Origin of the Brownian Motions. By Rev. J. Delsaulx, S.J. 5 
air, we find by Clausius’ theorem, mentioned above, that at the 
pressure of 15 millimeters, the probable pressure of vapour in 
cavities, the mean path of the molecules is of a millimeter. On 
the other hand, the most authorized measures assign to bubbles, 
dimensions inferior to of a millimeter. The value, therefore, of 
the ratio between the dimensions of the surrounding liquid and the 
mean path is in this case inferior to §. This is more than the 
theory requires for the manifestation of the Brownian motions. The 
smallness of the value found in this case for the ratio between the 
dimensions of the surrounding mass and the mean path of the mole- 
cules, is probably the result of the great resistance opposed by the 
liquid of the cavity to the Brownian motions. We know, in fact, 
that these liquids are ordinarily very concentrated saline solutions. 
After having explained, in conformity with the principles of 
thermo-dynamics, the movement of the Brownian gaseous bubbles, 
and the little masses of vapour in quartz, I shall endeavour in 
the same way to account for the movements observed in viscous 
globules, and solid granulations in liquids. According to me, all 
these movements result from the interior dynamic state that the 
mechanical theory of heat attributes to liquids, and are a remarkable 
confirmation of it. The following are, with regard to the question 
now occupying us, the points of doctrine admitted by science. 
In the molecular heat motions of solid bodies, “ the molecules 
oscillate around certain positions of equilibrium, which they never 
leave, as long as no extraneous forces act on those molecules. This 
movement, which may be considered as a vibratory movement, is of 
a very complicated nature. In the first place, a molecule’s consti- 
tuent parts can vibrate among themselves ; in the second place, the 
molecules themselves can vibrate. And these latter vibrations may 
consist either in an oscillatory motion of the centre of gravity, or 
in an oscillatory motion round this centre.” 
In liquids, “the molecules have not a determined position of 
equilibrium. They may oscillate in the body, and turn entirely 
round their centre of gravity, which can completely change its 
position. ... In a liquid, therefore, there is a movement of 
oscillation of rotation, and of translation of the molecules ; but this 
movement is such that it does not separate the molecules from one 
another. They maintain themselves even without any exterior 
pressure within the limits of a certain vol u me.” * 
That which distinguishes the heat motion of liquids from the 
thermal motion of solid bodies, is, among other things, the move- 
ment of translation with which the liquid molecules are animated. 
It is from having neglected to take into account this movement of 
translation in liquids and gases, that the author of the thermo- 
dynamic theory of the Brownian motions, mentioned in the begin- 
* Clausius, ‘Tlie'orie Me'canique de la Chaleur,’ 2 a partie, pp. 192 et 193. 
