From these two equations was eliminated and obtained in terms of . Introducing Perrin’s value of , De Broglie obtained from one series of measurements ; from another series on larger particles he got a mean value several times larger—a result which he interpreted as indicating multiple charges on the larger particles. Although these results represent merely mean values for many drops which are not necessarily all alike, either in radius or charge, yet they may be considered as the first experimental evidence that Einstein’s equation holds approximately, in gases, and they are the more significant because nothing has to be assumed about the size of the particles, if they are all alike in charge and radius, or about the validity of Stokes’s Law in gases, the -factor being eliminated. [Pg 150] The development of the oil-drop method made it possible to subject the Brownian-movement theory to a more accurate and convincing experimental test than had heretofore been attainable, and that for the following reasons: 1. It made it possible to hold, with the aid of the vertical electrical field, one particular particle under observation for hours at a time and to measure as many displacements as desired on it alone instead of assuming the identity of a great number of particles, as had been done in the case of suspensions in liquids and in De Broglie’s experiments in gases. 2. Liquids are very much less suited than are gases to convincing tests of any kinetic hypothesis, for the reason that prior to Brownian-movement work we had no satisfactory kinetic theory of liquids at all. 3. The absolute amounts of the displacements of a given particle in air are 8 times greater and in hydrogen 15 times greater than in water. 4. By reducing the pressure to low values the displacements can easily be made from 50 to 200 times greater in gases than in liquids. 5. The measurements can be made independently of the most troublesome and uncertain factor involved in Brownian-movement work in liquids, namely, the factor , which contains the radius of the particle and the law governing its motion through the liquid. Accordingly, there was begun in the Ryerson Laboratory, in 1910, a series of very careful experiments in Brownian movements in gases. Svedberg,[83] in reviewing this subject in 1913, considers this “the only exact investigation of quantitative Brownian movements in gases.” A brief summary of the method and results was published by the author.[84] A full account was published by Mr. Harvey Fletcher in [Pg 151] May, 1911,[85] and further work on the variation of Brownian movements with pressure was presented by the author the year following.[86] The essential contribution of this work as regards method consisted in the two following particulars: 1. By combining the characteristic and fully tested equation of the oil-drop method, namely, with the Einstein Brownian-movement equation, namely,