MICROSCOPICAL JOURNAL: TRANSACTIONS OF THE ROYAL MICROSCOPICAL SOCIETY, AND RECORD OF HISTOLOGICAL RESEARCH AT HOME AND ABROAD. EDITED BY HENRY LAWSON, M.D., M.R.C.P., F.R.M.S., I.-Thermo-dynamic Origin of the Brownian Motions. (Read before the ROYAL MICROSCOPICAL SOCIETY, June 6, 1877). THE Brownian, or molecular motions, have been hardly known more than fifty years. Robert Brown announced, in 1829, that when extremely minute solid particles, either organic or inorganic, are found suspended in pure water, or in an aqueous fluid, they display certain motions whose cause he was unable to discover, and which, by their irregularity and apparent independence, resembled to a remarkable degree the less rapid motions of the simplest infusoriæ. The smallest of these particles he called active molecules.* The motions discovered by Robert Brown in minute particles, and for that reason called Brownian motions, have since been observed by all naturalists. In fact, there is not one amongst them but must have been struck by the strangeness, the persistence, and the frequent apparition of these molecular motions in the field of the microscope; not one, I fancy, who has not tried to raise up, were it only by a corner, the veil which nature has cast upon the secret of their origin. Hitherto, it must be confessed, all their efforts have been fruitless: the sphinx has kept his enigma. A friend of mine has, I think, approached the nearest to the truth in investigating this matter. His opinion, the fundamental idea of which has been put in print,† may be expressed in these terms: "Every free particle, the molecules of which remain associated by their mutual actions as in the liquids and the solids, or by an external pressure as in the gas-bubbles in the mass of a liquid, must oscillate incessantly, if it is sufficiently small. These oscillations are a necessary result of the molecular vibrations which constitute heat; because each molecule, in vibrating, tends to displace the centre of gravity of the body to which it belongs. If this displacement is not commonly produced in the bodies we observe, it is because the effect of one, owing to the immense number of molecules, is always neutralized by that of another." The theoretical de* Ch. Robin, Traité du Microscope,' p. 526. Bulletin de l'Académie Royal de Belgique,' t. xli. p. 410. VOL. XVIII. B velopments into which I shall enter shortly, will show how much we ought to ascribe to this really ingenious, but much too incomplete idea. The Brownian motion of minute particles in suspension in liquids, is a movement of oscillation and of vibration, in situ, that is quick, irregular, and continuous. We do not remark there either translation or locomotion properly so called. The orientation of the oscillatory motion passes briskly, and without following any law, from one direction to another. In the cellules of the epidermis, the pigmentary granulations having less than five or six thousandths of a millimeter in diameter, are animated with this motion of vibration; the grains of chlorophyll in the green cellules, and probably all the cellular granulations whose surrounding liquid is not solidified, likewise manifest this movement. It is observed also in gold particles, in little grains of iridium, platinum, coal, lime, &c., &c., in milk globules, and more generally in all viscous globules immersed in water or in liquids that have little resistance. The phenomenon occurs also in the little gas-bubbles imprisoned in a liquid; for example, in the air-bubbles which are so easily formed by agitating soap and water. The Brownian motion is more active in heated liquids than in those of a low temperature. Supposing equal diameters, the oscillatory displacement is more rapid and more extended in fatty granulations than in metallic granulations whose density is very great. The duration of the phenomenon may be said to be without limit: M. Robin possesses aqueous preparations of charcoal dust, made more than twenty years ago, in which the Brownian motion still continues to manifest itself. In this respect, quartz rocks are yet more remarkable: the Brownian motion has been going on in them for millions of years. In fact, it is not a rare thing to find, in the quartz of geological strata, liquid cavities containing a gas-bubble in a state of perpetual agitation. It is a little bubble of vapour produced by the withdrawal of the liquid, and which the Brownian motion carries hither and thither into all the recesses of its transparent prison. Of all the physical phenomena that the microscopic study of rocks, so fruitful of surprising results, has revealed to us, this fact, first observed by Mr. Sorby, is certainly one of the most beautiful. My intention in this note is to show, that all the Brownian motions of small masses of gas and of vapour in suspension in liquids, as well as the motions with which viscous granulations and solid particles are animated in the same circumstances, proceed necessarily from the molecular heat motions, universally admitted, in gases and liquids, by the best authorized promoters of the mechanical theory of heat. I have been led to consider the phenomenon from this point of view, from the study I have made of the movements of Mr. Crookes' radiometer. I will begin by explaining 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 hold 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 consecutive 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 roooo of a millimeter for the ordinary pressure, while, according to the most recent observations, all air-bubbles whose diameter does not exceed of a millimeter, are, when imprisoned 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 pressure 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.† 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 experiments on the radiometer, the value of the ratio between the dimen *Annales de Poggendorf, 1876, No. 8. †Théorie Mécanique de la Chaleur,' 2e partie, p. 230. |