﻿104 S. P. Langley — Unrecognized Wave-lengths. 



Rendus of the Institute of France, January 18, 1886, and in 

 preliminary memoirs, we deferred giving the actual values, but 

 gave (explicitly as minimum values which we believed much 



within the truth) 5^ to 6^. That our caution led us to under- 

 state the even then most probable value, may be seen from the 

 statements just made, which are founded on still later obser- 

 vations. 



As we proceed farther out, extrapolation becomes, of course 

 more untrustworthy. We can only say that if the curve main- 

 tains its present inclination to the axis of X, the wave-lengths 

 of the extreme radiations recognized in the rock-salt prism must 

 indefinitely exceed 0-03 mm . 



"We have shown that the various complex formulas founded 

 on theoretical considerations differ from observation ; and as 

 we have remarked, they have the minor objection also of being 

 extremely difficult of application to practical uses, owing to the 

 inordinately tedious numerical computations involved where 

 many places are to be calculated. 



Struck by the resemblance of the actual curve of observation 

 as viewed in a large graphical construction, to a hyperbola, I 

 was therefore led some years ago to use the equation of the 

 hyperbola as an empirical one for interpolations in the infra-red 

 without attaching any physical meaning to it. The further the 

 investigation has been pushed in that part of the spectrum, the 

 more exact the resemblance has become. That it is noticeable, 

 will be seen on consulting Plate IV,* where the hyperbola does 

 not appear as a distinct curve, because its variation from the 

 smooth curve of observation cannot be recognized on this 

 scale. 



In obtaining this we have proceeded as follows : Having five 

 disposable constants, we have taken five nearly equidistant 

 points on the smooth curve of observation, remembering that if 

 the axis of T is not exactly asymptotic to the curve thus de- 

 scribed, we are not necessarily to impute the difference to the 

 equation chosen, since the condition that the curve of observa- 

 tion shall be rigorously asymptotic to this axis can in any case 

 only be satisfied by infinite exactness of measurement. 



It will be observed that my estimates of the extreme wave- 

 lengths are in no way founded on the use of this hyperbola, and 

 that I do not assert that it has any physical meaning. 



I have elsewhere observed that while Herschel in 1840, Dra- 

 per in 1842, Fizeau and Foucault in 1846, Lamansky in 1870, 

 together with others since, had observed bands in the infra-red 

 prior to 1881, yet that nothing was exactly known as to the 



* It should be mentioned that some of the observations on which the computa- 

 tions are founded have been added since this drawing was prepared for the 

 engraver. 



