On the Density and Refraction of Gaseous Elements. 269 



refractive energies of nitrogen, chlorine, and phosphorus are 

 nearly identical, as also of sulphur and oxygen. It will also 

 be observed that in N, CI, P this log. is double of that of 

 H, and S and three times that of half the log. specific re- 

 fractive energy of hydrogen. In the same way, the log. of the 

 specific refractive energy of mercury is 8 times, and arsenic 

 9 times this quantity. 



If we turn to column V. we find that oxygen has nearly 

 double the refractive energy of hydrogen, mercury 4, arsenic 

 8, sulphur, but not so closely, 12 times. 



Now all these coincidences arise from observation only, and 

 are independent of theory altogether. The probability that 

 they should be fortuitous is very small in so large a number 

 of instances. 



When we turn to the compounds, we again see indications 

 of the same law. Thus N 2 has log. specific refractive 

 energy half of similar log. of CO ; and the refractive energy 

 of Cy is very nearly 6 times that of hydrogen. All these 

 numbers may, roughly it is true, be united under a single 



law: thus, for hydrogen =15696, its logarithm is 19578, 



and half this is "09789 ; this is according to Prof. Everett's 

 data. Mr. Lupton's give '09374. If we multiply these suc- 

 cessively by 1, 2, . . . and 10, we shall find that almost all the 

 logarithms range between these two products, being less than 

 the greater and greater than the smaller. It is worth noticing 



IT TT 



that <r =1'57079, log - = 19612 — a curious coincidence 



which, if quite fortuitous, will nevertheless prove a help to the 

 calculator. 



I have not as yet attempted to express these relations under 

 an algebraic formula, although it is obvious that it might be 

 very readily done. I prefer to call attention to the existence 

 of these empirical relations, which hitherto seem to have 

 escaped notice. 



In some of the instances set forth in the Tables the density 

 was checked by calculation from the equivalents. This also, 

 it appears, opens another field of great interest. The well- 

 known relations between molecular weight and density lead 

 us to expect a relation between molecular weight and refrac- 

 tion, and this relation has been abundantly worked out in the 

 case of liquids by my friend Dr. Gladstone. I have not as 

 yet had time to work out this part of the subject com- 

 pletely, as though the calculations necessary present no 



Phil Mag, S. 5. Vol. 28. No. 173. Oct. 1889. X 



