EE. P. 635. A similar remark of the author has al ready been noticed in the article BRIDGE, at the end of the fifth section. In the form in which it is here ex pressed, it becomes still more objectionable : for with whatever part of a circular abutment a rafter equal to .the radius may be brought into contact, it is very plain that its opposite end can never be either 'higher or lower than the original centre of curva ture : and even if the curvature were made twice as great, so that the rafter might be equal to the dia. ' meter •of the circle, it would be necessary that the lower end should slide upwards on the abutment as much as the upper end fell, in order to preserve the contact ; and there would obviously be no force in • the structure capable of producing such a change as this. Any general curvature of the joint must there ' fore be totally useless ; but a judicious workman will snake it somewhat looser below than above, when there is any probability that the rafters will link, taking care however to avoid all bearing too near the surface, lest it should splinter ; and for these reasons combined, making the end a little prominent some what above the middle of the surface which rests on the, abutment. • With this precaution, the direction of the joint between a rafter and a tie beam ought to be made precisely perpendicular to the true thrust of the rafter, determined as already explained (Note CC) e for in the first place, unless we trust either to the friction or to the bearing cannot be more nearly horizontal than this; without danger of the rafters sliding outwards ; and in the second place, if we made it more nearly vertical, we should lessen the vertical pressure on the end of the tie beam, im mediately beyond the joint ; a pressure which gives firmness to the wood, by pressing its fibres more closely together, and. increasing their lateral adhe sion or rather internal friction. If however the tie beam were not deep enough to receive the whole of the rafter so terminated, without too great a reduc tion of its depth, it would be proper to make the joint a little flatter, or more horizontal, and to re strain the end from eliding upwards by an iron strap fixed in a proper direction. We should preserve the end of the rafter as little diminished in breadth as possible, when the tie beam is wide enough to re ceive it ; a moderate thiCkness, left on each side of the mortise in the tie beam, being sufficient to as sist in securing • the connexion of the endo of the beam with the intermediate parts.
FF. P. 635. The doctrine of the initial equality of the resistances to compression and extension, as stated in the article BRIDGE, enables us to demon strate that the transverse strength can never exceed one sixth of that which would be derived from the resistance of all the fibres, cooperating at the dis•••• tance of the whole depth from a fixed fulcrum, and acting with the weaker of the two powers appro. priate to the body. It is true that the results of some direct experiments seem to favour the opinion that the cohesive power is the weaker ; but where the flexure is already considerable, it is probable that this circumstance materially diminishes the primitive power of resisting compression, so that the principles, on which the calculation proceeds, are by no means strictly applicable to the case of a bar so broken.