it was possible to obtain the product without any reference to the size of the particle or the resistance of the medium to its motion. This quantity could then be compared with the same product obtained with great precision from electrolysis. The experimental procedure consists in balancing a given droplet and measuring, as in any Brownian-movement work, the quantity , then unbalancing it and measuring , and (; the combination of (24) and (25) then gives Since it is awkward to square each displacement before averaging, it is preferable to modify by substituting from the Maxwell distribution law, which holds for Brownian displacements as well as [Pg 152] for molecular velocities, the relation We obtain thus or The possibility of thus eliminating the size of the particle and with it the resistance of the medium to its motion can be seen at once from the simple consideration that so long as we are dealing with one and the same particle the ratio between the force acting and the velocity produced by it must be the same, whether the acting force is due to gravity or an electrical held, as in the oil-drop experiments, or to molecular impacts as in Brownian-movement work. De Broglie might have made such an elimination and calculation of in his work, had his Brownian displacements and mobilities in electric fields been made on one and the same particle, but when the two sets of measurements are made on different particles, such elimination would involve the very uncertain assumption of identity of the particles in both charge and size. Although De Broglie did actually make this assumption, he did not treat his data in the manner indicated, and the first publication of this method of measuring as well as the first actual determination was made in the papers mentioned above. [Pg 153] Some time later E. Weiss reported similar work to the Vienna Academy.[87] 2. Although it is possible to make the test of in just the method described and although it was so made in the case of one or two drops, Mr. Fletcher worked out a more convenient method, which involves expressing the displacements in terms of the fluctuations in the time required by the particle to fall a given distance and thus dispenses with the necessity of balancing the drop at all. I shall present another derivation which is very simple and yet of unquestionable validity.