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Fig. 5.

15. The parallelogram of forces may be illustrated in various ways by means of the apparatus of ssss1. Attach, for example, to the middle hook g 1·5 lb., and place 1 lb. on each of the remaining hooks e, f. Here the three weights are not equal, and symmetry will not enable us, as it did in the previous case, to foresee the condition which the cords will assume; but they will be observed to settle in a definite position, to which they will invariably return if withdrawn from it.

Let o p, o q (ssss1) be the directions of the cords; o p and o q being each of the length which corresponds to 1 lb., while o s corresponds to 1·5 lb. Here, as before, o p and o q together may be considered to counteract o s. But o s could have been counteracted by an equal and opposite force o r. Hence o r may be regarded as the single force equivalent to o p and o q, that is, as their resultant; and thus it is proved experimentally that these forces have a resultant. We can further verify that the resultant is the diagonal of the parallelogram of which the equal forces are the sides. Construct a parallelogram on a piece of cardboard having its four sides equal, and one of the diagonals half as long again as one of the sides. This may be done very easily by first drawing one of the two triangles into which the diagonal divides the parallelogram. The diagonal is to be produced beyond the parallelogram in the direction o s. When the cardboard is placed close against the cords, the two cords will lie in the directions o p, o q, while the produced diagonal will be in the vertical o s. Thus the application of the parallelogram of force is verified.