt, sylvine, and 

 fluorspar, the value obtained for a is always a small fraction. 

 In a homologous series of organic compounds each addition 

 of a methylene group adds an equal number of electrons to 

 the molecule, but as such addition also produces an approxi- 

 mately constant increment in the molecular volume, the 

 number of electrons in the unit of volume or the quantity 

 p/V m tends towards a constant value as we proceed to the 

 higher members of the series. As this applies to the elec- 

 trons of each class independently (except class I.) we ought 

 to find that the value of a which depends upon the number 

 of electrons of class III. (possibly also to a slight extent of 

 class IV.) in the unit volume approximates to a constant 

 value. The following table shows that numerical results 

 are quite in accordance with this view. p Y is put equal 

 to the number of linkages (class II. a) and a is calculated 

 from equation (11). As the compounds are aliphatic con- 

 dition (ii.) is satisfied. 



• Table VI. 



Substance. 



Pentane 



Hexane 



Octane 



Meth yl alcohol 



Pi- 



a . 



Substance. 



Pi- 



a . 



16 



11 



5 



11 



7 

 10 

 10 



•206 

 •220 

 •233 

 •223 

 •221 

 •246 

 •219 

 •238 

 •222 



Formic acid 



5 

 8 

 11 

 14 

 17 

 23 

 11 

 14 

 17 



•286 

 •271 



•275 

 •278 

 •279 

 •287 

 •277 

 •255 

 •262 



Acetic acid 





Butyric acid 



Ethyl alcohol 



n. Propyl alcohol 



Acetaldehycle 



Propaldehjde 



Acetone 



Valerianic acid 



OEnanthylic acid 



Methyl acetate 



Ethyl acetate 



Propyl acetate 



In view of the fact that N x , equation (8), is only an 

 .approximation to N 1 + N 2 -f-N 3 4- . . . . the uniformity in the 

 values of a is even greater than might have been expected*. 



In the following section we proceed to consider the bearing 

 of the present theory on the additive optical properties of 

 ■organic substances. 



* See Note 3. 



212 



