Thermodynamics of Radiation. 879 



on the side of long wave-lengths, where the comparison is 

 fairly easy. But if the differences are plotted as in figure (1) 

 (dotted curve), they amount, on the short wave-length side, 

 to something of the order of 20 per cent, of the maximum 

 ordinate, which considerably exceeds the possible limits of 

 error of the verification of Wien's or Planck's formulae in 

 this region. According to Walker's formula the thermal 

 intensity of the ultra-violet light of wave-length "29/jl in the 

 radiation from a black body at 727° G. (a dull red heat) should 

 be '154 per cent, of the maximum ordinate, and might be 

 detected with a sensitive thermopile. Asa matter of experi- 

 ment no radiation of this wave-length from such a source 

 can be detected by the most delicate photographic methods, 

 and it is much more likely to be of the order of 10~ 15 of the 

 maximum, as given by Wien's formula. The exponential rate 

 of diminution of the curve on the short wave-length side is 

 one of the most certain results of experiment, and it is one of 

 the strongest points of the present theory that the exponential 

 term in the formula follows so directly from the application 

 of Carnofs principle. 



Another method of comparing the formulae with experi- 

 ment is to observe the variation with temperature of the 

 intensity of a particular wave-length. Among the best 

 known applications of this method are the experiments of 

 Rubens on the Reststrahlen of quartz, fluorite, and rocksalt. 

 His experiments showed clearly that the distribution formula 

 must reduce to the Rayleigh type /c\~ 4 T for large values of 

 XT, but indicated appreciable deviations from Planck's 

 formula in the case of the quartz Reststrahlen. The difference 

 between his results and Planck's formula is shown by the 

 crosses representing the observations in fig. 2. Planck's 

 formula itself is represented by the base-line as in the 

 previous figure. 



Here again, as Rubens points out, comparison of the 

 relative values alone is experimentally possible. The values 

 given by the various formulae for radiation of wave-length 

 8*85 /ju, corresponding to the quartz Reststrahlen, with the 

 source at 1000° 0. and the receiver at 0° C, are accordingly 

 reduced to a common value, so that all the curves agree 

 at 0°O. and 1000° C, and the differences from Planck's 

 formula at intermediate points are plotted in terms of the 

 radiation at 1000° C. The observations are seen to agree 

 distinctly better with the thermodynamical formula (8) than 

 with Planck's. The observations on the Reststrahlen of 

 fluorite and rocksalt show a similar result, but are not so 

 decisive, because the formulae approximate so closely to the 

 Rayleigh type for long wave-lengths, and the observations are 



