Chap. VIII.

BRITAIN.

483

the iron work is made lighter. Vertical ribs seem the most natural and easy method, andif well braced might probably answer the purpose; but the increase of width towards theextremities is certainly the strongest method of steadying the arch. If the bridge was tobe made 50 feet wide at the crown, and 100 feet at the extremities, it would, in my opinion,be sufficient.

Mr. Jaynes Watt , of Heathfield, near Birmingham , thought that the width of the road-way of the bridge ought not to be less than 60 feet, including the parapets on each side.In respect to the effects of storms and common accidents, such an arch would be sufficientlystable, without being widened at the ends; but it would be more convenient if it were90 feet wide at each end, such extra width decreasing gradually, so that, at 150 feet fromeach end, it should be reduced to the width of 60 feet, from which points the sides would beparallel for 300 feet of the length. It appears to me, that the uprights which stand uponthe arch and support the roadway should be perpendicular, as well as the faces of theabutments above the spring of the arch, as the uprights would in that position be stronger.The segments of flat arches in the spandrills, if they acted at ail as arches, would have a pre-judicial effect, as they would push with great force against the abutments, in points wherethey were less able to resist than at the spring of the real arch. One reason for enlargingthe width of the bridge to 60 feet is, the very great concourse of carriages and passengers,which may be expected in that situation, and which 1 apprehend ■would be greater thannow cross at either London or Blackfriars Bridge, and surely 60 feet is narrow enough forany principal street in London , as this should be considered.

Mr. John Southern observed, that the pillars that carried the road being radii from thecentre, the weight per foot long of the road ought to decrease from the crown, or summitof the bridge, towards the abutments, in order to obtain the equilibrium of the arch ; andconsequently, instead of increasing in width, the road ought to decrease towards the abut-ments, supposing it to have the same depth of section. If it keep the same width, orhave parallel sides, it ought to get thinner towards the abutments, and still more so if itwiden.

By the plan it appears to be twice the width at the abutments that it is at the crown, inwhich case the thickness at the crown should be, to that at the abutments, nearly as twoand two-thirds to one, in order to affect the equilibrium : this is, however, on the suppo-sition that the weight of the arch is of little consideration in comparison with that of theroad, by which I mean the sleeper plates, Cornish flags, pavement, &c.

It is hence evident that the road may take any form in the plan, by making its thicknesscorrespond with the weight demanded by the equilibrium; but I must prefer parallel sides,because of the great, if not insuperable difficulty of making them curved ; and because I donot perceive that much advantage can be gained towards horizontal stability by that form,which seems, as I conceive, to be the main object, but which may be better attained bydiagonal braces.

Mr. William. Reynolds , of Colebrooke Dale, says, I have no doubt but the strength of thebridge is very materially affected by the increase of width towards the extremities, andwhich will operate in a favourable manner in every respect, as it not only strengthens thelateral bearing, but gives a greater abutment to the pressure endways, which will be veryadvantageous.

Mr. Charles Bage, of Shrewsbury , observed, it was an excellent thought to make thebridge wider at the ends than in the centre, not only for the convenience of the passage overit, Tmt for the opportunity it affords of giving firmness to resist tempests, or any otherhorizontal pressure.

The third question to be answered was highly important, as it demanded in what propor-tion should the weight be distributed from the centre to the abutments, to make the archuniformly strong ?

Dr. Nevil Mashelyne apprehended this question to relate to the principle of equilibration.But considering the question to be relative to the strength of cohesion of a perpendicularsection of the bridge, as opposed to the stress arising from the weight acting against it toovercome it, it appears to me to make the bridge equally strong from one end to the other ;the thickness of the rib frames should be diminished more and more in going from thecentre to the extremities of the bridge, and that in the inverse ratio of the square of theheight of the perpendicular section above the arch. This it is evident will much diminishthe quantity of materials and weight of the bridge, and thereby further strengthen thebridge, and lessen the expense. This subtraction of the materials, however, in goingtowards the ends, is contrary to what is required for an arch of equilibration, at least of acircular one.

Rev. A. Robertson , previous to answering this third query, stated the following particularsrelating to the circle, of which the arch of the bridge would be a part. The diameter is

—^—or 1449 T 8 3 feet, the circumference 4554-10103763. The length of the arch of thebridge will be 618-59872427 feet, and its magnitude 48° 54'. Having ascertained these

i i 2