152 Mr. W. Sutherland on Molecular Refraction. 



that for air the formula (w— 1) =A/) (1 + "00058^0) represents 

 the index at 21° up to a pressure of 14 metres of mercury, p 

 heing measured in metres; and from Van der Waal's equation 

 for air they deduce the relation 



^=A^^(1 + -00065^); 



hut this is erroneous, as the correct deduction from Van der 

 Waal's equation is 



^=A'Xl + -00077p). 



The equation which I have given, however (Phil. Mag. Aug. 

 1887), for air, and which is founded on Amagat's more ex- 

 tended data, while Van der WaaFs was obtained from Reg- 

 nault's, gives the relation d=k.'p (1 + '00060 p), which within 



n~~ 1 

 the limits of experimental error makes constant, seeing 



that, according to the experimenters, there is a possible error 

 of '00003 in the coefficient '00058. This agreement between 

 the optical and the mechanical experiments shows that the 

 formula obtained from Amagat's data for air will be of high 

 accuracy for manometric work. 



But we must see how far the modification of Gladstone's 

 formula to make it applicable to vapour affects its applicability 

 to compression experiments. Its effect is to divide the value 

 of the compressibility as used by Quincke by l + ccP'/in—l). 



Ethyl oxide and carbonic disulphide are the only two 

 bodies in the above table which occur in Quincke's table, and 

 it will be noticed that for these two c is markedly larger than 

 for the others, while there are two out of the four bodies in 

 Quincke's table for which Gladstone's formula gives too large 

 a compressibility. In the case of aether the above modifica- 

 tion reduces the calculated compressibility by 7 per cent., and 

 as it is already 1'5 per cent, too high leaves it 5*5 per cent, 

 too small; in the case of CSg the reduction is 11 per cent., 

 but as the excess is 3' 6 the modified Gladstone formula gives 

 a compressibility 7'4 per cent, too small. But this gives only 

 a rough estimate of the effect of the modification of the 

 formula, seeing that Quincke's specimens of sether and CSg 

 must have been far from pure, as his values of the compressi- 

 bility of these substances are much smaller than those of other 

 experimenters, but he did not desire chemical purity for the 

 end he had in view. Allowing for the larger values of the 

 compressibility of pure asther and CSg, we may say that the 

 modified formula gives the compressibilities 5 per cent, 

 smaller than the observed values, and this in cases where the 



