As a general rule, therefore, to find the common velocity after impact. Multiply the weights by the previous velocities and take their sum if the bodies move in the same direction, and their difference if they move in opposite directions, and divide the one or the other by the sum of their weights. The greatest will be the velocity after impact. (67.) The examples of the equality of action and reaction in the collision of bodies may be exhibited experimentally by a very simple apparatus. Let A, _fig. 6._, and B be two balls of soft clay, or any other substance which is inelastic, or nearly so, and let these be suspended from C by equal strings, so that they may be in contact; and let a graduated arc, of which the centre is C, be placed so that the balls may oscillate over it. One of the balls being moved from its place of rest along the arc, and allowed to descend upon the other through a certain number of degrees, will strike the other with a velocity corresponding to that number of degrees, and both balls will then move together with a velocity which may be estimated by the number of degrees of the arc through which they rise. (68.) In all these cases in which we have explained the law of “action and reaction,” the transfer of motion from one body to the other has been made by impact or collision. The phenomenon has been selected only because it is the most ordinary way in which bodies are seen to affect each other. The law is, however, universal, and will be fulfilled in whatever manner the bodies may affect each other. Thus A may be connected with B by a flexible string, which, at the commencement of A’s motion, is slack. Until the string becomes stretched, that is, until A’s distance from B becomes equal to the length of the string, A will continue to have all the motion first impressed upon it. But when the string is stretched, a part of that motion is transferred to B, which is then drawn after A; and whatever motion B in this way receives, A must lose. All that has been observed of the effect of motion transferred by impact will be equally applicable in this case. Again, if B, _fig. 4._, be a magnet moving in the direction B C with a certain quantity of motion, and while it is so moving a mass of iron be placed at rest at A, the attraction of the magnet will draw the iron after it towards C, and will thus communicate to the iron a certain quantity of motion in the direction of C. All the motion thus communicated to the iron A must be lost by the magnet B.