Elements or Carpentry

The theory (so to term it) of Carpentry is found-. ed on two distinct portions of mechanical sciences, i namely, a knowledge of the strains to which fratu-' ings of timber are exposed, and a knowledge of their relative strength.

We shall therefore attempt to bring into one point of view the propositions of mechanical science that are more immediately applicable to the art of Carpentry, and are to be found in various articles of our work, particularly Rooe and STRENGTH OF MATERIALS. From these propositions we hope to deduce such principles as shall enable an attentive reader to comprehend distinctly what is to be aimed at in framing timber, and how to attain this object with certainty : and we shall illustrate and confirm our principles by examples of pieces of Carpentry which are acknowledged to be excellent in their kind._ The most important proposition of general me chanics to the carpenter is that which exhibits the composition and resolution of forces ; and we beg, our practical readers to endeavour to form very dis tinct conceptions of it, and to make it very familiar to their mind. When accommodated to their chief purposes, it may be thus expressed: 1. If a body, or any part of a body, be at once pressed in the two directions AB. AC (fig. I. Plate XLVIII.), and if the intensity or force of those pressures be in the proportion of these two lines, the body is affected in the same manner as if it were pressed by a single force acting in the direc tion AD, which is the diagonal of the parallelo gram ABDC formed by the two lines, and whose intensity has the same proportion to the intensi ty of each of the other two that AD has to AB or AC.

Such of our renders as have studied the laws of motion, know that this is fully demonstrated. Such as wish for a very accurate view of this pro position, will do well to read the demonstration given by D. Bernoulli, in the first volume of the Comment. Petropol., and the improvement of this demonstration by D'Alembert in his Opuscides and in the Comment. Taurinens. The practi tioner in Carpentry will get more useful confi dence in the doctrine, if he will shut his book, and verify the theoretical demonstrations by actual ex periments. They are remarkably easy and convinc-1 ing. Therefore it is our request that the artist, who is not so habitually acquainted with the subject, do not proceed further till he has made it quite familiar to his thoughts. Nothing is so conducive to this

•as the votaid s since this- only re. quirts thetrifiing expence of two small-pulleys and few yards of whipcord, we -hope that none of our -- practical omit-it: They willthank us for this injunction.

2. Let the threads Ad,

AN, and A-Ec (fig. 2.), -have the weights d, and c,•appended to-them, and two-of the threadirbe- laid over the pulleys F and -E. By this apparatus the knot A will be drawn in the directions AB, AC, and AK, •if the sum of the weights•1i and c be greater than the-single-weight d, the assemblage will of itself settle hr a certain deter mined fermi if -you pull the knot A out of its place, it will always return to it again, and will -rest in no other position. For 'example, If the • three weights are equal, the threads will always make equal angles, of 120 degrees each, round theknot. If one of the weights-b• three pounds, another four, and- the third five, the angle opposite to the -stretched by the pounds will always be'square, &c. When the knot '-A is thus in- erilibrio, we must infer,•that the ac tion• of theweight 'd, in the direction Ad, is in di -mot' opposition to the 'combined action of b in the thieetion AB, and of 4 in the direction AC. 'There fore,ritwe produce dA to artypoint•D,•and take AD to represent the -magnitude of the force, or pressure by' the'weight d, thepressures exerted on A by the weights -b and the directions AB, AC, are in equiealent to a pressure•acting• in the •n tonio!) AD;' whose intensity' we have represented by AD. -If •we-now Measure off by se scale AF aed AR, the lines AB and- AC, hawing the same propor tions to •AD 'that the weights 6 and c have- to the weight- di-andif we draw DB and we•shall find DC to be equal and parallel - to AB, and 113B•equal and parallel' to AC 1- so' that AD is•the diagonal • of w paridlelogram ABDC. 'We shall find thivedways to be the case, whatever Are the weights made use of; only we must* take -care that the weight which we came to act without the intervention' of a pulley be less than the'sum -of the' other two : if any one of the weights exceeds the sum of the other two, it prevail, and drag them along with it.