1 72 Dr. L. Silberstein or Radiation 



An equally good agreement has been obtained in the case 

 of aluminium, for which the suitable value of T c is about 

 92 degr. absol. But since w = T c /T enters in our formula 

 always in the same way, the above example will suffice. 

 With regard to the above numerical values of T c , it will be 

 well to remark that they nre altogether different from those 

 of Debye's " characteristic temperature." This is due to 

 the circumstance that our assumptions, leading to (13) and 

 (19), have nothing in common with the theory of Debye, 

 which is based on the concept of " quanta " and is con- 

 structed on non-electromagnetic lines'*. In fact, the series 

 (19 a), although consisting of alternately positive and nega- 

 tive terms in (T c /T) 2 , (T c /T) 4 , &c, as that of Debye, has 

 entirely different coefficients. Unlike Debye's, the proposed 

 formula is in intimate connexion with that for the emission. 

 But a somewhat detailed comparison of the two, utterly 

 different, points of view w T ould be out of place here. In 

 fact we have stopped here to consider specific heats at all 

 only for the sake of illustration of the formula (13) for 

 the mean energy of the electric source. 



But before leaving this subject a few more remarks seem 

 indispensable. The above table is broken off at about 45 

 (i. e. a few degrees below T c ) not because the practical 

 application of (19), instead of the series, was laborious, but 

 solely for the reason that our specific-heat curve, corre- 

 sponding to a constant <? , does not descend steadily right 

 down to zero, but in approaching the absolute zero of 

 temperature begins to go up and down. The amplitude of 

 these oscillations does not even decrease indefinitely but 

 tends to a finite and comparatively large value. Indeed, 

 using (9) and (17) in the rigorous formula (19), we find, for 

 very large values of to = T c /T, 



OR = 3[l-i<r><»] = 3(1-* cos 2 w ), 



i. e. incessant oscillations between 1*5 and 3, which is utterly 

 unlike any facts of experience. This apparently undesirable 

 behaviour of the curve at lowest temperatures, which fully 

 corresponds to what I have expected beforehand, is intimately 

 connected with the peculiarity of the radiation curve (14) 

 in consisting of an infinite number of branches, contained 

 between the consecutive zeros of g(w). The first of these 



* Cf. P. Debye's paper "Zur Theorie der spezifischen Warnien," 

 Annul, der Physik, vol. xxxix. (1912), pp. 789-839, from which the 

 " observed ' ? values of Table IV. have been taken. Debye's " charac- 

 teristic temperature "' (9) is, for Ag, 215°, and for Al, 396° absol. For a 

 comparison of coefficients see Debye's formula (12'). 



