Mr Gam'phell, Discontinuities in Light Emission. 519 



But, if we take account of the quantity 77^, the matter becomes 

 rather more complicated. On the bundle of energy theory the 

 value of 7f is of no importance for comparative measurements, 

 for ft) and therefore, presumably, 7f are the same for each bundle, 

 whatever the intensity of the light. But on the spherical wave 

 theory the value of rf is of great importance, since changes in the 

 intensity of the light are due to changes in the value of to. 



The evaluation of if cannot be made until some knowledge of 

 the mechanism by which the electrons are liberated is obtained. 



But the general theory of probability indicates that -^ will in- 



. crease as to decreases. On two simple assumptions, which give 

 results that probably differ from the truth in opposite directions, 

 we can calculate the value of t]'^. Thus, if we assume that the 

 light disturbance liberates an electron whenever, in passing 

 through a layer of constant thickness, it meets a system in some 

 special condition, it is easy to show that rf = to. But that as- 

 sumption involves the conclusion that a single light disturbance 

 might liberate an indefinite number of electrons, if only it met 

 a sufficient number of suitable systems — a statement which is 

 obviously untrue, since the liberation of electrons doubtless re- 

 quires the expenditure of energy and the amount of energy in 

 a single disturbance is limited. 



Taking an assumption which represents the other extreme, we 

 may suppose that each disturbance can liberate only one electron, 

 and that it will only liberate one electron if it chances to meet a 

 suitable system before its energy is rendered unavailable for the 

 purpose by passing through the photoelectric layer, or by reflection 

 or by some other cause, to is now the chance that a disturbance 

 will meet such a system before its energy is lost, and a well- 

 known formula shows that 



rf = (o (1 — w). 

 Hence on the first assumption 



on the second assumption 



In the latter case, whatever the value of to, being, of course, 

 less than 1, ^y^ will be proportional to w, that is, to the intensity 

 of the light, and no distinction can be made between the two 

 theories. In the former case a distinction can be made only if to^ 

 is not small compared to to. 



Now, if Planck's theory of the " elementarwirkungsquantum " 



