138 Proceedings of the Royal Society of Edinburgh. [Sess. 
atoms. We know that the vibrators in different atoms are capable in the 
aggregate of furnishing vibrations of all frequencies from those of the 
extreme infra-red spectrum to those of the X-rays ; so L and C must vary 
from one vibrator to another. We know, moreover, that in vibrators 
which are geometrically similar to each other in all respects, both L and 
C are proportional to the linear dimensions of the vibrator : and since it 
seems on the whole likely that elements so fundamental and so multi- 
tudinous as these vibrators will be fashioned after the same pattern, it is 
most natural to assume that the vibrators contained in different atoms 
resemble each other in every respect except that of scale : which implies that 
if Cj, relate to one vibrator and C2, relate to another, then 
L.2 C 2 
This does not, however, lead to the consequence that L/C is a constant 
number, since L and C have different dimensions: and indeed the dimen- 
sions which L/C has in one system of units {e.g. the electrostatic system) 
are different from the dimensions which L/C has in another system of 
units {e.g. the electromagnetic system). If, however, we multiply vg by 
e^, where e denotes electronic charge, we obtain a quantity whose dimen- 
sions are the same in every possible system of units: and this quantity, 
being the same for all vibrators, must therefore be a natural constant. 
Now the dimensions of this quantity are found at once to be 
(Mass) (Lengfch)^ (Time)~^; 
that is to say, they are the dimensions of Action. We are thus led to 
infer that there exists in the universe a natural constant of Action : or 
rather, since it is now a well-established experimental fact that there exists 
a natural constant of Action, we are encouraged to believe that our assump- 
tion which led to this inference was justified. Let us then denote the 
natural constant 
by so that 
( 18 ) 
where h is a natural constant of Action. According to this view, the 
existence of a natural constant of Action simply indicates that the 
Hertzian oscillators in the atoms are similar to each other in structure 
and differ only in scale. 
