extinguishes them at the end of a longer or shorter time, according to circumstances. [It must not be inferred from this explanation, that the particles of a fluid transmitting an undulation have any tendency to vibrate for ever: on the contrary it has been admitted by the best writers on the theory of sound, that all the motions which constitute it, as considered in a fluid, are completely transitory in their nature, and have no disposition to be repeated after having been once transmitted to a remoter part of the fluid. TR.] Let us now consider in what manner the fluid is agitated by these oscillations of the solid plane. The stratum immediately in contact with it, being urged by the plane, receives from it at each instant the velocity of its motion, and communicates it to the neighbouring stratum, which it forces forwards in its turn, and from which the motion is communicated successively to the other strata of the fluid; but this transmission of the motion is not instantaneous, and it is only at the end of a certain time that it arrives at a determinate [p118] distance from the centre of agitation. This time is the shorter, as the fluid is less dense, and more elastic; that is, composed of particles which possess a greater repulsive force. This being granted, let us assume, in order to facilitate the explanation, the moment when the moveable plane is returned to the initial situation, after having performed two complete oscillations in opposite directions: at this moment, the nascent velocity, which it had at first, is transmitted to a stratum of the fluid removed from the centre of agitation by a distance which we may represent by _d_. Immediately afterwards, the velocity of the moveable plane, which has a little augmented, has been communicated to the stratum in contact with it: “hence _it_ has passed successively through all the following strata;” and at the moment when the first agitation arrives at the stratum of which the distance is _d_, the second has arrived at the stratum immediately before it. Continuing thus to divide, in our imagination, the duration of the two oscillations of the moveable plane into an infinity of small intervals of time, and the fluid comprehended in the length _d_, into an equal number of infinitely thin strata, it is easy to perceive, by the same reasoning, that the different velocities of the moveable plane, at each of these instants, are now distributed among the corresponding strata; and that thus, for example, the velocity which the plane possessed at the middle of the first oscillations in the direction of the motion, must have arrived, at the instant in question, at the distance 3/4 _d_: so that it is the stratum at this distance which possesses at the moment the greatest direct velocity; and in the same manner when the plane arrived at the limit of its first direct oscillation, its velocity was extinguished, and the same absence of motion will be found at the distance 1/2 _d_.