332 Mr. T. P. Dale on the Index of Refraction and 



specific gravity in far greater proportion than it raises the 

 value of the refractive and dispersive powers. No simple 

 relation between either density and v — 1 or the quantity 

 denoted by h is as yet apparent. I have tried the square 

 and cube, and the square root and cube root of h, as well as 



the simple power. I have noticed above that . is in case 



d 

 of some isomeric bodies nearly a constant, but this may be a 

 mere coincidence. It is, however, worth noticing, as \/Ti 

 enters the coefficient k of Airey's equation cited above. When 

 the logarithms are at hand, the calculations are so simple 

 that even in the absence of any theoretical considerations it 

 seemed worth while to try them. 



It will be observed that the equation, by (£) and (77), 



a sin 6 = sin m0 



is impossible if a sin 6 is greater than unity. Now as a is 

 the ratio of two wave-lengths in free aether, denoted in this 

 investigation by X : X 1? we may ask what happens if the ratio 

 of Xi the upper wave-length to X the lower exceeds the ratio 

 unity. Now in all cases yet examined, with the exception 

 of selenium, this shorter wave-length is beyond violet and 

 indeed the visible spectrum. In selenium it must he some- 

 where near E ; in solid phosphorus and sulphur it is beyond 

 the furthest limit of the spectrum towards its more refrangible 

 end, given by Prof. Langley, i. e. 0*3727. The results are 

 given for these three substances in Table IV. annexed. It 

 will be seen that phosphorus reaches the limit at about 2684 

 and sulphur at nearly 2664. We may observe as a coinci- 

 dence that the behaviour of selenium in relation to light is 

 remarkable, while its red colour shows that the violet end of 

 the spectrum is absorbed. The results in Table V. are sup- 

 plemental, calculated to the nearest minute, from determina- 

 tions recently supplied by Dr. Gladstone, of v for water and 

 alcohol. 



Abstract of Results. 



1. That the relationship between the limit of refraction (v) 

 found by the equation a sin 6 = sin md, where a is the ratio 

 of two wave-lengths in free sether and m the corresponding 

 ratio in the medium, give a value which has the property 



expressed by the equation — j— a constant, where d is the 



density of the medium and v its limit of refraction at the same 

 temperature. 



