﻿S. P. Langley — Unrecognized Wave-lengths. 101 



are acquainted* gives entirely correct results on extrapolation, 

 but that among the best are Briot's and Wiillner's. We have 

 computed the wave-lengths corresponding to indices of refrac- 

 tion from observed deviations in the visible spectrum according 

 to these formulae. The curve from Cauchy's formula we do 

 not give, because (at least when not more than three terms are 

 taken from observations in the. visible part of the spectrum), 

 its results are here of little value, since it declares all the radia- 

 tions we are now actually dealing with, to be impossible of dis- 

 crimination at all. Eedtenbacher's formula we have also 

 shown in a previous memoir to be scarcely worth further con- 

 sideration. The graphically constructed values are obtained 

 by applying the formula of Briot, 



/— i = a + &-?r+c-?r r + & — ).-- -- t0 tne four points: 



A (A=0^7601. w=l-53670) 



D 2 (A=0^5889. w=l'54418) 



b x (A=<y-5183. «=l-54975) 



Hj (A = 0^3968. w=l*56833) 



and the formula of Wtillner, In 2 —-1=: — PA 2 -|-Q — — — — V to the 



three points : 



A (AzrO^-7601. w=l-53670) 



b x (A= 0^5183. w=r 1-54975) 



H 1 (A=0^3968. w=l*56833) 



All these are in the visible spectrum, and from them the con- 

 stants a, b, c, k, P, etc., are determined. With their aid we 

 next enquire, by the formula, what wave-lengths correspond to 

 certain given indices, and the resultant values in the infra-red 

 are then plotted from these computations. It is, however, only 

 just to observe that the wide departure from observation here, 

 shown is by no means to be wholly attributed to error in the 

 formula, for minute errors of measurement, such as are always 

 present even in the observations in the visible spectrum, are 

 immensely exaggerated by extending the curve through extra- 

 polation. Wiillner's formula, for instance, would give a line 

 closely coincident with our curve in the infra-red if we took all 

 our points for computation from that part of the spectrum. A 

 similar remark may be made of Briot's equation, whose actual 

 tracing, however, with the constants we obtain from the visible 

 spectrum, shows that beyond a certain point, the curve which is 



* That proposed by Ketteler has come to the writer's knowledge too late for 

 trial here. 



