Comjjlete Emission function. 385 



t.<£'(tT) is again a function of the product rT. Maxima of 

 type III, occur when these derivatives (12) and (13) are 

 infinite, i. e. when r = r m and the negative sign occurs. For 

 maxima of type II.., these derivatives must equal zero : such 

 a maximum is obtained by using the positive sign and finding 

 the real root of an equation of the third degree in r. For 

 the value r m = 0, (12) and (13) give maxima of type L, 

 T max T== const., characteristic of perfect radiators. Also for 

 Tm = 0, (10) and (11) assume the forms (8) and (9), as they 

 should. We may note in passing the coincidence of these 

 maxima of the emission-period function with those of the 

 reHexion-period and absorption-period functions, and that 

 the maxima of the refraction-period and electromagnetic 

 rotation-period functions are included among them. 



Function (10) agrees well with the scant data at present 

 available on the emission of partial radiators. Using the 

 values of the constants n and B determined by Paschen and 

 by Lummer and Pringsheim, giving r m a value corresponding 

 to the infra-red, (10) gives a curve closely resembling that 

 obtained by Rubens and Aschkinass * for carbon dioxide. 

 Two maxima, t x and t 2 , of different intensity near together, 

 give curves similar to those obtained by Rosenthal f for 

 quartz and mica. A number of maxima near together give 

 the characteristics of an emission-band. For periods con- 

 siderably greater than the greatest maxima of type II. or III. 

 the effect of the presence of the several maxima is vanishinglv 

 small, and (10) gives the same emission-curve as (8). Nearer 

 the greatest r m , and within a few octaves of it, the emission 

 by (10) is much less than that given by (8). The detect in 

 the Wien-Planck-Paschen formula in this region was noted 

 by Rosenthal. On the shorter period side of any maximum 

 the emission by (10) falls off much more rapidly to a much 

 smaller value than is given by (8). Thus, in the region of 

 the lined spectra, the radiation is practically all confined to 

 the lines themselves. 



The polar maxima, r l5 t 2 , ... t„„ may perhaps be identified 

 wirh ionic, molecular, or atomic period. Mathematically con- 

 sidered, they may be functions of any argument except 

 temperature. If we consider them hyperbolic functions of 

 the time — that is, consider them damped wave-periods — the 

 polar factor vanishes at intervals, and the integrated effect is 

 that of a short faint continuous spectrum on either side of the 

 spectrum-line. If we consider them functions of the ordinal 

 numbers, we obtain a simply related series of lines. They 



* Rubens and Aschkinass, Wied. Ann. lxiv. p. 595 (1898). 

 t Rosenthal, Wied. Ami. lxviii. p. 796 (1899;. 



