230 Electrical Origin of the Radiation from Hot Bodies, 



when they come into collision with the surrounding mole- 

 cules, will give rise to Pontgen rays ; and thus the Rontgen 

 rays emitted from the target struck by the cathode rays consist 

 of two parts, one due to the impact of the primary cathode 

 rays ; this part, if the preceding considerations are correct, 

 ought to be the same for all bodies ; the other part, due to 

 the stopping and starting of the secondary cathode rays, will 

 depend upon the metal of which the anti-cathode is 

 constructed. 



If the collision between a corpuscle and a molecule is 

 regarded as arising from a strong repulsion between the two 

 when they come very close together, then we can show that 

 if, as the Second Law of Thermodynamics requires, the time 

 of a collision varies inversely as the square of the velocity of 

 the corpuscle before it came into the neighbourhood of the 

 molecule, the repulsion between the corpuscle and the mole- 

 cule must vary inversely as the cube of the distance between 

 them. 



By taking the acceleration during impact to be propor- 

 tional to —z — ^, we have arrived at the law of distribution 

 a 2 -f 1* 



expressed by the equation 



E cc~e~^d\, 



which is the form suggested by Lord Rayleigh (Phil. Mag. 

 [5] xlix. p. 539). 



At high temperatures this expression does not seem to 

 agree with the experiments as well as the one suggested by 

 Planck, i. e.j 



c 

 1 €~W 



Exec - 5 -^d\. 



1 — e ^ 



To find the kind of collision that would give Planck's 

 form, we see that if f(X) represents the acceleration at the 

 time X, we must have 



J +oo i r e —qa 1 J 



_J\\) cos q\ d\ = q* [ j— ^ J ; 



i r« p+<» t 



f(t) = - I 1 f(X) cos q\ . cos qt . dq . d\ 



I? J J-co 



i J e-w } I 



or, since 



M-l£ 



