Mr. W. Sutherland on Molecular Refraction. 145 



medium by a certain mean medium. The whole form of 

 Lorenz's final result depends on his application of a mean 

 solution to a discontinuous medium to which it does not actu- 

 ally apply as regards the elements of the medium ; and as this 

 is not justifiable a priori, it is interesting to examine how 

 its results are experimentally verified, and the history of physics 

 does not contain a more striking example of the experimental 

 verification of a purely theoretically deduced formula than 

 that obtained by Lorenz and Prytz (Wiedemann, xi.). They 

 examined some 15 or 16 compounds both in the liquid and 

 vapour state, and found {n'^—l)/{n^ + 2)d in almost every case 

 to be practically the same in both states, and, considering the 

 great difference in density of the two states, no more searching 

 single test could have been applied by Lorenz to his theory. 

 On the other hand, when Gladstone's formula (n — l)/d was 

 tested by the beautifully accurate determinations of Lorenz 

 and Prytz, it was found to fail signally in bridging over the 

 great gap in density between liquid and vapour. This fact 

 at once arrested the attention of those engaged in the investi- 

 gation of molecular refraction, and Landolt, Briihl, and others 

 proceeded to adopt Lorenz's expression because it possessed 

 two great advantages over Gladstone's, it had a theoretical 

 foundation and a better experimental verification. 



But meanwhile Quincke {Sitzungshericlite der kon. preuss. 

 Akad. der Wissen. Berlin, 1883, and Phil. Mag. 5th series, 

 vol. xvii. 1884) tested the three refraction formulse of Newton, 

 Gladstone, and Lorenz in another manner, by varying the 

 density not by heat, but by hydrostatic pressure. His method 

 consisted in measuring the change of index of a liquid when 

 subjected to a certain pressure. Now each of the three rival 

 formulse gives a value for the change of density in terms of 

 the change of index, so that from the optical measurements in 

 each case a value of the compressibility of the liquid could be 

 deduced. Quincke's test consisted in comparing these three 

 calculated values of the compressibility with his own actual 

 measurement. He appHed the method to 10 hquids of diverse 

 properties. His results showed that Lorenz's theory is 

 defective. In every case Lorenz's formula gave too small a 

 value for the compressibility. Newton's is too large, while in 

 6 cases Gladstone's gave too small a value, and in 4 too large. 

 The mean percentage errors, according to the three formulse, I 

 have found to be —14 for Lorenz's, +17 for Newton's, and 

 — 1'6 for Gladstone's. 



This ought to furnish logicians with an instructive example 

 in the theory of evidence, that Lorenz's formula stood the test 

 of comparison between liquid and vapour states, but failed 



Fhil. Mag. S. 5. Vol. 27. No. 165. Feb. 1889. L 



