The law of Dulottg and Petit would be an immediate consequence, if we should assume (1) that the heat absorbed by the solid is all ex pended in accelerating the motions of translation and rotation of the molecules, (2) that the mole cules of solid bodies all have the same num ber of degrees of freedom, (3) that the kinetic energy of translation of a molecule is the same (at any given temperature) whether the sub stance in which it exists is gaseous or solid, and (4) that the Boltzmann law of the parti tion of kinetic energy is fulfilled in solids. The first of these assumptions cannot be rigorously true either for solids or for liquids, and even in gases it is probably only closely approxi mate. The second assumption is also unlikely to be true of solid bodies in general, though solids may possibly be divisible into a small number of classes, in such a way that all the members of any one class will conform to it. When every reasonable allowance has been made for recognized uncertainties and sources of inaccuracy, the evidence that still remains is sufficient to suggest, as intimated above, that something akin to the Boltzmann law for gases holds true even in solids. Moreover, by making the assumption that a law of this general nature holds true in liquids, investigations have led to experimental results in good general agreement with those obtained by wholly different and totally independent methods.
Among the interesting and important re sults obtained by assuming that in liquids the kinetic energy of translation is distributed in accordance with the Boltzmann law those ob tained by Perrin deserve conspicuous mention. (See BaowNiAu MOVEMENT). Perrin experi mented with emulsions of various kinds, in which extremely small solid particles were sus pended in liquids of a lesser specific gravity— extraordinary care being taken to have the particles uniform in size and as nearly spheri cal as possible. The most trustworthy re sults were obtained with gamboge or mastic, the gum being dissolved in alcohol and then precipitated by pouring the alcoholic solution into a large volume of water. Uniformity in size was assured by a careful fractional centrif ugalization of the precipitated particles, while suspended in distilled water — a kilogramme of the original mastic furnishing, after several months, a fraction containing a few deci grammes of spherules of acceptable size and uniformity. The size and density of these spherules were then determined by several dif ferent methods, which gave concordant results. In the experiments that were considered by Perrin to be most reliable, the radii of the spherules were 0.367 of a micron — a micron being the thousandth part of a millimeter. As suming that particles of this size, when sus pended in a liquid, will comport themselves like molecules so far as the distribution of kinetic energy is concerned, so that the average kinetic energy of translation of the gum particles will become equal, after a time, to the average kinetic energy of translation of the molecules of the liquid in which they are suspended, it is possible to obtain, from a study of the visible particles in an emulsion, definite information respecting the invisible molecules composing the liquid in which the emulsion is suspended. Perrin made use of no less than four different methods, in endeavoring, in this way, to ascer tain the number of molecules in a gramme molecule of matter, and he gives a general ac count of all four in his book on atoms. Sur prisingly concordant results were obtained. In his simplest method, the emulsion was allowed to stand until the suspended particles in it had attained a permanent state of distribution —a condition which could be verified by making a miscroscopic examination of the emulsion, from time to time, at certain selected points. When
the final state was reached, the number of solid particles per cubic millimeter of the fluid mass was greatest at the bottom of the contain ing vessel, and diminished in a regular manner with increasing height. A careful study was made, by means of the microscope, of the dis tribution of the solid particles at different heights, and by assuming that this distribution is determined by the same laws that bold in connection with gaseous molecules, it was found to be possible to determine the number of molecules in a gramme-molecule of matter of any kind. The idea upon which this work was based is exceedingly ingenious, and consists, as will be seen, in assuming that by working with fine-grained emulsions, where we have positive and definite knowledge of the mass, size, number, motions and distribution of particles that approach molecules closely enough to be presumably governed by similar laws, we can draw accurate conclusions as to the mole cules themselves. From his most trustworthy series of experiments, Perrin concluded that Avogadro's number (that •s, the number of molecules in a gramme-molecule of matter) is 68.2 X 10". If this number be accepted as cor rect, it follows that the mass of . hydrogen atom is 1.47 X 10' grammes, from which we can easily obtain the mass of the atom or mole cule of any other substance, the atomic or mole cular weight of which is known.
Ingenious and important as Perrin's meth ods and results are, it is probable that future physicists will value them mainly for the light that they throw upon molecular behavior rather than because they afford us a means of deter mining Avogadro's number. In fact, we al ready have another and probably superior de termination of the number of Avogadro, made by a totally different method, and based upon assumptions fewer in number and more likely to be generally admitted. Millikan, in his ad mirable and classic researches, found the value of the electron to be 4.774 X absolute electrostatic units; and as the Faraday con stant (or quantity of electricity required to lib erate one gramme-atom of a monovalent ele ment by electrolysis) is known to be 9,650 absolute electromagnetic units (or 2,894 X 10" absolute electrostatic units), it follows that (2,894 X 10") ÷- (4.774 X 10') =60.62 X lOn separate and individual electrons are concerned in the deposition of one gramme-atom of such an element. Hence we infer that 60.62 X 10' is the value of Avogadro's number. This ap pears to be an unexceptional and exceedingly accurate method, provided we admit that one and only one electron is liberated or neutralized, for every atom of the monovalent element that is deposited,— an assumption which approaches closely to certainty, and which is far more likely to he true than are some of the assumptions that underlie other methods of determining Avogadro's number. Accepting Millikan's value of this number, it is easy to show that the mass of a hydrogen atom is 1.662 X grammes, and that the number of molecules in one cubic centimeter of gas at 0°C. and 760 millimeters pressure, is 27,050,000,000,000,000, 000. Millikan believes the probable error of his determination of the electron is only about the thousandth part of the concluded value as stated above, and if that estimate is justifiable, the values given above for Avogadro s number, for the mass of the hydrogen atom, and for the number of molecules in a cubic centimeter of gas, may be considered to be correct to the i.ame degree of relative certainty,— that is, each may be considered subject to a probable error of the thousandth part of its own value.