This was the form which Einstein originally gave to his equation, a very simple derivation of which has been given by Langevin.[76] The essential elements of this derivation will be found in Appendix C. The first careful test of this equation was made on suspensions in liquids by Perrin,[77] who used it for finding the number of molecules in a gram molecule. He obtained the mean value , which, in view of the uncertainties in the measurement of both and , may be considered as proving the correctness of Einstein’s equation within the limits of error of Perrin’s measurements, which differ among themselves by as much as 30 per cent. II. QUANTITATIVE MEASUREMENTS IN GASES Up to 1909 there had been no quantitative work whatever on Brownian movements in gases. Bodoszewski had described them fully and interpreted them correctly in 1881. In 1906 Smoluchowski[78] had [Pg 148] computed how large the mean displacements in air for particles of radius ought to be, and in 1907 Ehrenhaft[79] had recorded displacements of the computed order with particles the sizes of which he made, however, no attempt to measure, so that he knew nothing at all about the resistance factor . There was then nothing essentially quantitative about this work. In March, 1908, De Broglie, in Paris,[80] made the following significant advance. He drew the metallic dust arising from the condensation of the vapors coming from an electric arc or spark between metal electrodes (a phenomenon discovered by Hemsalech and De Watteville[81]) into a glass box and looked down into it through a microscope upon the particles rendered visible by a beam of light passing horizontally through the box and illuminating thus the Brownian particles in the focal plane of the objective. His addition consisted in placing two parallel metal plates in vertical planes, one on either side of the particles, and in noting that upon applying a potential difference to these plates some of the particles moved under the influence of the field toward one plate, some remained at rest, while others moved toward the other plate, thus showing that a part of these particles were positively electrically charged and a part negatively. In this paper he promised a study of the charges on these particles. In May, 1909, in fulfilling this promise[82] he made the first [Pg 149] quantitative study of Brownian movements in gases. The particles used were minute droplets of water condensed upon tobacco smoke. The average rate at which these droplets moved in Broglie’s horizontal electric field was determined. The equation for this motion was The mean was next measured for a great many particles and introduced into Einstein’s equation: