a double floor, taken in a transverse direction to the binding joists. A, A, exhibit sections of the binding joists; DE, part of a bridging joist; M, N, ceiling joists; and EF, EF, parts of ceiling joists. It may be readily seen that the tenons of the binding joists are made in the same manner as described in the preceding design for a girder and joists.

Fig. 6 exhibits a method whereby a piece of timber may be framed between two parallel pieces, which are supposed immoveable. In order to make close work, the extremity of the tenon, and the bottom of the mortise at one end, are made to assume the arc of a circle, with its centre in one edge of the mortise; and the extremity of the tenon, and the bottom of the mortise at the other end, in a concentric arc from the same centre. The mortise at this end being much longer than the breadth of the tenon, there will be a large part of the mortise still open, which may be afterwards filled up. Instead of the bottom of the mortise, in this instance, being formed in the arc of a circle, it may be cut parallel to the edge, at the deepest part, as it will not impede the transverse piece going into its place. In forming the mortise and tenon, at the end where the centre is placed, there is no necessity for the mortise and tenon to form an entire quadrant, but the bottom may be parallel, and the edge only which is opposite the centre made circular. This useful mode of framing is much used in ceiling, joisting for double floors, &c. and the long mortises cut in this manner are called chase mortises.

If it be required to notch one piece of timber to another, or to connect the two, so as they may form one right angle, with an equal degree of strength in each, then each piece should be notched half through, and afterwards the two should be nailed o pinned together. Fig. 7 represents two pieces of timber framed after this manner; and fig. 8 shows the socket of one piece, which receives the neck or substance of

the other.

A piece of timber may be joined at right angles to another in the manner of fig. 21, which is a longitudinal section in the direction of the fibres of both pieces. A mortise is made in the one piece to correspond with its breadth, which is to form the perpendicular; the edge of the tenon is then cut with a dove-tail notch, so that the piece may be at right angles with the other, and a wedge or key is next driven from the other edge of the tenon, which forces it quite close. When the timber of which the piece containing the dovetail may be formed, is not quite dry, the tenon will shrink in proportion to its breadth, by which circumstance the perpendicular piece will become liable to be drawn out from the other to a certain degree. This defect is remedied in the section exhibited at fig. 22, where, instead of the edge of the tenon being cut in the form of a dovetail, a notch is made in it. Fig. 23, shows another view of the perpendicular piece with the wedge.

Figs. 24, 25, 26, exhibit the methods used for the meeting of a brace and straining piece under a truss beam. Of these methods the first is the best.

Fig. 27 exhibits a method of securing a collar beam at one extremity, and preventing it from being pulled away at the joint, by a bolt made to pass through the rafter, at the angle formed by their meeting.

Fig. 28 represents one form of the heel of a principal rafter, with the socket cut in the end of the tie beam to receive it; this method, however, is defective in strength, because the small part cut across the fibres of the beam being too near its extremity, it will become liable to be forced away, in consequence of its having to sustain the entire force of the rafter.

Fig. 29 is intended to remedy this defect, by formning two abutments equally deep into the beam; a mode which not only produces a resistance to the rafter, fully equal to that in the former method, but adds to it the strength of the intermediate_part contained between the two abutments. The intermediate part in this mode, from having the fibres cut across, is easily split away.

Another mode of forming a double resistance, is shown at fig. 30. In this ngure it will be ob served that the heels of the rafter and the soel of are cut parallel to the fibres of the tie beam, the end of the rafter forming one abutment, and tenon the other, which has the effect of removing it farther from the extremity.

Fig. 31 represents the best mode of forming a resistance on the heel of the rafter and socket at the extremity of the beam. The abutment, by this plan, is brought nearer to the inner part of

The strutting of a floor is of great use when the joists are thin and deep, in preventing their buckling pressure; but for this purpose there is another method called keying, which consists in framing short pieces of timber between the joists; but as the mortises which receive the tenons weaken the joists, and as the keys cannot be in a straight line, and since this method adds' considerably to the expense, this practice is not so eligible as that of strutting. Single joist flooring may be used to any extent not exceeding sixteen feet; but when it is desirable to preserve the ceiling free from cracks, and to prevent the passage of sound, a framed floor is necessary.

