OF ARTS AND SCIENCES. 



407 



TABLE II 

 Alcouol 



Alcohol, 1. 



A'a. 



1.405095 

 1.4572;)5 

 1.448895 



CS., 1.03111. 



.Vy. 



1.492206 

 1.483356 

 1.474506 



T. 



0° 

 15°. 

 30° 



, (continued). 

 AND CSj. 



d. 



0.995330 

 0.977600 

 0.959990 



I. 



435.0 

 435.0 

 434 9 



433.0 

 425 3 

 417.5 



Mean, 435.0 



r = 433 — 0.5166 T. 



In this table, xVa and Ny represent the indices of refraction of the 

 substances named at tlie temperature T, d the corresponding densities, 

 and / the interferential constants. The indices and densities are com- 

 puted from Wiillner's formulas given in Table I. Each of these linear 

 formulas was deduced from a larsre number of direct observations made 

 at different accurately observed temperatures. The values of the in- 

 dices and densities calculated from them are therefoi'e more reliable 

 than those obtained by single direct observations. In the cases of all 

 the substances examined, Table II. shows clearly that the interferential 

 constants are, for very considerable ranges of temperature, independent 

 of the temperature itself. Wiillner's formulas cited in Table I. show 

 that in all cases the co-efficients k and k' are very nearly equal, so that 

 Na and Ny decrease very nearly in the same ratio as the temper- 

 ature rises. The formula defining the interferential constant, 



1 ( 



^=n( 



1)t-(«i-1) 



A, 



I 



^iT 



then shows that the densities must deci-ease very nearly in the same 

 ratio with the differences of the indices, since / is constant for each 

 substance. A careful examination of the values of the interferential 

 constants given in Table II. shows that in some cases the values dimin- 

 ish very slowly as the temperature increases, suggesting that in these 

 the quantity / is a linear function of the temperature. It will, how- 

 ever, be remarked that the diminution noticed is in the first place 

 extremely small, aud secondly that it is not uniformly present. I con- 

 sider myself, therefore, fully justified in considering / as constant for 

 each substance. In the particular case of carbonic disulphide, I have 

 computed its value for 48° C, which is the boiling-point of the Ii(|uid. 

 It will be remarked that, in the case of this substance, the diminution 

 of / with the temperature is quite uniform, but that the total diminu- 

 tion for 48° is only 0.32 % of the value at 0°. It must, furthermore, 

 be remembered that it is scarcely probable that the density of the disul- 



