516 Mr Campbell, Discontinuities in Light Emission. 



A little consideration soon discovered an explanation for the 

 results obtained so obvious that it ought to have been foreseen. 

 Equation (9) § 7 of the previous paper gives 



where x^ is the mean square fluctuation in the number of electrons 

 emitted, N the number of light impulses per second, m the number 

 of electrons liberated by a single impulse and 77^ the mean square 

 fluctuation in w. The reason for the very large value of x^ when 

 the reflecting lamp is used is to be found in the large value of if. 

 Some further considerations as to the value of if when a plain 

 open lamp is placed before the cell will be given later. Here it 

 need only be noted that, in this case, all light impulses which fall 

 upon the active surface of the cell have very nearly the same power 

 of setting free electrons. The only variations in this power arise 

 from slight differences in the distance of different parts of the 

 filament from the cell, or slight differences in the angle at which 

 the light from different parts of the filament is incident about the 

 cell. The greater part of the variation in w for different light 

 impulses probably arises from effects connected with the nature 

 of ionisation : it is unlikely that the value of rf would be much 

 reduced if all light impulses had exactly the same power of 

 forming electrons. 



But in the case of the lamp nearly surrounded by a reflecting 

 surface matters are very different. Part of the light which passes 

 out through the tubes has travelled a much longer distance within 

 the bulb than other parts, and has undergone many more re- 

 flections. Its intensity is reduced both by the increase in distance 

 and by the loss suffered in reflection by an imperfect reflector. 

 Even if each point of the filament emits in each elementary cone 

 light of the same intensity, the intensity of the light emitted from 

 different points and in different directions will not be the same 

 when it arrives at the active surface. Accordingly, superimposed 

 on the variations of co due to variations in the process of ionisation, 

 there will be variations, probably of far greater amount, due to 

 variations in the intensity of different light disturbances when 

 they arrive at the cell. 



It would be possible by suitable calculation to obtain some 

 measure of the amount of the latter fluctuations, but even for 

 very simple cases, differing considerably from the enclosure of 

 complex shape which surrounds an Osram lamp, the work is very 

 laborious and complicated: it has not been thought worth while 

 to make even an approximation in the absence of any knowledge 

 as to how close the approximation would be. 



We have also to take into account the fact that the convection 



