344 The Gladstone " Law " in Physical Optics. 



An examination of this table will show that for the same 

 temperature limits there is a fair approach to constancy in 



the ratio ^-. 



Thus the indices of the first seven substances all give 

 ratios very near to 1*031. This is specially striking if we 

 take particular cases like the first two on the list — heptane 

 and methylene di-iodide — as shown in the following short 

 table : — 



- 



Temp. 



Density. 



Between the same temp, limit. 



Eatio of 

 Densities. 



Ratio of 

 Indices. 



Heptane 



o 



12 



89 

 8 



87 



0-6903 

 0-6230 

 3348 

 3139 



} ■" 



I 1-07 



10317 

 10325 





Methyl Di-iodide 



It is also noteworthy that this same ratio (1*03) holds good 

 in the case of those substances whose tendency to tautomerism 

 is productive of anomalies. These are aeetyl-acetone, methyl- 

 acetyl-acetone, and ethyl- a cetyl-ace tone, which give abnormal 

 values for /3, and which differ from all other substances, even 

 when tested by the Lorentz formula. Of course the ratio 

 1*03 is not preserved all the way down this group ; the lower 

 members fall to about 1*026. Whether this means only a 

 slight departure from the other value, or whether it indicates 

 a breakdown of the suggested constant relationship can only 

 be decided when many more accurate temperature observations 

 are obtainable. The ratio altogether breaks down in the case 

 of such substances as water, which, as I have suggested, show 

 special relations to refractive index by reason of varying 

 molecular complexity. 



The last column in the foregoing table gives the ratio of 

 the logarithms of temperatures and indices. Further research 

 may make this column more valuable than it now appears. 



Taken altogether, the table affords ground for believing 

 that there are close relationships between refractive index 

 and temperature, and, further, that the ratio of change for a 

 particular temperature interval may be the same for many 

 different liquids. 