The ceiling joists in double floors are generally put in after the building is up; if, therefore, they are fixed by means of mortises in the sides of the binding joists, to relieve tenons on their ends, the space between every other two mortises must be grooved out alternately upon the opposite sides of the two adjacent binding posts; by this means the ceiling posts may easily be put in their places by inserting the tenon in each ceiling joist in the mortises at one end, and sliding the tenon on the other end along the groove in the arc of a circle, until the ceiling joist come at a right angle with the binding joist. The long mortises or grooves in the sides of the binding joists are called chace mortises or pulley mortises. The ceiling joists may be thirteen or fourteen inches apart; the thickness of the bridging joists and ceiling joists need not be greater than what is sufficient to resist splitting by the driving in of the nails in order to fix them. It has been found by experience, that two inches is a sufficient thickness for the purpose.

In double framed floors, the distance of bridging joists in the clear ought to be about twelve inches, and should never exceed thirteen. It is a good practice to plane the upper edges of the bridging joists straight, because, when the boarding is laid, the faces for walking upon will be more regular than if the boards had been laid down upon the edges of the bridging joists when rough from the saw.

We have now to consider the subject of the strength of timber, one of the most important in the art of carpentry; since, without a due regard to it, no erections can possibly be made, but what depend solely on chance for their success. Yet, of all the branches of the science of architecture, none, perhaps, has received sc little elucidation from the investigations of the learned. Nor will the cause of this seeming neglect appear problematical, when it is considered that there is none requiring such vast and expensive apparatus, more close and continued application, or more judgment and practical experience to obtain any decisive conclusions. Accordingly, in our own country, experiments have never been made on a scale sufficiently large to be of much importance as a guide in practice; and we owe to the liberality of the ancient monarchy of France nearly all the knowledge we possess on this most interesting subject. Messrs. Buffon and Du Hamel, about the middle of the last century, were directed by that government to make a variety of experiments; they were furnished with ample funds and apparatus, and all the forests of

France were at their disposal for subjects. The reports of M. de Buffon may be found in the Memoirs of the French Academy for the years 1740, 1741, 1742, and 1760; and those of M. Du Hamel in his work, Sur l'Exploitation des Arbres, and sur le Conservation et la Transportation de Bois. The essential parts of them we shall notice presently.

The strength of all bodies consists in the cohesion of their particles, and as this cohesion admits of many modifications, in its various appearances of hardness, elasticity, and softness, the texture of bodies must be taken into account before we can arrive at mathematical demonstrations on the subject: and the experiments recorded, have been, for the reasons before assigned, so few, limited, and doubtful, as to produce no principles on which to ground our future calculations.

A general idea of the force of the attraction of cohesion may be obtained from the instance of a lever, in which, by the compression of one end, a strain is occasioned in a distant part. In order to understand its nature with precision it will be necessary to review such general laws as are immediately necessary as a guide in mechanical operations.

First. We have presumptive evidence to prove that all bodies are elastic in a certain degree, that is, when their form or bulk is changed by certain moderate compressions, it requires the continuance of the force producing the change, in order to continue the body in its altered state, and, when the compressing force is removed, the body recovers its original form and tension.

Secondly. That whatever may be the situation of the particles composing a body, with respect to each other when in a state of quiescence, they are kept in their respective places by the balance of opposing forces.

Thirdly. It is an established fact, that every body has some degree of compressibility, as well as of dilatability; and when the changes produced in its dimensions are so moderate, that the body completely recovers its original form on the cessation of the changing force, the extensions or compressions bear a sensible proportion to the extending or compressing forces; and, therefore, the connecting forces are proportioned to the distance, at which the particles are diverted, or separated, from their usual state of quiescence.

Fourthly. It is universally observable, that when the dilatations have proceeded to a certain length, a less addition of force is afterwards sufficient to increase the dilatation in the same degree. For instance, when a pillar of wood is overloaded, it swells out, and small crevices appear in the direction of the fibres. After this, it will not bear half of the previous load.

Fifthly. That the forces connecting the particles composing tangible or solid bodies, are altered by a variation of distance, not only in degree, but also in kind.

