492

HISTORY OT ENGINEERING.

Book I.

that a reduction can be made in the materials, so as to make them less than in the otherbridge, though it may reduce them to an equality in the two bridges. If an ellipticalarch was adopted instead of the circular one, a bridge might be made sufficiently strong,equally durable, more convenient, and with great reduction of expense.

Rev. A. Robertson .—Supposing the span of the arch to remain the same, and the arch tospring 10 feet lower, the crown of the arch would be 75 feet, and the diameter of the circlewould be 1275 feet. Let A B I), E 13 G, be the two arches, whose strength are to becompared, A E, D G being each equal to 10

feet, and perpendicular to the horizon. Take r

any point II in the arch, A 13 D, and draw thestraight line H K perpendicular to thehorizontal line E G, and cutting the archE 13 G in F. Then the diameter of the

circle of which A 13 D is a part being

1 G 13

feet, and the diameter of the circle of whichE 13 G is a part being 1275, the strength of the

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upper arch at II will be to the strength of the under arch at F, as 1275 to - ,

51 to 58 nearly.

The span and height being the same, if the arch consisted of the flat side of an ellipse itwould be weaker than the circular arch : if it consisted of the other side of an ellipse, it wouldbe stronger.

Mr. Playfair .—Were the entire elevation of the arch to be 75 feet instead of 65 feet, aconsiderable addition would be made to the strengtli of the bridge. The radius of thearch as at present proposed is 725 feet nearly ; if the elevation were 75 feet, the spanremaining 600, the radius would be shortened to 637 feet 6 inches, and the strength ofthis latter arch, in as far at least as it depends on the wedge-form figure of the frames,would be to that of the former in the inverse of that proportion, or as 725 to 637, or as 8 to7 nearly.

In this I suppose the weight and strength of the iron frame-work to remain the same.As more weight would no doubt be required in this second construction than in the first,the real advantage gained would not be so great as has been just stated, or as a seventhpart.

As to the elliptic arch, I do not think that any advantage would be obtained by intro-ducing it in the room of the circular. An elliptic arch, indeed, might be so employed asgreatly to lessen the horizontal thrust on the abutments, but the curvature at the crownwould be rendered so small that the bridge would be greatly weakened at that point,deriving there no advantage from its figure, and depending on the mere strength of theiron.

Mr. J. Robeson .—Making the arch spring 10 feet lower will diminish the thrust on theabutment one-fifth, as also at the crown, and by giving more curvature at the crown willmake longer joints. This will greatly strengthen the bridge, but this advantage will belost by making it elliptical, not from a want of equilibration, because this structure shouldnot be compared with masonry, but for want of long joints near the crown, and an oppor-tunity of using better disposed diagonal braces. Such a degree of ellipticity as will besensible to the eye and graceful will certainly make the bridge extremely weak in themiddle.

Dr. Charles Hutton . — Should the arch spring 10 feet lower than in the design, thebridge would be more stable, because the thrust or pressure on the abutments would bedirected lower down, and more into the solid earth, and in general, the lower the springingof the arch, the more firm the abutments and stable the bridge, if the height of the crownabove the springing of the bridge be the same. But the greatest advantage would be bymaking the bridge in the form of an elliptical arch instead of the circular one, in all thearticles of strength, duration, convenience, and expense. For, as the elliptical flanksrequire less filling up than the circular, this will produce a great saving in the iron work,and this same reduction of materials in the flanks towards the abutments is the very causeof greater strength by reducing the weight there, nearer to the case of equilibration, sincethat very extraordinary mass employed in the flanks of the circular arch destroys theequilibrium of the whole by an overload in that part. The elliptical arch will also bemuch more convenient, as it will allow of a greater height of navigation way between thewater and the soffite of the arch. The elliptical arch is also a much more graceful andbeautiful form than the circular arch.

Mr. Atwood .— It does not appear to me that there would be any material difference inthe strengtli and duration of the arch, whether it is constructed in an elliptical or circularform, all the parts being executed equally well in both cases. The expense, it maybe pre-