Absolution of Energy by Electrons. 71 



ch 



as e^V is sensibly different from unity. For the wave- 



c7i 

 length 4/x or 4xl0 _4 cm. and = 300, tttz * s about 17, 



and the complete radiation is infinitesimal compared with 

 what it would be did Lorentz's formula (3) represent reality 

 Yet Hagen and Kubens found that for these waves there was 

 no corresponding increase in the coefficient of absorption over 

 that for very much larger values of X. It is, therefore, the 



ch 



emission which decreases by containing e E ^ as a factor. 

 What the numerical data of last paragraph show, is that 

 this factor is of order unity when the period of the 

 waves is the same as the time spent by an electron on 

 its free path. For greater wave-lengths and longer periods 

 than this, Lorentz's formula (3) will hold ; for smaller 

 periods we shall require (4) to represent the facts by 

 reason of the rapid decrease in the emission. 



The notion of free paths and collisions is not altogether 

 helpful when we have to do with electrons moving in a 

 metal. If we think of the electron as completely deflected 

 by its collision w T ith a molecule, and remaining after that 

 with unchanged velocity till the next collision follows, it 

 becomes impossible to account for the actual nature of the 

 radiation. Quite apart from all questions of dynamics as 

 a mere matter of Fourier analysis, it is certain that the vast 

 mass of the energy emitted would be of the same period as 

 the time of a collision, and that is about 10~ 15 of a second, 

 taking the diameter of a molecule as 10~ 8 . Up to waves of 

 this period the emission ought to increase, not decrease, with 

 decreasing w T ave-length. 



The difficulty may be escaped by abandoning the notions 



of free path and collision in sharp contrast. The free path 



will be defined as the average distance an electron moves 



before its velocity is so changed that it retains no observable 



connexion with its original velocity. The length of this free 



. . . . 



path, the distance within which the original direction of 



motion still persists, measures the mobility of the electron. 

 It is w T ith that we deal in experiments on conduction. 

 The main part of the energy emitted must be of periods 

 not small compared with the time spent on a free path 

 thus defined. The Fourier analysis can predict that con- 

 sequence and it is independent of any dynamical theory 

 whatever. Wien's law therefore, vdiich makes the wave- 

 length \ m of maximum radiation vary inversely as 0, may 

 be interpreted as a direct consequence of the experimental 

 fact that the time for a free path varies in the same ratio. 



