146 Mr. W. Sutherland on Molecular Refraction. 



decidedly under the difference of density produced by a few 

 atmospheres' pressure. It should be mentioned that in 1874 

 Mascart ( Comp. Bend. Ixxviii.) showed, by experiments on the 

 change of index of water under pressure, that Gladstone's 

 formula gives very nearly the correct compressibility, while 

 Newton's fails. 



Ketteler, developing the theory worked out by Sellmeier, 

 Meyer, Helmholtz, and himself to account for dispersion, 

 obtains a different form of expression connecting index and 

 density, which, in a recent paper (Wiedemann's Ann. 1888), 

 is presented in the form 



(n^-l){v-fi)=c{l+ae-'''), 



where v is the molecular domain (usually called molecular 

 volume) and /3 is the true volume of the molecule, c, a, and k 

 being constants and t the temperature. The hypothesis on 

 which this is based is that discontinuous sether and the mole- 

 cules may be imagined to be replaced by two homogeneous 

 continuous media both filling the same space, but with an 

 action between the two media partly of a frictional nature. 

 As the above expression involves four ai'bitrary constants, it 

 necessarily permits of great accuracy in the representation of 

 experimental results. Ketteler as yet has applied it to only 

 two substances, water and alcohol, which are hardly suitable 

 for testing any theory relating to molecular structure, as there 

 is an abundance of experimental evidence to show that their 

 molecular condition is exceptional. With experiments made 

 over a wide range of temperature he has determined the values 

 of the constants, so that we can test his formula as to its power 

 to give the correct compressibility. 



Proceeding as Quincke does with the other three formulae, 

 we find that Ketteler's formula would give for the com- 

 pressibility the value according to Newton's multiplied by 

 (I'l— /3)/ui, In this way we find the following values of the 

 compressibility, multiplied by 10^, as compared with the ex- 

 perimental and Gladstone values : — 





Experimental. 



Ketteler. 



Gladstone. 



Water . 



. . 46-14 



42-1 



46-04 



Alcohol . 



. 101-41 



97-2 



100-2 



So far as these two cases go, Ketteler's four-constant 

 formula gives inferior results to Gladstone's one-constant 

 expression. 



After this sketch of the history of the subject the following 

 summary of the conclusions of various experimenters as to 



