( 418 ) 
the amplitude of f. Moreover the phasis of br is f. As however 
all phases occur equally frequently the distribution of the quantities 
[bai] will be the same as that of the quantities [/,], so that the 
chance that baj is contained within certain limits may be repres- 
ented by: 
2 
bn 
1 
cya 
In order to find the distribution of the vibrations we may reason 
as follows. Starting from a certain initial condition the molecules 
will entirely lose their original vibrations by radiation. The vibrations 
in the direction of the X-axis, which they absorb from the field, 
are dependent on the component of the vibrations of the ether, 
and not on the g- and A-component. As the f-, g- and A-compo- 
nents are independent of each other, also az, ay and az, caused by 
them, must be independent of each other, and as all directions occur 
with the same frequency, the distribution of the a’s must also be 
that of Maxwerr. The chance that the quantity an is contained 
within given limits, may therefore be represented by: 
oar ® where C=4n Vie 1). 
1 Fg 
é 5 Aly) » 
fv 
In order to arrive at this result the solution of the differential 
equation for a, is not necessary. In this way however the condition 
is not yet perfectly determined. From the value found for az appears 
that if a molecule were exposed to an electric wave of constant 
intensity, it would have assumed the amplitude b after an infinite 
time. If a molecule is placed in a region where the amplitude of 
the electric force has a definite value, it will have been for some, 
though it be a short, time in a region, where the amplitude of the 
electric force did not differ much from that definite value. So it 
will have already assumed part of the amplitude 5. The probability 
of the action of a force f on a molecule with a vibration a, cannot 
be simply represented by: 
2 2 2 2 
Jy tS a, + a 5 
bee 1 Ke oc 
ee Ra e df, dfg dan daa , 
1) Proc. Roy. Acad., Dec. 1899. Pag. 322. 
