404 Prof. S. P. Langley on Invisible Heat-spectra 



boiling water or melting ice are those to which the chief 

 interest attaches, in connection with the temperature of the 

 soil, and as these are not well shown on the same scale of 

 ordinates with that of the red-hot copper, we give an inde- 

 pendent representation of these two in fig. 1, but upon the 

 wave-length, not the prismatic scale. Their maxima of heat 

 fall at points in the normal spectrum which (as we explain 

 later) are only approximately determinate on this scale, but 

 which are probably at least as low as the points (/) corre- 

 sponding to the boiling-watermaximum, and (g) corresponding 

 to the position of the maximum ordinate in the spectrum of 

 ice at the melting-point, or lower. No attempt is made in 

 this figure to represent the relative amounts of heat in the 

 solar and Leslie-cube curves, but only their positions on the 

 wave-length scale ; and here also it will be understood that 

 the latter curves really extend far further to the right than 

 the limits of the plate admit of showing them. 



These observations, then, show a real though slight progres- 

 sion of the point of maximum heat toward the shorter wave- 

 lengths as the temperature rises. The position of the maximum 

 ordinate of the lower curves is of course more difficult to 

 determine, on account of their flatness. 



The whole heat-spectrum from most of these sources, it is 

 interesting to note, passes through the prism at angles which 

 the theories of our text-books have heretofore pronounced 

 impossible. The existence of these radiations, and the relative 

 amounts of heat for each deviation, are certain, for these devia- 

 tions are determined by the spectro-bolometer, in most cases 

 with a probable error of less than a minute of arc ; but when 

 we pass to the next stage of our work, the determination of 

 the corresponding wave-lengths, we cannot speak with such 

 confidence. We have calculated the wave-lengths for some 

 of the observations by means of Wiillner's new formula*. 

 This formula, 



n 2 -l=-PX 2 + Q ;v 2^^ 



where P, Q and X m are constants, depending upon the nature 

 of the refracting substance, to be determined by observation, 

 is founded on Helmholtz's theory, but he has tested it by our 

 own observations with the glass prism. We have found the 

 calculated values to agree with similar ones obtained ^ directly 

 from the curve representing the relation between n and X. for 

 rock-salt, which is shown in the woodcut, by measurements 

 pn points whose wave-lengths were known from our prior 



* Wiedemann's Annalen, Band 33, S. 307. 