Having now enumerated the principal modes, in which cohesion confers strength on solid bodies, we proceed to consider the strains to which this strength may be opposed.

These strains are three in number, viz.—
First. A piece of matter may be torn asunder:

-to this strain king-posts, tie-beams, stretchers, &c. &c. are liable.

Second. It may be crushed :—as in the case of pillars, truss beams, &c. &c.

Third. It may be broken across, as may happen to a joist or lever of any kind.

With respect to the first strain, it may be observed, that it is the simplest of all strains, and that the others are but modifications of it; it being directly opposed to the force of cohesion, without being influenced, except in a slight degree, in its action, by any particular circumstances. When a body of considerable length, such as a rope, or a rod of wood, or metal, has any force exerted on one of its ends, it will naturally be resisted by the other, from the effect or operation of cohesion. When this body is fastened at one end, we may conceive all its parts to be in a similar state of tension, since all experiments on natural bodies concur to prove, that the forces which connect their particles in any way whatever, are equal and opposite.

If, therefore, the cohesion be equal, that is, if the body be of a homogeneous texture, the particles will be changed from their natural state, and separated to equal distances. Of course the connecting powers of cohesion thus excited and exerted, in opposition to the straining force, are also equal. This force, therefore, may be so increased as gradually to separate the particles of the body more and more from each other: and, in a relative proportion, the power of cohesion will be weakened, till a fracture ensues, and the body itself is quickly broken in all its parts. If the external force be only sufficient to produce such a curvature on the body that when it is withdrawn it will recover its former state, it is clear that this strain may be repeated as often as is required, and that the body which has withstood it once will always withstand it. should be borne in mind, however, that we here speak only of occasional strains, for it is a fact no less well known than important, that a body will not suffer a permament strain of more than one half of what it will bear when first imposed

It

In stretching and breaking fibrous bodies, though the visible extension is frequently very considerable, it does not solely arise from the increasing the distance of the particles composing the cohering fibre, but is chiefly occasioned by drawing the crooked fibre straight. In this respect a great diversity prevails, as well as in the powers required to withstand a strain. In some woods, such as fir, the fibres on which the strength most depends, are very straight, and woods of this nature, it should be remarked, are generally very elastic, and break abruptly when overstrained; others, as oak, have their resisting fibres very crooked, and stretch very sensibly when subjected to a strain. These kinds of woods do not break so suddenly, but exhibit visible signs of a derangement of texture.

With respect to the absolute force, it seems hardly necessary to mention, that the trunk of a tree is formed of numerous longitudinal fibres, which, by annual growth, are formed in rings, or nearly in the form of concentric circles. These, by their united force of cohesion, resist separation, and the strength, therefore, is proportioned

The following are a few useful facts concerning the tenacity of wood: It is generally agreed that the heart of a tree is the weakest part, and that this weakness increases with the age of the tree. The fact is denied by Buffon, who, however, does not prove his assertion.

The outer fibres called the blea, are also weaker than the rest.

The wood is stronger in the middle of the trunk than at the root, or the springing of the branches, and the wood of the branches is weaker than that of the trunk.

The wood on the northern side of European trees is weaker than the rest, and that on the southern is the strongest.

The heart of a tree is never in its centre, but always nearer the north side, and the annual plates are consequently thinner on that side. The tree is strongest where the annual plates are thickest; the reason of which is, that the trachea or air-vessels, which form the separation between these plates, are weaker than the simple ligneous fibres.

From the experiments of Muschenbroek we have some useful information as to the absolute strength of different woods. They were all formed into convenient slips, and part of the slip was cut away to a parallolepiped, one-fifth of an inch square, and therefore the twenty-fifth part of a square inch in section. The following is the table in which the number of pounds denotes the absolute strength of a square inch :-

It should be observed that the writer assigns a much greater tenacity to these woods than othe's who have treated on the subject; the reason for the great difference however is, that he gives the weight that will just tear them asunder; while others, as Mr. Emerson, give that which may be suspended to them with safety.

Muschenbroek gives a very minute detail of his experiments on the ash and walnut, in which he states the weights required to tear asunder slips taken from the four sides of these trees, and, on each side, in a regular progression from the