128 LECTURE XIV. 



their attempts to procure an equilibrium, as have been followed by the 

 most mischievous consequences. Examples of this might be pointed out in 

 the bridges of our own country and the churches of others ; but if we are 

 masters of the true theory of pressure, we shall be able to avoid similar 

 errors, without examining the particular circumstances which have oc- 

 casioned these accidents. (Plate XII. Fig. 165.) 



The principles of equilibrium, which are employed in architecture, are 

 equally applicable to many cases in carpentry ; and where the work is 

 principally calculated to withstand a thrust, there is little difference in 

 the operation of the forces concerned ; but where a tie is introduced, that 

 is, a piece which resists principally by its cohesive strength, the parts often 

 require to be arranged in a different manner. The general principle, that 

 three forces, in order to retain each other in equilibrium, must be propor- 

 tional to the sides of a triangle corresponding to their directions, is suf- 

 ficient for determining the distribution of pressure in almost all cases that 

 can occur. The conclusions which have been drawn from this principle, 

 and from other similar considerations, respecting the strength of materials, 

 will also be of great use in directing us how to determine the best forms for 

 beams, rafters, and timbers of all kinds, and how to arrange and connect 

 them in the best manner with each other. 



The employment of the cohesive strength of materials in carpentry in- 

 troduces a difficulty which scarcely exists in architecture. Two blocks, 

 placed on each other, resist the force of a weight compressing them, as ef- 

 fectually as if they formed but one piece : but they have no sensible cohe- 

 sion to enable them to withstand a force tending to separate them, and if 

 they are required to co-operate by their cohesive strength, some mode of 

 uniting them must be found. For this purpose, it is generally necessary to 

 sacrifice a considerable portion of the strength of the materials employed. 

 The most usual mode is to place the ends of the pieces side by side, first 

 reducing their dimensions, where a regular outline is required ; and to 

 procure a firm adhesion between them by means of external pressure, or to 

 employ the natural adhesion of some parts which are made to project be- 

 yond the rest in each piece, and receive in their interstices the correspond- 

 ing projections of the other piece. 



Where the adhesion is produced by external pressure only, it is of ad- 

 vantage to subdivide the joints into a considerable number of parts, as is 

 usually done in the masts of ships, and to make the junction of any two 

 pieces, following each other in the same line, as distant as possible from 

 any other junction ; for in this manner, the loss of strength may be di- 

 minished almost without limit, provided that the distance between the 

 joints be great enough to afford a firm adhesion to each part. The junction 

 may also be formed by an oblique line ; but the obliquity must be so great 

 that any lateral pressure may increase the stability of the wedge, the length 

 being in a greater proportion to the depth than the pressure to the adhesion 

 that it occasions ; and the pieces must be pressed together very forcibly by 

 means of hoops or bolts. (Plate XIII. Fig. 166... 168.) 



Where the natural adhesion of some projecting parts in each piece is em- 

 ployed, the projections must be sufficiently long to secure their strength, 



