I 



ON THE STRUCTURE OF COVERED WAYS. £43. 



site for the stability of an oblique facipg,, composed of rect- the stability of 

 angular bricks or stones only, both with and without the ^^^^ 

 consideration of the effects of friction. The simplest case 

 that can be proposed is that of two bricks meeting each 

 other, and standing on a perfectly smooth and horizontal 

 plane, the centre of gravity of each' being vertically above 

 the lowest angle (Fig. 10). But if the base be widened, 

 the surfaces supporting the bricks must be rendered oblique. 

 The weight of the brick acts on a lever of vvliich the length 

 is A B (Fig. 11), in turning it round the point B; and this 

 is resisted by the horizontal thrust at C acting on the lever 

 B D, hence the horizontal thrust must be to the v^eight as 

 A B to B D, and making BE— A B, the horizontal thrust 

 at B combined with the \veiglit will act in the direction 

 D E, and the brick Will be supported by a surface B F per- 

 pendicular to D E. Supposing the thickness of the brick 

 inconsiderable, the centre of gravity bein^g in the line B C, 

 taking B G half B H, the line C G will be perpendicular 

 to the surface on which it will rest in equilibrium ; and this The same prin- 

 theorem may be of considerable use in carpentry, for find- ojetotheabut* 

 ing tlie best possible direction for the abutment of a rafter, mentof a raf- 

 If the abutment is in the direction of the end of t]ie4>lock 

 Fig. 12, describe on half the diagonal, A B, the semicircle 

 B C D A; and C B, or D B, v/ill show the position of a 

 line, which being made horizontal, the block will be sup- 

 ported in equilibrium. If the horizontal line cross the cir- 

 cle between C and D the end B will slide downwards, but 

 if between A and J>, or B and C, it would be urged up- 

 wards, but the bearing will be transferred to the lower cor- 

 ner, and the whole will remain at rest: and this will be the 

 case in all positions, when the circle falls wholly within the 

 side of the block, that is, when its thickness is not much 

 less than half its length. Thus two common bricks would Bricks in an 

 remain firm in all elevations if placed with the narrow sides ^|;^clined posi- 

 of their ends lowermost; even without any friction: but the narrow sid# 

 with the wider sides lowermost, they would slide down the '*^°^"^*'^'^' 

 abutments if the distance of their ends were more than about 

 twO; and less than fourteen inches. 



The last additional circumstance which requires to be ex- Effects of frio 

 amlned, with regard to the stability of bricks or stones in *^^^* 

 R 2 oblique 



