WAVE-LENGTHS IN THE INVISIBLE PRISMATIC SPECTRUM. 161 



are to be the same, we Lave ?i | , — | y = (A„ — A,) y^, whence y = —"-— x Vu which at 



\A„ A,,/ ■ n 



tlie limit becomes y = i/i. lleuce to obtain the new ordinates the old ones must be multiplied 



by the reciprocals of the factors for abscissie, or by . 



The curve EF, Fig. 3, if represented by a formula, would give rise to an expression of the form 

 <7=((^)A, the abscissa' measured along AB being pro])ortional to the wave-lengths, and the ordi- 

 nates parallel to CD to the deviations. Since tan »=''=',?■',, the factors for multinlvin"' 



dX (tX.dn ' • *' 



the prismatic ordiuates may be computed, provided the curve EF can be exactly expressed 

 by a formula, and for the preliminary reduction this was done, the values of being cominited 



from Brtot's formula, and -- from the relation m=^'" .- (" + "). When, however, it was showu by 



the measurements of obscure rays that Briot's formula, obtained by observations in the visible 

 spectrum, does not exactly express the law of dispersion, the table of factors thus prepared was of 

 course abandoned, and the graphical method described above was substituted. 



I have drawu in this way (on a smaller scale than that of the normal or i)rismatic curves and 

 following the smooth curve in the former as my original) four different schemes for the distribution 

 of the energy. Curve B, Plate XXI, represents the distribution of solar energy after absorption by 



our atmosphere on the scale of wave- frequency (general equation of interpolating curve a;=- pro- 



A 

 posed by Mr. Stoney). Curve C, Plate XXI, represents the distribution according to a proposal 

 (.r=log A) of Lord Rayleigh. 



Curve D {y=G) Plate XXI, is quite difierent from any of the preceding. It gives the distribu- 

 tion on a scale I have never seen proposed, but which I have found useful. In this the bounding 

 curve is a straight line parallel to the axis of X. This construction is not well suited to exhibit the 

 cold bands, but if we consider only the general distribution of the energy, we shall find that curve 

 D is not merely suggestive as illustrating what has already been remarked here as to the conven- 

 tional character of the methods of showing this distribution, but that it has more practical uses 

 for in this last construction it is easily seen that the sums of the energies between any two wave 

 lengths whatever are directly proportional to the distance between their ordinates, measured on 

 the axis of X. If, then, we desire (for instance) to know what relation the invisible bears to the 

 visible heat, or to inquire about what point in the spectrum the energy is equally distributed these 

 and similar problems are solved through curve D by sim^jle inspection. 



I have not been able yet to repeat the preceding determinations upon the lower part of the 

 spectrum as often as I could wish. They are susceptible of improved accuracy by still longer 

 experiment, but I think that within the limits of error indicated they may already be useful. I 

 should add t^at throughout this investigation I have received constant and valuable aid from Mr. 

 J. E. Keelee, not only in the graphical constructions, but in the experiments and in the compu- 

 tations, through all the details of which his aid has been more that of a coadjutor than an assistant. 



Allegheny Observatory, Allegheny, Pa., October, 1883. 



Note. — Since the above was in type I have seen the interesting article by M. H. Becqueeel 

 in the Annales de Chimie for September, 1883. 

 S. Mis. 110 21 



