Chap. VIII.

BRITAIN.

479

make the tin take hold of the iron, but this is not necessary. The great pressure and thebullet joggles will prevent all change of figure.

After all, I own I still prefer Mr. Burdon’s construction of the arch. Ilis method ofcombining the abutments of the cast-iron rails of his frames with the wrought-iron strapsseems finely calculated for procuring a close union of the parts. A judicious artist willperceive, that by a proper forming of the holes in the three pieces (the cast-iron rail betweenthe two wrought-iron straps), the drawing of the keys into these holes will draw the twocast-iron ends closer together, and press them hard into each other. Thus, when keys aredrawn into the holes, the two parts of the cast-iron bar which is between the straps willhe forced hard together. I observe, also, that Mr. Burdon’s arch has three rails, and theLondon arch has but two; at least the middle rail of pierced work does not seem to forma line of abutment supporting the middle of each subjoint. I think that this mode offraming at Wearmouth might be extended to the next circle, which is in the middle ofthe Gothic arcade. The effect of the straps which form this circle would be prodigious instrengthening the whole.

Dr. Milner on this question supposes the whole mass of the bridge to be cut into a greatnumber of thin slices, bounded by planes parallel to each other, and all of them parallel tothe plane of the arch of the bridge; then it may be said, that all those parts of the ironwork, whether they be called ribs, bars, rods, braces, frames, or by any other names, all thatcan be properly considered as lying in the above-mentioned planes, or so extending betweenany of them in the direction of the said plane, as to contribute to the formation of the arch,and also to the strength of it, considered as a geometrical curved line, or rather as a bentiron rod of small thickness; all the parts of the work coming under this description act aswedges, both by gravity and pressure, but all the parts which serve merely to bind togetherthe above-mentioned slices, and which act in directions perpendicular to the said parallelplanes, which are the boundaries of the slices of the bridge, are to be considered as weightonly ; and such portions of iron as come under neither of these descriptions must be dividedby just reasoning, upon the well-known principles of the resolution of forces, and a due con-sideration of all the circumstances, and then be placed part to one account, and part to theother.

It appears that in regard to an iron bridge of the magnitude of that proposed, not onlythe weight of the iron made use of, but also its elasticity, and still more its cohesion, arepowers which enter into every part of the investigation of the construction. The con-sideration of these powers presents a very difficult subject, but unless something be settledrespecting them, every conclusion that pretends to any thing like precision must be ab-solutely fallacious. How should the steps in an argument be probable, when the premisesare all conjecture ? As far as mere weight is concerned, the mathematicians very readilydetermine curves of equilibration as they are called, and it certainly deserves very seriouslyto be considered, whether after all it may not be the safest way to dispose of the weight insuch proportion as to make all in perfect equilibrio, on the supposition that there wasneither cohesion nor elasticity in the materials.

If the natural powers of the iron in regard to its cohesion, elasticity, and strength ingeneral, under all the circumstances in which it may be employed in this occasion, couldbe ascertained with any tolerable degree of exactness, then it would be undoubtedly the bestmethod to take into consideration all those powers so estimated, and also the gravity of thematerials, and reduce the whole to a rigid calculation proceeding upon a sound theory, antito rely upon the conclusion in practice; but if there be too much reason to suspect that thepowers above-mentioned cannot be estimated from any known facts, with the requisitedegree of probability of being near the truth, then the question will be whether in thatcase it may not be most prudent to compute merely upon the weight of the materials andtheir action as wedges , considered as the data, and so to determine the curve of equilibration.To a bridge constructed upon the principles last-mentioned, so that the tangential forcesshould be in perfect equilibrio, and destroy each other at every point of the curve, theremight still be superadded all the advantage which a good mechanic can give to it, by makingthe most skilful use of the powers of cohesion, elasticity, &c. of the metal.

There are, however, two objections to be offered, the first is, that though the above-men-tioned powers of cohesion, elasticity, &c., may be allowed to be entirely beyond the reach ofcomputation ; when we have in view a s^ucture like this, yet we may still be sure that thesepowers are very considerable. We may in many cases be quite sure that a power is verygreat, though we are unable to say how great; and under such circumstances, it is not tobe dissembled that no person can foresee whether the effect of a great unknown power maynot be to overturn in a great measure the geometrical reasoning itself, respecting the curvesof equilibration ; or whether, therefore, it might not be better to hazard and compute uponsome hypothesis or conjecture, respecting the strength and effect of these powers, ratherthan to leave them entirely in the dark, and proceed upon the partial consideration of mereweight and wedge action, when we are sure that other powers are actually present. Thesecond objection arises from a considerable practical difficulty which must occur in executing