S. P. Langley — Observations on Invisible Heat-Spectra. 11 



These observations, then, show a real though slight progression 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 ac- 

 count 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, is 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 confi- 

 dence. We have calculated the wave-lengths for some of the 

 observations by means of Wiillner's new formula,* 



A —A m 



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

 the refracting substance, to be determined by observation. 



This formula Wiillner founds 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 be- 

 between n and X for rock-salt, which is shown in Plate 4, by 

 measurements on points whose wave-lengths were known from 

 our prior observations up to about 23,000 of Angstrom's scale. 

 Beyond this point we have continued the curve both by com- 

 putation and by graphical extrapolation. We do not disguise 

 from ourselves the danger of all extrapolations, although ours 

 rest, it will be seen, on a wholly different basis from the ones 

 depending on formulae derived from the visible spectrum alone, 

 since our curve has been already followed by direct observa- 

 tions until it is almost coincident with a straight line. Up to 

 this point then (within the limits of error already elsewhere 

 given) there is no doubt, and unless there is some utter change 

 in the character of the curve, such as we have no reason to 

 anticipate, a tangent from the last part will not differ very 

 greatly from the immediate course of the curve itself, and will 

 at any rate meet the axis of abscissas sooner than the curve can. 

 If we assume then the prolongation of the curve to agree with 

 this tangent, we evidently assume a minimum value for all the 

 wave-lengths measured by it, and that is what we have done. 



We are not prepared yet to speak of these wave-length 

 values as exactly determinate, and they are here given as first 



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



