Theory of the Equivalent of Refraction. 185 



In contradistinction to this series of M, the Biot's refractive 

 powers f ) show, on the other hand, no such regular se- 



quence of values. I shall here disregard the numbers which I 

 have reckoned for m } and give below the numbers [D(II 2 0) = 1] 

 given by Haagen*: — 





u-1 



m= V- 





u-1 



Oxygen 

 Sulphur 



. 0-1813 

 . 0-4606 



Phosphorus 

 Arsenic 



. 0-4710 

 . 0-2510 



No agreement can be perceived from these numbers between 

 the optical values of these substances (which are so nearly allied 

 chemically), although such agreement was clearly manifested in 

 the above comparison of the values of M. 



There are some who certainly will not fail to point to the 

 small deviations of M from the absolute values of the multiples. 

 But I think that everyone who considers the matter impartially 

 will recognize the law of multiples as that which determines, in 

 the first approximation, the numerical values of the elements. 

 And hence I consider that the above comparison has sufficiently 

 proved that the optical function of the elements shown by the 

 Newtonian refractive power M follows the law of serial factors. 



I consider that such a regularity, when we fully consider the 

 analogous chemical series, furnishes a further proof of the cor- 

 rectness of the views which I have hitherto held. 



Finally, I must mention the important fact that I have suc- 

 ceeded, by means of the optical atomic numbers (also a conse- 

 quence of my equation ].), in deriving the crystalline form of 

 compounds from the volumetric values of the elementary atoms 

 occurring in the compoundf. 



Thus one relation follows another in an unconstrained man- 

 ner, and no one is in contradiction with the facts. The hypo- 

 theses which have been hitherto forced simplify themselves in 

 many respects, and unexpected new relations appear at every 

 step. 



In the preceding I have declared my adhesion to the hypo- 

 thesis of simple factors, and I even consider such an hypothesis, 

 similarly to the method of volumetric calculation, necessary to 

 establish the truth and possibility of an optical function. 



I must here add that the defenders of the formula {fju — 1)V 



* Pogg. Ann. vol. exxxi. p. 127. 



t Schrauf, Physikalische Studien, pp. 240-248. Pogg. Ann. vol exxx. 

 p. 433. Physik der Krystalle, chap. xi. pp. 160-172. 



