unrecognized Wave-lengths. Ill 



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 observa- 

 tion, as viewed in a large graphical construction, to a hyper- 

 bola, 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 notable will be seen on consulting Plate VI.*, 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 Y is not exactly asymptotic to the curve thus 

 described, we are not necessarily to impute the difference to 

 a fault in the equation chosen, since the condition that the 

 curve of observation 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, 

 Draper in 1842, Fizeau and Foucault in 1846, Lamansky in 

 1870, with others since, had observed bands in the infra-red 

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

 wave-lengths of these bands, even to those who discovered 

 them. It is very likely that the (probably telluric) absorp- 

 tion-band in the solar spectrum placed on our chart ( Comptes 

 Rendus, Sept. 11, 1882) at 1^*38 has been recognized by 

 more than one of the above-mentioned observers, yet so little 

 was known as to its actual position even a few years since, 

 that we find the elder Draper, in reviewing these discoveries 

 in 1881, and speaking with the authority of one who was 

 himself a discoverer, expressing his doubt as to the possibility 

 of any wave-length so great as l^'OS having really been 



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

 computations are founded have been added since this drawing was pre- 

 pared for the engraver. 



