ON ARCHITECTURE AND CARPENTRY. 163"" 



pressure of a fluid, which is nearly elliptical, the logarithmic, and the pa-' 

 rabolic curves, allowing to each its due proportion of influence, we may 

 estimate, from the comparison, which is the fittest form for an arch intended 

 to support a road. And in general, whether the road be horizontal, or a 

 little inclined, Ave may infer that an ellipsis, not diff'ering much from a 

 circle, is the best calculated to comply as much as possible with all the con- 

 ditions. (Plate XL Fig. 155.) 



The tier of bricks cut obliquely, which is usually placed over a window 

 or a door, is a real arch, but so flat as to allow the apparent outline to be 

 horizontal. Mr. Coulomb observes, that the greatest strength is obtained 

 by causing all the joints to tend to a single point: but little dependence can 

 be placed on so flat an arch, since it produces a lateral thrust which may easily 

 overpower the resistance of the wall. For the horizontal force, required to 

 support each end of any arch, is equal to the weight of a quantity of the 

 materials which are supported by its siimmit, supposed to be continued, of 

 their actual depth, to the length of a semidiameter of the circle of which the 

 summit of the arch is a portion. This simple calculation will enable an ar- 

 chitect to avoid such accidents, as have too often happened to bridges for want 

 of sufficient firmness in the abutments. The equilibrium of a bridge, so far 

 as it depends only on the form of the arch, is naturally tottering, and the 

 smallest force which is capable of deranging it, may completely destroy the 

 structure; but when the stones or blocks composing it have flat surfaces in 

 contact with each other, it is necessary that the line expressing the direc- 

 tion of the pressure be so much disturbed, as to exceed at some part the li- 

 mits of these surfaces, before the blocks can be displaced. When this curve, 

 indicating the general pressure which results from the efiect of a disturb- 

 ing force, combined with the original thrust, becomes more remote from 

 the centre of the blocks than one sixth of their depth, the joints will begin 

 to open on the convex side, but the arch may still stand, while the curve 

 remains within the limits of the blocks. 



It is desirable that the piers of bridges should be so firm, as to be able not 

 only to support the weight of half of each adjoining arch, but also to sustain, 

 in case of the failure of one of those arches, the horizontal thrust of the other; 

 and the same condition is obviously necessary for the stability of walls of any 



