( 419 ) 
as would be the case if electric force and vibration were indepen- 
dent of each cther; but these quantities are dependent on one 
another. If the above expression held true for the probability of 
the action, the way of motion would satisfy conditions, exactly cor- 
responding to those which Prof. BOLTZMANN assumes for the case 
of molecular thermal motion, in order that the motion may be called 
“molecular-irregulated.” 1) In reality however, the way of motion is 
here molecular-regulated or as I would call it partially regulated. 
Totally regulated the condition would be, if the a, was entirely 
determined by f; if e.g. am had everywhere assumed the value br. 
The way of motion will be regulated in a higher degree as the 
quantity 
pees 
afi, Hide ddy , aide 
dt ot ma 
ae dy ack, gent ae. 
: 0 
is smaller. Here 2 represents the fluction of /, in a point which 
does not move from its place, a the total fluction of the quantity 
f; for a molecule which moves with a velocity, the components of 
which are oe ‘ ay and aes 
dt dt dt 
I have however not yet succeeded in finding the law according 
to which the motion is regulated. 
At first sight it may seem strange that the condition of maximum- 
entropy should possess a certain order, whereas for the case of the 
molecular thermal motion of a gas we consider the total irregularity 
as condition for the maximum-entropy. In order to solve this 
seeming contradiction we must take notice of the fact that we are 
here concerned with the action of forces. Now we know that the 
action of external forces which varies so slowly from point to point 
that they may be thought constant throughout regions which though 
small, are still measurable and contain many molecules (e.g. gravity), 
causes the density to be not everywhere the same in the condition 
of maximum-entropy, so that we have ,molar regulation.” But then 
it is not to be wondered at that the electric forces of radiation, 
which cannot be thought constant throughout regions of measurable 
dimensions, should cause a “molecular-regulation’”’. 
Even though we had succeeded in determining the regulation in con- 
1) »Molekular-ungeordnet.” BoLTzMaNN, Gastheorie I, Tag. 21, 
