Incident to the discharge of all fire-arms, great and small, is a phenomenon of which we have to speak, because it is one which in the mounting of heavy ordnance especially has to be taken into account. And as it also illustrates in a very direct way one of the most general laws of nature, while people often have very vague and erroneous ideas of its cause and operation, it deserves the reader’s attention. In gunnery it is called the _recoil_, and is familiar to anyone who has ever fired a pistol, fowling-piece, or rifle, in the kick backwards felt at the moment of the discharge. This law is in operation whenever the condition of a body in respect to its rest or motion is changing. That is, whenever a body at rest has motion given to, or if when already moving it is made to go faster or slower, or to stop, or when the direction of the motion is changed from that in a straight line. Now although these changes or actions are frequently occurring before our eyes, the operation in them of Newton’s third law of motion does not generally present itself to common observation. This third law was stated by Sir Isaac Newton thus:—“To every action there is always an opposite and equal reaction.” Now the expanding gases due to the gunpowder explosion press the bullet forwards and the barrel (with its attachments) backwards, with the same pressure in both cases, but at the end of the bullet’s passage along the bore the same velocity is not imparted to the two bodies, because the same pressure acting for the same time on bodies of unequal _mass_ always produces velocities that are inversely proportional to the _masses_. The reader should try to acquire this conception of _mass_, remarking that it is a something quite distinct from that of _weight_. A given lump of metal, for instance, would have exactly the same _mass_ in any part of the universe, whereas its weight would depend upon its position; as, for instance, at the distance from the earth of the moon’s orbit, it would _weigh_ only as 1/3600th part of its weight at the earth’s surface, and if it could be carried to the very centre of the earth it would there have no weight at all. Though the lump of metal will have different weights at different parts of the earth’s surface, it has been found (by experiment) that the weights of bodies at any one place are proportional to their masses. Therefore the same numbers that express the weights of bodies might also express their masses; but for certain good reasons these quantities are referred to different units. In England a piece of metal weighing 32 lbs. under standard conditions is said to have mass = 1; and so on. As with the _same pressure acting for the same time_, the velocities imparted are inversely proportional to the masses, it follows that the number expressing the velocity multiplied by that representing the mass in each such case of action and reaction will give the same product, or in other