Chai*. XXIII. •

CENTERING.

1397

strength sufficient to resist aportion of the weight whichis applied to it, but also to resistanv effect arising from partialmovement, or from imper-fections in the timber or in theworkmanship of their framing.

Timbers, which have greatweights to support, and whichare pressed in the direction oftheir length, should be as manyinches square as they are longin feet, or from a twelfth to atenth of their thickness in length:when drawn in the direction of Rtheir length, from a thirtieth toa twenty-fourth: and bearers,loaded at right angles, or per- Apendicular to their length, froma twenty-fourth to an eighteenth.

A centre for a semicircular archwith a tie-beam may be determinedaccording to the rules before given :for an ellipsis the same rule isapplicable: for an elongated ellipsis,the timbers may be similarly ar-ranged.

In examining the stiffness of cen-tres, the c^ief point for our consider-ation is, where do the arch-stonesfirst begin to press upon them,and what is the pressure exertedby the several voussoirs? We haveseen that stone placed upon an in-clined plane does not begin to slide,unless it slope a little more than30° from the horizontal plane; con-sequently any stone which did not slideupon its bed would not bear at all uponthe centre. Hard stone laid in mortarslides when the angle is beyond 34°, andone of a soft nature will remain firmwhen the angle which its joint makesis as much as 45° ; this point has beentermed the angle of repose, and if wesuppose the pressure to be representedby the radius, the tangent of the anglewill represent the friction; hence if wecall the pressure unity, the friction willbe 0-625, or according to Perronet 0*8.

The next course of voussoirs after theangle of repose will press upon the centre, as will every succeeding course, with an in-creased weight. The relation between the weight of a vcussoir and its pressure upon thecentre in a direction perpendicular to the curve of the centre may be determined by thefollowing equation, W (sin. a — f cos. a) = P ; where W is the weight of the arch-stone,P the pressure upon the centre,/the friction, and a the angle which the plane of the lowerjoint of the arch-stone makes with the horizon.

When the angle which the joint makes with the horizon is —

Fig. 2325.

34°

36

38

40

42

44

46

P =P =P =P =P =P =P =

•04 W•08 W•12 W•17 W•21 W•25 W•29 W

48°

50

52

54

56

58

60

P

P

P

P

P

P

P

•33 W•37 W•40 W■44 W•48 W•52 W•54 W