Chat. VIII.

BRITAIN.

489

of the arch, and 7583 tons for the horizontal thrust in direction M E, being the pressures ateach end of the bridge. We may therefore estimate the greatest pressure on the east, orabutment frame, at about 8000 or 9000 tons.

Mr. Atwood .— The weight of the highest or middle sections being denoted by unity,the proportions of the pressures on all the other sections in respect to unity will be found inthe fourth column of the table. If the highest section should weigh 100 tons, it appearsfrom the table that the pressure on the first section, or rather the pressure between the firstand second section, will be 7300 tons, and the pressure on each of the abutments will he8100 tons. It may be added, that according to these dimensions, the weight of each semi-arch will be 3350 tons, and the weight of the entire arch 6700 tons.

The fifth question proposed was, What additional weight will the whole bridge sustain,and what will be the effect of a given weight placed on any of the fore-mentioned sections ?

Dr. Nevil Maskelyne stated, that an additional weight laid upon any part of the bridgewill be supported by the two abutments, each bearing its share in the inverse ratio of itshorizontal distance from the weight. The stress of the weight on the part it lies on is asthe weight, and the product of the horizontal distances from the two ends of the base, andits stress upon the centre of the bridge will be to the stress there arising from the pressureof the whole bridge, as the weight laid on is to the whole weight of the bridge.

Let us suppose the additional weight laid upon any part of the bridge to be that of aloaded waggon, which we will suppose to be 7 tons ; there is no doubt but that this bridgemay easily be made strong enough to support this by the connection of its parts ; but as theload might be laid on, so as to press upon the iron plate in the interval between two ad-jacent ribs, it will be proper to calculate the thickness it may be necessary to give to theplate to sustain such pressure. I find that if the interval of the ribs be 6 feet, a plate of 8inches thick will be above four times stronger than what would barely support the weight.

Rev. A. Robertson. — The maximum weight which the bridge will sustain depends uponthe strength of cast-iron, and, as far as I know, experiments have not been made to ascer-tain the strength of cast-iron. As far, therefore, as relates to the first part of this query,there are not data sufficient for determining by calculation the weight required.

The effect of a given weight placed over a given point of the arch may be ascertainedin the following manner. Let A, 13, D, E, F,represent the bridge, and suppose a given weightto be placed upon the point H, in the roadway ;let the straight line H, K, be perpendicular tothe horizontal line A, F, and meet it in K; thenthe effect of the weight on H, will be as therectangle under the parts A K, K F, of thehorizontal line. The pressure of a given weightwill therefore be greatest when it is over themiddle part cr crown of the arch.

Mr. J. Robeson. — The only portion of the arch which can be sensibly affected by anoccasional load is the crown, and 40 or 50 feet on each side of it. This is already carryingabove 300 tons of roadway; I imagine that any load which can occasionally collect in thatportion will be a mere trifle in comparison to this load. We have already seen, that itwill increase the mutual compression about of its own weight. If laid on at 180 feetfrom the crown, this must he increased in. the proportion of 2 to 5, because it is supposedto lie on the crown; but I do not think that this increased compression is of any im-portance. The chief risk is from the vertical strain, and it was for this reason that Irecommended diagonal ties, diverging from the lower angle of the middle joint. If avery strong horizontal transverse tie of wrought-iron went across the bridge in this place,ties could be attached to it, and to the underside of the roadway, at considerable distanceson each side, which would suspend the intervening portion from parts which have a moreextensive vertical connection, and would, in short, make it a more obtuse wedge.

Dr. Charles Hutton . — It is perhaps not possible to pronounce exactly what additionalweight the bridge will sustain without breaking, as it depends on so many circumstances,some of which are not known. But considering the great dimensions and strength of thearch-frames and of the whole fabric, we are authorised to conclude, that there is no possibleweight which can pass over any part of the bridge, even heavy loaded waggons, whose pressurecan be great enough to cause any danger to such strong and massy materials, and especiallywhen it is considered that by connecting all the frames together, by proper bond andotherwise, as mentioned in the answer to the first question, the local additional pressurewill soon be distributed through the whole series of the iron framing.

Mr. Atwood. — The sections being adjusted to equilibrium are to be tied or joinedtogether by a method described in a detached drawing; this is intended to prevent anychange in the positions of the sections, in consequence of occasional weight which may bebrought to press on any part of the arch: any such additional force of weight, if not

Fig. 485.