On the Principles of Arches. 243 



represented by ac; then, lines being drawn parallel to the di- 

 rections of thJ bars, ci will represent the weight on the angle 



^ Now^ suppose the depth of the joints to be equal dh, and let 

 the weight at D be the same as before; then, if the load at D 

 was sufficient to disturb the equilibrium; the bars would turn 

 on the points d, f, and I ; therefore, we find the force at E 

 that would balance the pressure at D, is nieasured by ck, and 

 the stability of the system will be as the difference between ck 



''"if die "load at E, equal ci, was sufficient to disturb the equi- 

 librium, it is evident the bars would turn on the ?omtshe and 

 . ■ then the stress at E being ci, the weight that would balance 

 it at D, is c Z; and the difference between cl and-ta, equal La, 

 will express the stability: but had the system been uniformly 

 stable, the differences should have been equal : Therefore a sy- 

 stem which would be in equilibrio were the joints without sen- 

 sible depth, is not of uniform stability when the depth of the 

 ioints is of some magnitude. ^ j ^i, ♦ •<. 



We conceive that a bridge ought to be so constructed that it 

 may resist the action of a weight moving along it, with an equal 

 force at any part of its length; and the greatest stress that 

 could possibly come upon it ought not to produce a sensible 

 effect on the arrangement of the arch-stones. Equnibnum, it 

 we understand the\erm, signifies a balance of parts which vvou.d 

 be deranged by the slightest pressure partially applied ; there- 

 fore, the form that gives equilibrium to a bridge, a roof, or a 

 dome, is the worst that can be adopted. . ^i, , • 



There is yet another objection we have to make, and that is 

 to the method of finding the thickness of the piers. The piers 

 ought to be considered as a part of the arch, and the stabihty 

 of the whole should be investigated at the same time ; for the 

 stren-tli of the piers must be computed from the forces acting at 

 the places of fracture, which is not always at the sprmgnig of 



^^'It^'would be easy from what has been said, to determine the 

 stability of any given bridge, for the place ot fracture might be 

 nearly ascertained bv inspection ; and find the centre of gravity 

 of each of the segments into which the jomt of fracture divides 

 the semi-bridge; then the stability both at the crown and the 

 haunches mi^i.t lie determined. For finding the directions of 

 the forces, sec Mr. Southern's paper. Philosophical Magazine, 



"'^A^'iicte' formed on the principles of uniform stability w'ould 

 certainly be the most scientific; but considerabKdeviations from 

 that form may be made, without any other bad ehects Oian 



