To explain the way in which the stiffness of a rope modifies the operation of a machine, we shall suppose it bent over a wheel and stretched by weights A B, _fig. 182._, at its extremities. The weights A and B being equal, and acting at C and D in opposite ways, balance the wheel. If the weight A receive an addition, it will overcome the resistance of B, and turn the wheel in the direction D E C. Now, for the present, let us suppose that the rope is perfectly inflexible; the wheel and weights will be turned into the position represented in _fig. 183._ The leverage by which A acts will be diminished, and will become O F, having been before O C; and the leverage by which B acts will be increased to O G, having been before O D. But the rope not being inflexible will yield partially to the effects of the weights A and B, and the parts A C and B D will be bent into the forms represented in _fig. 184._ The form of the curvature which the rope on each side of the wheel receives is still such that the descending weight A works with a diminished leverage F O, while the ascending weight resists it with an increased leverage G O. Thus so much of the moving power is lost, by the stiffness of the rope, as is necessary to compensate this disadvantageous change in the power of the machine. CHAP. XX. ON THE STRENGTH OF MATERIALS. (330.) Experimental enquiries into the laws which regulate the strength of solid bodies, or their power to resist forces variously applied to tear or break them, are obstructed by practical difficulties, the nature and extent of which are so discouraging that few have ventured to encounter them at all, and still fewer have had the steadiness to persevere until any result showing a general law has been obtained. These difficulties arise, partly from the great forces which must be applied, but more from the peculiar nature of the objects of those experiments. The end to which such an enquiry must be directed is the development of a _general law_; that is, such a rule as would be rigidly observed if the materials, the strength of which is the object of enquiry, were perfectly uniform in their texture, and subject to no casual inequalities. In proportion as these inequalities are frequent, experiments must be multiplied, that a long average may embrace cases varying in both extremes, so as to eliminate each other’s effects in the final result.