The ends of a cord are fastened to two small spring balances; to the centre e of this cord a weight of 4 lbs. is attached. At a and b are pegs from which the balances can be suspended. Let the distances ae, be be each 12", and the distance ab 16". When the cord is thus placed, and the weight allowed to hang freely, each of the cords ea, eb is strained by an amount of force that is shown to be very nearly 3 lbs. by the balances. But the weight of 4 lbs. is the only weight acting; hence it must be equivalent to two forces of very nearly 3 lbs. each along the directions ae and be. Here the two forces to which 4 lbs. is equivalent are each of them less than 4 lbs., though taken together they exceed it.
Fig. 10.
27. But remove the cords from ab and hang them on cd, the length cd being 1' 10", then the forces shown along fc and d are each 5 lbs.; here, therefore, one force of 4 lbs. is equivalent to two forces each of 5 lbs. In the last lecture ([Art. 19]) we saw that one force could balance two greater forces; here we see the analogous case of one force being changed into two greater forces. Further, we learn that the number of pairs of forces into which one force may be decomposed is unlimited, for with every different distance between the pegs different forces will be indicated by the balances.
Whenever the weight is suspended from a point half-way between the balances, the forces along the cords are equal; but by placing the weight nearer one balance than the other, a greater force will be indicated on that balance to which the weight is nearest.
EXPERIMENTAL ILLUSTRATIONS.
Fig. 11.
28. The resolution or decomposition of one force into two forces each greater than itself is capable of being illustrated in a variety of ways, two of which will be here explained. In [Fig. 11] an arrangement for this purpose is shown. A piece of stout twine ab, able to support from 20 lbs. to 30 lbs., is fastened at one end a to a fixed support, and at the other end b to the eye of a wire-strainer. A wire-strainer consists of an iron rod, with an eye at one end and a screw and a nut at the other; it is used for tightening wires in wire fencing; and is employed in this case for the purpose of stretching the cord. This being done, I take a piece of ordinary sewing-thread, which is of course weaker than the stout twine. I tie the thread to the middle of the cord at c, catch the other end in my fingers, and pull; something must break—something has broken: but what has broken? Not the slight thread, it is still whole; it is the cord which has snapped. Now this illustrates the point on which we have been dwelling. The force which I transmitted along the thread was insufficient to break it; the thread transferred the force to the cord, but under such circumstances that the force was greatly magnified, and the consequence was that this magnified force was able to break the cord before the original force could break the thread. We can also see why it was necessary to stretch the cord. In [Fig. 10] the strains along the cords are greater when the cords are attached at c and d than when they are attached at a and b; that is to say, the more the cord is stretched towards a straight line, the greater are the forces into which the applied force is resolved.
29. We give a second example, in illustration of the same principle.