18. Let Fig. 4 be inverted, and supported at C, as represented in Fig. 6, and a weight hung at each end, so as to balance one another; then the proportion of the strains would remain precisely the same; and it shows how a powerful lever may be framed, and also makes us acquainted with the nature of the strains produced in a solid beam when it performs the office of a lever. The tie A B is in a state of tension, the beams A C and B C are compressed; in a solid beam the same thing takes place, the side next the support is always compressed, and the opposite side is always in a state of tension. It may be observed that when the frame is inverted, as in Fig. 6, and the tie A B is perfectly straight, there is no strain on the piece C E. But if the tie were of the form shown by the dotted line A g B, then the piece g E C would be compressed; and, on the contrary, if the tie were of the form represented by the dotted line A h B, the piece h C would bo in a state of tension, or drawn in the direction of its length. It is the same with a solid beam, as when it becomes bent in any considerable degree new forces are called into action, and it always bends considerably before breaking; consequently, rules that do not include the effect of the forces that are brought into action by the bending of a beam, cannot perfectly agree with experiments. The investigation of the stiffness of beams, which is the most useful to the carpenter, being confined to the first degrees of flexure, is not liable to this objection.

Fig. 6.