If we preserve the parts above mentioned, the instrument will possess the property of having vibrations of a constant amplitude if sufficient energy be kept up in the pile. In fact, when the amplitude is sufficiently great to cause the style, s, to touch the plate, I, it will be seen that at such a moment the current no longer passes through the electromagnet, and the vibration is no longer maintained. The amplitude cannot exceed an extent which shall permit the style, s, to touch I. Under such conditions, the duration of the vibrations remains exactly constant, as does also the vibratory intensity of the entire instrument. The measurement of time, then, by an instrument of this kind is, indeed, as perfect as it could well be. This complication in the arrangement of the apparatus has no importance as regards those tuning forks the number of whose vibrations exceeds a hundred per second, for in such a case these are given an amplitude of a few millimeters only; but it would be of importance with regard to instruments whose number of vibrations is very small, and to which it might be desirable to give great amplitude; for then, as I have long ago shown, the duration of the oscillation would depend a little on the amplitude, but a very little, it is true. I shall not refer now to the applications of these instruments in chronography, but will rather point out first the applications in which they are destined to produce an effective power. For this purpose it is necessary to make them pretty massive. The number of the vibrations depends upon such massiveness, and it is necessity to know the relation which exists between these two quantities in order to be able to construct an instrument under determinate conditions. I made in former years such a research with regard to tuning forks of prismatic form, that is to say, of a constant rectangular section continuing even into the bent portion where the parallel branches are united by a semicylinder, at the middle of which is the wrought iron rod as well as the branches. The _thickness_ of the instrument is the dimension parallel to the vibrations; its _width_ is the dimension which is perpendicular to them, and its _length_ is reckoned from the extremity of the branches up to the middle of the curved portion. It is found that the number of vibrations is independent of the width, proportional to the thickness, and very nearly inverse ratio of the square of the length, provided the latter exceeds ten centimeters. If we represent the length by l, the thickness by e, and the number of vibrations by n, we shall have the following formula: n = k x ( e / l squared ) in which k is a constant quantity whose value depends upon the nature of the metal of which the tuning fork is made. This constant varies very little from steel to malleable cast iron, and it may be taken as equal to 818270.