[ 268 ] 



XXXV. On a Relation existing between the Density and Re- 

 fraction of Gaseous Elements and also of some of their 

 Compounds. By Kev. T. Pelham Dale, M.A* 



IN my former paper which I presented to the Society! I 

 touched upon the empirical relations discoverable be- 

 tween the specific refractive energies of selenium and sulphur. 

 The present state of the data, however, relating to these sub- 

 stances is so far unsatisfactory that we are not furnished with 

 refractive indices and density taken from the same specimen 

 at the same temperature. Thus there is a doubt as to the 

 density to be chosen as normal, in consequence of the differ- 

 ence due to the allotropic conditions in which these substances 

 are found. This difficulty may be to a certain extent eluded 

 by taking both densities and calculating the specific refractive 

 energy for both. The result is, in the case of selenium and 

 sulphur, that in both substances the mean values are not very 

 far apart. 



The question, however, of the relation between the refrac- 

 tive indices of the elements is of so great interest, that it 



appeared advisable to calculate the value of of all 



chemical elements for which data existed, giving both refrac- 

 tive index and density in the state of gas or vapour. This 

 would include the refractive indices of hydrogen, oxygen, and 

 nitrogen, and the importance of these is obvious. Then, again, 

 the calculated densities derived from atomic weights might 

 be used in cases where an observation was wanting, and as a 

 check where these existed. A very few trials revealed 

 relations which it was impossible to overlook. 



These relations among the numbers found are set forth in 

 the accompanying Tables. 



These tables are arranged in columns. The first, column I., 

 contains the name of the substance. Column II. its index of 

 refraction less unity, or /* — 1. Column III. its density. 



Column IV. its specific refractive energy, or — -=— . Column 



V. the ratio of fi — 1 in the substance to the similar number 

 for hydrogen. The upper row of numbers in each line are 

 natural numbers, and those immediately under are the man- 

 tissse of their common logarithms. Examining this table in 

 detail, it is seen at once that the logarithms of the specific 



* Communicated by the Physical Society : read May 25, 1889. 

 t Phil. Mag. Jan. 1889, p. 50. 



