The electron can be apprehended in the cathodic ray by the study of its essential properties; and J.J. Thomson gave great value to the hypothesis by his measurements. At first he meant to determine the speed of the cathode rays by direct experiment, and by observing, in a revolving mirror, the relative displacement of two bands due to the excitement of two fluorescent screens placed at different distances from the cathode. But he soon perceived that the effect of the fluorescence was not instantaneous, and that the lapse of time might form a great source of error, and he then had recourse to indirect methods. It is possible, by a simple calculation, to estimate the deviations produced on the rays by a magnetic and an electric field respectively as a function of the speed of propagation and of the relation of the charge to the material mass of the electron. The measurement of these deviations will then permit this speed and this relation to be ascertained. Other processes may be used which all give the same two quantities by two suitably chosen measurements. Such are the radius of the curve taken by the trajectory of the pencil in a perpendicular magnetic field and the measure of the fall of potential under which the discharge takes place, or the measure of the total quantity of electricity carried in one second and the measure of the calorific energy which may be given, during the same period, to a thermo-electric junction. The results agree as well as can be expected, having regard to the difficulty of the experiments; the values of the speed agree also with those which Professor Wiechert has obtained by direct measurement. The speed never depends on the nature of the gas contained in the Crookes tube, but varies with the value of the fall of potential at the cathode. It is of the order of one tenth of the speed of light, and it may rise as high as one third. The cathode particle therefore goes about three thousand times faster than the earth in its orbit. The relation is also invariable, even when the substance of which the cathode is formed is changed or one gas is substituted for another. It is, on the average, a thousand times greater than the corresponding relation in electrolysis. As experiment has shown, in all the circumstances where it has been possible to effect measurements, the equality of the charges carried by all corpuscules, ions, atoms, etc., we ought to consider that the charge of the electron is here, again, that of a univalent ion in electrolysis, and therefore that its mass is only a small fraction of that of the atom of hydrogen, viz., of the order of about a thousandth part. This is the same result as that to which we were led by the study of flames.