244" OW THE STRUCTURE OF COVERED WAYS, 



t'f ,<'>.0':ivv'j ,,',iiyih\\^ :■■■ -i"^.''; • . iii'.i .i,'-. "tJifl 'J/jl.Si' 



oblique aitiiations, is the effect of friction or adliesion. Tnis 

 force may be corL5i(^eied, ii) all practical .inyefefigaiions, as 

 proportional to tlie mutual pressure of the surfaces concern- 

 Convenient ed; arid the mo^t convenient way of estimatirisr its mai^ni- 

 niode of mea- I -^ .. : . .. ,: . .^ ; ., v i ' ' 'i 



suring it. tude is to incline the surbices to the horizon, until they begin 



to sl'd^ on each other. The angle at which this happens 

 will be always very nearly il* pot exactly the same for sur- 

 fages of the same kind, and it may with propriety be called 

 Angle of re- the angle of repose : and it is obvious, that any other force 

 poic. acting on the surface in the same angle as that in which the 



^orce of gravity acts in this inst;ance, will be completely ob- 

 yiated by the resistance of the surface : and the friction will 

 be to the pressure as the tangent of the angle of repose to 

 the radius. If therefore the surface A B (Fig. 13) is cal- 

 culated to resist the presswe of the block A without frictioti, 

 by making the angles B A C and BAD each equal to the 

 angle of repose, we may determine the greatest and least 

 inclination which will be sufficient for retaining the block 

 by the assistance of the friction or .idhesion ; the stability 

 being greatest of all in the original situation A B. In the 

 same manner the rectangular block A B, (Fig. 14) will «be 

 supported by its abutment a$ long as the horizontal line B C 

 crosses the semicircle within the line AD, DAE being 

 equal to the angle of repose. 

 Caseofafacing When two blocks of equal dimensions form an overhang- 

 on elchsidV *"o facing on each side of a triangular aperture, (Fig. 15) 

 the upper one is in the same predicament as if it rested sim- 

 ply on a fixed abutment; the lower oUe is retained in its 

 ^situation by the force of friction only. If ABC be the 

 ^aiigle of repose, the direction of the force supporting each 

 of the upper blocks will be B C ; and if the vertical line 

 B D represent tlie weight of the block A, B C will be the 

 resisting force, and AC the friction, which Counteracts the 

 tendency of the block B to descend along the abutment. 

 Worst possible and this force is represented by E B'. In order therefore to 

 position. flj^^ the postion in which the block B will most readily slide 



away, we must make the proportion of E B to AC a max- 

 imum ; and this will happen, when the mean of ^le angles 

 T> B A and D B C is equal to half a right angle. For the 



