Origin of the Brownian Motions. By Bev. J. Belsaulx, S.J. 3 
the movements of Mr. Crookes’ radiometer. I will begin by explain- 
ing according to this theory the Brownian motion of gas-bubbles. 
In estimating the pressure exerted by a gas on the walls of the 
containing vessel, Clausius attributes to all the molecules a medium 
velocity, in such a manner, however, as not to alter the total vital 
force of the gas. Thus determined, the pressure is found to be the 
same at each point of the walls of the vessel. 
In order to bold good, this hypothesis of Clausius evidently 
requires that the dimensions of the vessel be incomparably greater 
than the mean length of path of a molecule between two con- 
secutive collisions. Besides, we cannot use this hypothesis, when, 
by the rarefaction of the gas or by the contraction of the envelope, 
the dimensions of the vessel and the mean length of path of the 
molecules become quantities of the same order. Then, and this is 
precisely what takes place in the little bubbles of gas immersed in 
a liquid, the pressure exerted by the gas upon the different points 
of the envelope, and which are no longer subject to the law of the 
total communication of pressure, varies with the time for the same 
point, and are very different at the same instant at different points. 
The investigations of M. Finkener upon the radiometer fully justify 
this assertion.* 
In fact, in the atmosphere the mean length of path of the 
molecules is about rsiisis of a millimeter for the ordinary pressure, 
while, according to the most recent observations, all air-bubbles 
whose diameter does not exceed -$1-$ of a millimeter, are, when im- 
prisoned in a liquid, in a permanent state of molecular agitation. 
In this case, as is evident, the ratio of the dimensions of the 
envelope to the mean length of path of the molecules is represented 
at its maximum value by the number twenty. Now, it results from 
the numerical tables of M. Finkener, in regard to the movements 
observed in the radiometer, that the total communication of pres- 
sure produced by variations of velocity in any part of the gas, 
ceases in the air, at least partially, when the ratio of the dimensions 
of the vase to the mean length of path of the molecules is less 
than 3000. We can easily see this, by applying to the numerical 
data with which we are concerned, the following theorem of 
Clausius : the mean length of path of a molecule is to the radius 
of its sphere of action as the total space occupied by the gas is to 
the part of this space, which is really filled by the spheres of action 
of the molecules. t It follows that in the radiometer the mean 
length spoken of is inversely proportional to the number of the 
molecules, and consequently also inversely proportional to the 
density and to the pressure of the gas. In M. Finkener’s experi- 
ments on the radiometer, the value of the ratio between the dimen- 
* ‘ Armales de Poggendorf,’ 1S76, No. 8. 
f ‘ The'orie Me'canique de la Chaleur,’ 2 f partie, p. 230. 
B 2 
