382 Prof. P. G. Nutting on the 



r> 



The parameters A and n in (8) and the parameter B have 

 been limited only to positive real quantities, $ x and <f> 2 must 

 have no positive real roots, n in (9) is real and positive and 

 equal to the degree of cj> 2 less the degree of $j, and v is less 

 than n. Both functions show the logarithmic congruency 

 observed by Paschen, and both give Stefan's law as particular 

 cases. Function (8) may be easily identified with the formulas 

 of Wien, Planck, and Paschen. Koveslighety's function 



\2 



E = At 2 T 4 /(t 2 T 2 + c 2 )' 



is a particular form of (9). It is, however, not in agreement 

 with Stefan's law; for by it the total radiation — the integral 

 of Edr from zero to infinity — is proportional to T instead 

 of T 4 . If we extend <p x and cb 2 to include exponential as well 

 as algebraic functions, as we may without violating the con- 

 ditions imposed, the Wien function (8) becomes a particular 

 form of (9), in which n = and v is negative, since it is less 

 than n. The emission formula of Weber * 9 



E = C\-V T - 1 / 6 ™ 2 , 



and of W. Michelson f, 



E = CT s / 2 \- G e- a ^ T , 



are open to objection, for both give infinite emission at very 

 high temperatures, even of waves of long period. Also the 

 derivative of each is infinite for T = 0, instead of zero of high 

 order as it should be. Michelson's formula, further, does not 

 give the \ TO T= const, law now so well established. 



Extension to Partial Radiators. 



In order that the complete emission function may express 

 the emission of imperfect radiators, such as quartz, carbon 

 dioxide, or sodium vapour, we must impose upon it at least 

 two other kinds of emission maxima besides that maximum 

 varying inversely as the temperature which it already has. 

 The complete function must then contain at least three 

 distinct types of emission maxima, namely : — 



I. Maxima which vary in position according to the 

 A max T = const, law. This constant appears to be different 

 for different sources, being about 8 x 10~ 12 deg. sec. for black 

 or inclosed sources and larger for others %. This class of 

 maxima appears to be characteristic of all substances at 



* Weber, Berl. Sitzb. ii. p. 938 (1888/. 

 t W. Michelson, Journ. d. Phys. (2) vi. p. 467 (1887). 

 % Cf. Lummer and Pringsheim, Ver. d. D. Ph. Ges. i. p. 222 (1899) ; 

 H. Rubens, Wied. Ann. lxix. p. 580 (1899). 



