Lastly, employ all the three pieces, F B, A H, D c, with the same wire attached as before. There can be no doubt but that the weight which breaks all the four wires must be = a A H, or twice A a.
The reader cannot but see that the wires perform the very same office with the fibres of an entire beam, L ti, held fast in the four holes, D B c, and E, of some upright posts.
In the experiments for verifying this, by breaking slender bars of fine deal, we get complete demonstration, by measur ing the curvatures produced in the parts of the beam thus held down, and comparing them with the curvature of a beam simply laid on the props B and c; and there are many curious inferences to be made from these observations.
We may observe, by the way, that we learn from this case, that purlins are able to carry twice the load when notched into the rafters, that they carry when mortised into them, which is the most usual manner of framing them. So would the binding joists of floors; bat this would double the thick ness of the flooring. But this method should be followed in every possible case, such as bres-summers, lintels over several pillars. &c. These should never be cut off and mortised into the sides of every upright ; numberless cases will occur which show the importance of the maxim.
We here remark, that the proportion of the spaces B C NI, or B c and L B, has a very sensible effect on the strength of the beam a e ; but we have not yet satisfied our minds as to the rationale of this effect. It is undoubtedly connected with the serpentine form of the curve, of the beam before fracture. This should be attended to in the construction of the springs of carriages. Thee are frequently supported at a middle point (and it is an excellent practice), and there is a certain proportion which will give the easiest motion to the body of the carriage. We also think that it is connected with that deviation from the best theory observable in Buffon's experiments on various lengths of the same scantling. The three of the beamgdiminished much more than in the inverse proportion of their lengths.
We have seen that it depends entirely on the position of the pieces in respect of their points of ultimate support, and of the direction of the external force which produces the strains, whether any particular piece is in a state of extension or of compression. The knowledge of this circumstance may
greatly influence us in the choice of the construction. In many cases we may substitute slender iron rods for massive beams, when the piece is to act the part of a tic. But we must not invert this disposition ; for when a piece of timber acts as a strut, and is in a state of compression, it is next to certain that it is not equally compressible in its opposite sides through the whole length of the piece, and that the coin ' pressing force on the abutting joint is not acting in the most equable manner all over the joint. A very trifling inequality in either of these circumstances (especially in the first) will compress the beam more on one side than on the other. This cannot be without the beam's bending, and beeoming concave on that side on which it is most compressed. When this happens, the frame is in danger of being crushed, and soon going to ruin. It is therefore indispensably necessary to make use of beams in all cases where struts are required of considerable length, rather than of metal rods of slender dimensions, unless in situations where we can effectually pre vent their bending, as in trussing a girder internally, where a cast-iron strut may be firmly cased in it, so as not to bend in the smallest degree. In eases where the pressures are enormous, as in the very oblique struts of a. centre, or arch frame, we must be particularly cautious to do nothing which can facilitate the compression of either side. No mortises should be cut near to one side ; no lateral pressures, oven the slightest, should be allowed to touch it. We have seen a pillar of fir, inches long and 1 in section, when loaded with three tons, snap in an instant when pressed on one side by 16 pounds, while another bore 41- tons without hurt, because it was enclosed (loosely) in a stout pipe of iron.