A.—_MATHEMATICS AND PHYSICS. 33 
same time we measure the contact difference of potential K between 
them, we find that K is equal to the difference between their threshold 
frequencies multiplied by this same constant h divided by the electronic 
charge e. 
These results, as well as others which I have not time to enumerate, 
admit of a very simple interpretation if we assume that when illumi- 
nated by light of frequency n the electrons individually acquire an 
amount of energy hn. We have seen that in order to account for 
thermionic phenomena it is necessary to assume that the electrons 
have to do a certain amount of work w to get away from the emitter. 
There is no reason to suppose that photoelectrically emitted electrons 
ean ayoid this necessity. Let us suppose that this work is also definite 
for the photoelectric electrons and let us denote its value by hm. ‘Then 
no electron will be able to escape from the metal until it is able to 
acquire an amount of energy at least equal to hn, from the light— 
that is to say, under the suppositions made—until n becomes at least 
as great as m. Thus ™, will be identical with the frequency which 
we have called the threshold frequency, and the maximum energy of 
any electron after escaping will be h (n—m). 
The relation between threshold frequencies and contact potential 
difference raises another issue. We have seen that the contact potential 
difference between two metals must be very nearly equal to the difference 
between the amounts of work w for the electrons to get away from 
the two metals by thermionic action, divided by the electronic charge e. 
The photoelectric experiments show that the contact electromotive force 
is also nearly equal to the differences of the threshold frequencies multi- 
plied by */,, It follows that the photoelectric work hn, must be equal 
to the thermionic work w to the same degree of accuracy. We have 
to except here a possible constant difference between the two. I do 
not see, however, how any value other than zero for such a constant 
could be given a rational interpretation, as it would have to be the 
same for all substances and frequencies. The photoelectric and ther- 
mionic works are known to agree to within about one volt. To decide how 
far they are identical needs better experimental evidence than we have 
at present. The indirect evidence for their substantial identity is 
stronger at the moment than the direct evidence. 
I do not think that the complete identity of the thermionic work w 
and the photoelectric hn. is a matter which can be inferred a priori. 
What we should expect depends to a considerable extent on the con- 
dition of the electrons in the interior of metals. We cannot pretend 
to any real knowledge of this at present; the various current, theories 
are mere guesswork. Unless the electrons which escape all have the 
same energy when inside the metal we should expect the thermionic 
value to be an average taken over those which get out. The photo- 
electric value, on the other hand, should be the minimum pertaining to 
those internal electrons which have most energy. The apparent sharp- 
ness of the threshold frequency is also surprising from some points 
of view. There seems to be scope for a fuller experimental examination 
of these questions. 
I have spoken of the threshold frequency as though it were a 
