Mr Campbell, Discontinuities in Light Emission. 315 



§ 9, We cannot estimate the value of 7f until we know (and 

 we are not likely to know in the near future) the causes of the 

 fluctuations of w. But, from the general theory of probability, it 



is certain that -^ will diminish as co increases. Further the same 

 or 



quantity will, almost certainly, diminish as the number of electrons 

 which come under the influence of the light beam increases : for 

 o) fluctuates because all those electrons are not in the same con- 

 dition, and in a very large collection of electrons the distribution 

 of electrons of different properties is likely to be very nearly the 

 same. Accordingly, on the older theory of light, we should expect 



— to be very small : for any light disturbance is spread over the 



whole surface of the cell and of the optical train, and acts upon a 

 vast number of electrons. But, on the theories of light which 

 form the basis of this experiment, the area of the surface affected 

 by any one light disturbance is very small and the number of 

 electrons in that surface may possibly be as small as one. With 

 these considerations in mind, let us consider how observations of 

 the fluctuation of the measuring instrument might be applied to 

 test the rival theories. (It must be remembered that, in any 

 comparable series of experiments, f{t) will be the same, so that 

 Ot^ is proportional to x^jr.) 



In the first place we might compare the fluctuations of X— X', 

 i.e. the fluctuations of the balanced cells, (1) when we know that 

 the two beams are independent and (2) in the case in which we 

 wish to discover if they are independent. The ratio of the 

 fluctuations in (1) to those in (2) should be 1 if the beams in 



(2) are independent, and — z= — if they are dependent. If jf 



ff _ 



TT' 



were the same in both cases and — were large compared to 1, 



the two ratios might well be indistinguishable : it is for this 



reason important to note that —^ is certainly not likely to be 



large on the ' spherical wave ' theory of light. If that theory be 

 true we should expect the ratio in case (2) to be much greater 

 than that in case (1); if the 'bundle of energy' theory be true 

 we should expect the two ratios to be equal. The objection to 

 this method of test is that it is difficult to ensure that the optical 

 trains and the entire apparatus remain the same, when the change 

 is made from the beams known to be independent (probably two 

 different lamps) to the beams which it is desired to test. 



In the second place, we may compare the fluctuations of 



21—2 



