cylinders of equal thickness A B and C D to be joined together at C B, so that the two axis’s E F, and F G lie in one straight line. Let the axis E F be divided into two equal parts at H, and the axis F G into two equal parts at I. Then because the cylinder A B would be upheld at rest by a power applied in H equal to the weight of this cylinder, and the cylinder C D would likewise be upheld by a power applied in I equal to the weight of this cylinder; the whole cylinder A D will be supported by these two powers: but the whole cylinder may likewise be supported by a power applied to K, the middle point of the whole axis E G, provided that power be equal to the weight of the whole cylinder. It is evident therefore, that this power applied in K will produce the same effect, as the two other powers applied in H and I. It is farther to be observed, that H K is equal to half F G, and K I equal to half E F; for E K being equal to half E G, and E H equal to half E F, the remainder H K must be equal to half the remainder F G; so likewise G K being equal to half G E, and G I equal to half G F, the remainder I K must be equal to half the remainder E F. It follows therefore, that H K bears the same proportion to K I, as F G bears to E F. Besides, I believe, my readers will perceive, and it is demonstrated in form by the geometers, that the whole body of the cylinder C D bears the same proportion to the whole body of the cylinder A B, as the axis F G bears to the axis E F[53]. But hence it follows, that in the two powers applied at H and I, the power applied at H bears the same proportion to the power applied at I, as K I bears to K H. Now suppose two strings H L and I M extended upwards, one from the point H and the other from I, and to be laid hold on by two powers, one strong enough to hold up the cylinder A B, and the other of strength sufficient to support the cylinder C D. Here as these two powers uphold the whole cylinder, and therefore produce an effect, equal to what would have been produced by a power applied to the point K of sufficient force to sustain the whole cylinder: it is manifest, that if the cylinder be taken away, the axis only being left, and from the point K a string, as K N, be extended, which shall be drawn down by a power equivalent to the weight of the cylinder, this power shall act against the other two powers, as much as the cylinder acted against them; and consequently these three powers shall be upon a balance, and hold the axis H I fixed between them. But if these three powers preserve a mutual balance, the two powers applied to the strings H L and I M are a balance to each other; the power applied to the string H L bearing the same proportion to the power applied to the string I M, as the distance I K bears to the distance K H. Hence it farther appears, that if an inflexible rod A B (in fig. 15.) be suspended by any point C not in the middle thereof; and if at A the end of the shorter arm be hung a weight, and at B