^246 ON THE STRUCTURE OF COVERED WATS. 



of blocks in which is almost always the case with the materials common- 



poi,i ions, j^, employed, two pairs of equal blocks meeting each other 



in this manner will be secure from sliding in every possible 



When more, position. If there are mqre than two blocks on each side, 



or if the lower blocks are larger than the upper one, the 



force tending tp support thp lower ones, which is deriv«p<l 



from the pressure of the upper one, is twice the impiediate 



friction occasioned by its weight, since the same pressure 



acts in two different places, and as long as this exceeds the 



difference between the friction and the relative weight of the 



lower block or blocks, they will be secure from sliding along 



Friction of ^|jg abutments. For example, in the case of comrrion bricks 



common bricks "' " . . . 



half the pres- pr stone, the friftion is at least half of the pressure ; for if 



sure. a brick he placed with the short side of its end downwards 



on another which is gi:adui|lly raisecj, it will full over before 

 it slides; we may therefore safely estimate the friction as 

 equal to half tlie pressure, the tangent of the angle ABC 

 heing '5, its sine •446, and its cosine '892. Now if the 

 18 bricks miglit whole aperture be supposed equilateral, the sine of 1) B A 

 cleof 60^"^" will be *5, and its cosine '866; and the sine of D B C near- 

 ly '06', and the friction A C will be to the weight B D ^s 

 •45 to 1, and to E B as () to IQ, so that 18 bricks on each 

 side might be secured from sliding by .the double effect pf 

 the upper pair. 

 Two modes in There are however two other ways in which such a struc- 

 which >!i y ture might give way: the lower portion revolving on its 

 w*y, lowest point, and the higher either moving with it towards 



the opposite side, or sliding upwards in a contrary direction: 

 and in order that the pile may stand, it is obvious that it 

 must possess sufficient stability in both these respects. 

 When there aie only two equal blocks on each side, it is 

 • easy to determine whether or no their breadth is sufficient to 

 prevent their both falling inwards, by^describing round the 

 triangle ABC (Fig. 10), a segment of a circle, making 

 D E vertical, and joining A E, which mu?>t either coincide 

 with the diagonal A F, or be below it. If there are more 

 ^han two pieces on each side, in order to determine the sta- 

 bility of any joint A B (Fig. 17), let A C and D E be ho- 

 rizontal, and F E vertical, draw D B C^ make E H zn E G, 

 and II 1 horizontal and equal to half A C ; tlien if F I fall 



belovv 



