402 PROCEEDINGS OP THE AMERICAN ACADEMY 



be one millimeter. If now we divide the expression given by the den- 

 sity of the substance of which the plate is composed, d, we shall have 



The quantity I, as thus defined, I call the "interferential constant." 

 It expresses the number of bands in the spectrum between two rays 

 the indices of which for the given plate are n^ and nj, for a thickness 

 of the plate equal to a unit of density. I shall endeavor to show, by 

 the discussion of a number of observations, that the quantity / is for 

 each substance a characteristic optical function which, for all the cases 

 which the present state of science enables us to discuss, is independent 

 of the temperature, and which may therefore be regarded as a new 

 physical constant. 



For the purpose of testing the character and value of the new con- 

 stant, I have selected the extensive series of observations made by 



« — 1 

 Wullner* in his examination of the function - — t— , a function which 



a 



Landolt and Dale and Gladstone in their extended investigations have 

 assumed to be constant for the same ray and the same substance. 

 Wiillner determined with great care the indices of refraction of a 

 series of liquids for the three hydrogen lines O, F, and G at different 

 temperatures, together with the corresponding densities. He found 

 that, for very considerable ranges of temperature, the three indices 

 and the corresponding densities could be represented very closely by 

 linear functions of the form n = rio — Id and d =^ do — bf. AViill- 

 ner's general results are given in Table I., in which JVa and My rep- 

 resent the indices of refraction at 0° C for the rays C and G, d and T 

 the corresponding densities and temperatures. 



"With the data here reproduced, "W^iillner computed for each liquid 



A —1 

 the value of the function — - — , in which A represents the term in 



Cauchy's formula 



which is independent of the wave length, and D the density. The 



general result of his investigation is that the functions — j- — or , 



cannot be regarded as perfectly constant, either when the densities are 

 made to vary by heating or cooling or by mixing one liquid with 

 another. 



* Pogg. Ann., T. 133, p. 1. 



