108 burgess: wien's spectral equation 



1 1 



since S\ and therefore — ~ — is a variable, depending on the 



specific emissive properties of the substance. 4 Applied ibr ex- 

 ample, to the computation of the absorption coefficient of liquid 

 copper 5 for green light, assuming that the value of A for red is 

 0.15, Pirani's method gives an absurd result, i.e., 0.06 instead of 

 0.35 for A 55 . 



It would lessen indefinitely the number of necessary observa- 

 tions if, in the general case, it were possible to compute the absorp- 

 tion coefficient for any wave length when that for one wave length 

 is known. No such mathematical relation exists, however. 

 Similarly, it is impossible either mathematically or graphically 

 to find an exact, general relation between the true temperature 

 of a substance and the apparent temperatures given by observa- 

 tions with light of two or more wave lengths except in terms of the 

 absorption coefficients, A\ x and A\ 2 , when equation (3) takes the 

 form 



In 1 -! = 5 i n h + ±n-±)+ln^ 

 I 2 Xx T\\ 2 Xi/ Ax, 



in which the observed ratio Ii/I* is corrected for the sensibility 

 of the eye. This equation may be solved graphically, among other 

 ways, by plotting lines of Axi/A x 2 = constant with values of 

 I1/I2 or its logarithm as abscissae and of T or t, or their recipro- 

 cals as ordinates. There are, however, in certain cases, some of 

 the metals for instance, convenient, simple empirical approxima- 

 tions connecting apparent temperatures with true, which may be 

 expressed graphically. 6 Although it is impossible graphically 

 or otherwise, to pass from one value A\ t to another Ax 2 unless 

 the energy curve of the substance is known for these regions, yet 

 it is possible to use equation (2) for the comparison of results of 

 observers who have used different values of c. 



4 Holborn and Henning, Sitzber. Beilin Akad., 12: 311. 1905. G. K. Burgess, 

 Bull. Bur. Standards, 1: 443-447. 1905. 



* G. K. Burgess, Bull. Bur. Standards, 6: 111-119. 1909. 



6 Waidner and Burgess, Bull. Soc. Franc, de Phys., 200-204. 1907. Jour, de 

 Phys., October. 1907. 



