Theory of the Equivalent of Refraction. 



179 



action of the change of volume declares itself in the law of the 

 refractive power ; the change in the molecular path has, on the 

 other hand, a secondary, very insignificant positive or negative 

 influence upon the function X„ of the luminous propagation. 



The proof of these statements is given by the numerous data 

 in my " Studies/' However, I may here collect the most im- 

 portant facts to prove that, by comparing different bodies for 

 equal temperatures, even of the most diverse volumes, we may 

 look upon the retarding forces X„ as constant, or even as equal. 

 According to formula (II.), the constancy of M proves the con- 

 stancy of X„. 





D. 



fi. 



M. 



NV- 





1-4 



3-5 



0-9181 



1-0 



3-95 



4-20 



2-73 



2-94 



0-996 



0-940 



0-917 



0863 



0-781 



0-961 



0-799 



0-858 



1-720 

 2-434 

 1-3089 

 1-3330 



mean 2*499 

 2-560 

 mean 1-5801 



1-6178 



1-376 



1-357 



1-409 



1-390 



1-322 



1-387 



1-377 



1-400 



0-001809 

 0-001820 

 00010046 

 00010048 



mean 0-001 7167 



00017098 



0-0007185 



0-0007115 



0-001160 



0-001157 



0001391 



0-001398 



0001239 



0001243 



0001451 



0-001450 



001266 

 0-01271 

 001584 

 001559 

 001416 

 001376 

 0-01672 

 001630 



a. Carbon* j aihuwuic 



, , Tr . f Ice 



b. Water < „, , 



L Water 





c. Titanic acid... | R ^ e ;•;•;•;;;•;;•; 



d. Carbonate of J Iceland spar 





nn , rA , f Propionic acid 



e. C 3 H 6 2 ■{ tr * , T * £ i 



i Formate of etnyle ... 



f C 7 H 14 O 2 J CEnanthylic acid 



■'■ " \ Acetate of amvle 



g. C 2 H 4 0, /Aldehyde 



2(C 2 H i O)t Butyric acid 



h. C 5 H 10 O /Valeral 



2(C 5 H J0 0) 1 Valerianate of amyle. 



These examples will certainly amply suffice to prove that we 

 may consider the function X v as constant as soon as the bodies 

 are compared at the same temperature. Examples g and h even 

 show that, for the polymers of optically identical elements, X v is 

 not merely a constant but has the same value. 



In regard to the polymers of optical allomeric elements, I 

 must refer to my " Studies "f. 



In view of the examples given, it may fairly be doubted 

 whether new analytical formulae are necessary to establish the 

 relation between density and the indices of refraction. 



Moreover I did not satisfy myself with the above-mentioned 

 facts alone before I decided upon the assertion that the retarding 

 forces X w always bear the character of constants for equal tem- 

 peratures. A further proof, for instance, is possible, based upon 

 formula II. If we multiply both sides of this equation (II.) with 

 the chemical equivalent P, we obtain on the left the Newtonian 



* For the calculation of M, the density of air is taken =1. 

 t Compare Schrauf, 'Studies/ p. 215 ; Schrauf, Physik der Krystalle, 

 p. 310. 



N2 



