The theory that the particles of all solid bodies may be in a state of continuous vibration and motion, though there may be no means of rendering their motion visible, has not been refuted by deductive reasoning; but, on the other hand, it is in accord with the theory that “motion communicates itself among material bodies, and is never lost; when it appears to be so, it in fact only passes from the moving body into other bodies which are at rest, or are endued with a less velocity, and at length it becomes insensible in consequence of its enormous diffusion. In fact, motion can only be destroyed by motion; resistances and friction disperse it, but do not destroy it.” The laws of statics and dynamics are well established, and are fully described in many admirable works upon mechanical philosophy; so far as the subject of this book is concerned that which is required to be answered is the question. Have the deleterious effects of vibration upon earthwork in various conditions been determined so as to be of practical value? Not by experiment upon a large scale, nor is it probable that they will be; but they have been deduced from experience, reasonable inference, and experiments on a small scale, as has been before mentioned. The effect of vibration is usually more marked in cuttings than in embankments, although it may nearly approach when they are of little depth or height: because a train in a cutting is contained within the area excavated, whereas in an embankment it is without the area deposited. In a cutting vibration commences upon the formation level and the toe of the slopes, the latter the most vulnerable parts and those most strained. In an embankment it proceeds through the formation to the base and the toes of the slopes which are necessarily the most distant. On the other hand, the material in an embankment is generally in a looser and lighter condition, and therefore more inclined to move and to suffer from vibration. It may also be greater upon one side consequent upon the “lurching” of the engine and carriages. Obviously, vibration is increased with the speed and weight of a train; probably a short, heavy train travelling at high speed causes a more deleterious effect than a long heavy train travelling at a slow speed: also the higher an embankment or the deeper a cutting the greater the area of the cross section. Assume a train weighs 100 tons, and the weight of the earth is 112 lbs a cubic foot, or 0·05 of a ton; it might be considered that the effects of vibration would be less as the areas increased. Consider the formation to be 18 feet in width and the slopes 1½ to 1, the respective areas of cross section would be as follows:—