﻿102 S. jP. Langley — Unrecognized Wave-lengths. 



its geometrical representation, from being concave to the axis 

 of X, becomes convex, so that the relation between n and X 

 would, according to it, be represented by a sinuous line, and 

 this is not so within the limits of these observations. Its fair 

 agreement with observation then, within the limits of the vis- 

 ible spectrum and the upper part of the solar infra-red, are all 

 that can be claimed for it. 



Our conclusion is that all theories of dispersion known to 

 us prove inadequate to predict the relation between wave- 

 length and refraction. 



The actual relation from direct investigation is here given 

 for the first time from the observations of the past year, which 

 it will be seen, thus confirm and greatly extend the results 

 of* 1882 and 1884. Their most salient feature is still per- 

 haps that already noted, i. e. while the curvature, as far as 

 we can follow it, grows less and less, at the last point at which 

 we can view it the curve is not only all but sensibly a straight 

 line, but one making a very definite angle with the axis of X. 

 This obviously means that beyond this point n is nearly a 

 linear function of X or that the simple equation n=aX would 

 very closely represent this portion of the curve. It means 

 also that, as far as these observations extend, we find scarcely 

 any limit to the index of the ray which the prism can transmit 

 except from its own absorption. 



I do not, it will be observed, undertake to advance without 

 limit beyond observation, or to discuss what would happen 

 with wave-lengths so great that the index became or negative, 

 as it would with an indefinite prolongation of the curve, if its 

 direction remain unaltered. An intelligible physical meaning 

 might perhaps be attached to these cases ; but I here confine 

 myself to the results of direct observation, and to the now 

 established fact that the increase of the crowding together of 

 the rays at the red end, which is so conspicuous a feature in 

 the upper prismatic spectrum, has almost wholly ceased ; and 

 that the dispersion has become approximately uniform, the 

 action of the prism here being assimilated to that of the diffrac- 

 tion grating itself. 



I shall not venture to treat of the theoretical import of 

 this, further than to remark that the ordinary interpretation 

 of Cauchy's theory will apparently lead us to conclude that 

 dispersion must sensibly cease at the point where the wave 

 is so long that the size of the components of matter is negligible 

 in comparison. In other theories also, there appears to be a 

 point below which the index of refraction should never fall, 

 and we might anticipate that the curve would accordingly tend 

 to become parallel to the axis of X. Of course we can- 

 not assert from observation that it will not finally do so, but 



