ON THE STRUCTURE OF COVERED WAYS. £47" 



below B, tlie structure will not i^ive way at the joint A B. 

 The demonstration may easily be deduced from the princi- Two modes ia 

 pie of the equality of the horizontal thrusts in the case of'^'^^'^^^^^^y 

 - an equilibrium : and it may be shown, that, if the aperture way. 

 be equilateral, 15 common .bricks on each side will stand, 

 but 16 will give way at the sixth joint from the summit. 

 The stability is howeyer less considerable with respect to the 

 second mode of failure, in which the upper brick slides out- 

 wards, while all below it fall inwards (Fi^.18). In this 

 case the angular motion of the two portions is initially equal, 

 the points A and B remaining fixed. The velocities of the 

 centres of gravity reduced to a vertical direction are as the 

 distances C D, D E; in order therefore that there may be 

 an equilibrium without friction, the weight of the upper 

 portion must be to that of the lower as D E to C D ; and 

 in all cases the force of A D, tending to support D F, is to 

 the weight of D F, acting at its centre of gravity, as 



A G , C D to F G . D E, or as A G . ^ to F G. The 



friction of the upper block, of \vhich the magnitude may 



be determined in the manner already shovyn, will act upon 



the Vvhoje length of the arm F G, while the weight of D F 



acts only on the length of half I) E, consequently its effect 



ijiustbe considered as increased in the ratio of D E to twice 



F G. Thus if we take the example of an equilateral aper- 7 bricks would 



ture, constructed wjth 8 common bricks on each side, and ^^^"'^ ^y ^^^''' 



. , ■ ,. T • 1 /-( TTx Ml 1 ^ • 1 -•-.. T-. o^Vn weight t 9 



without cement ot any kind, C U will be 9*3 inches, U E would not, 



2*7, and F G 21 ; hence the brick A will produce imme- 

 diately a force equivalei^t to the weight of 3*4 bricks, and 

 by its friction, which is ^% of its weight, another force equi- 

 valent to the weight of 7 more ; consequently the sum of 

 both will be fully adequate to the support of the 7 bricks 

 which form the lower portion of ttje structure. But if we 

 mulve the same calculation for bricks, we shall find that 

 they will not stand without sdme external support. 



It is pbyious that in all these cases the addition of any This compared 

 bad at the e^ummit of the structure would very materially ^'*^ ^^^ *^*^^* 

 increase its stability, and that even a block, of sufficient 

 magnitude to till up the angle only, would enable us cotisi- 

 4er:ibly to extend the base. It is also plain, that an inclined 



facing" 



