When there is but one space or span, and no middle piers, nearly half the chains are taken up in fastening; but the same fastening would serve for any number of spaces.

The smith's work will cost two or three cents per pound, and the carpenter's work is not worth naming.

The scantling will cost about as much as the plank for flooring. No scaffolding is necessary for raising the bridge.

With allowance for thickness at the ends of the links, and wasteage in making, &c. a chain of inch and half square bar will weigh sixteen pounds per foot-one of inch bar will be about seven and a half pounds per foot. About one fifteenth of the span will give curve sufficient, and one fifth the weight of the chains will be iron sufficient for suspenders, bolts and keys.

An estimate on these principles for a bridge of 500 feet between the abutments, with only one pier, will not amount to seven thousand dollars, exclusive of abutments and pier. Compare this with the Philadelphia Schuylkill bridge of the same extent, which cost sixty-five thousand dollars after the abutments and the two piers were completed; total expense, three hundred thousand dollars.

It is believed that saving the expense of one pier, the duration of materials, facility of erection, as well as repairing, is worthy of public attention.

There is no reasonable doubt, that in some extraordinary case this kind of bridge will be extended to one thousand feet, when the subject shall be fully understood; and should it ever be necessary, I would undertake to satisfy any person concerned, that it is capable of a still greater extension.

As the bridge has no support but the chains, two things ought to be accurately understood; i. e. how much iron can bear at a direct pull endwise, and what it can bear in the other positions in which it is to be employed. As to the first, my experiments agree with the opinions of those who have investigated the subject; but I have made my calculations at 60,000 lbs. to the inch square bar, which is something less than the strength of iron of the lowest quality.

But what a chain will bear when the two ends are fastened, and the weight affixed to the middle, or rather equally distributed along it, is a question that I presume may be determined by fastening one end of a line, and extending the other horizontally over a pully

whirl with a given weight attached to it, (say 10 lbs.) then let as many pounds be placed along the middle part at distances horizontally equal. The middle part of the line will then represent the chains loaded as when supporting the bridge. The end that hangs in the manner of a plummet, determines the tension, and the pullywhirl equalizes it between the two parts. The conclusion is unavoidable, that a line or chain will bear just as much with the curve of the middle part, as it would bear attached like a plummet; and this will be found equally true in a long distance as in a short one; so unequivocally true is it that the balance at the end determines the tension that the line was as tense before any weight was put on the middle part, as when the ten pounds were affixed to it. The same ten pounds will balance fifteeen or eighteen pounds, provided the line is permitted to sink until the balances find their proper level or equipoise. It is also clear, that when there is little or no curve, one pound creates more tension than ten, when the curve is greatly larger. I have stated the strength of the chain at 60,000 lbs. per inch bar, when the sinking or curve is nearly one sixth of the span. By some hasty experiments that I have made, it appears that with a sinking of one ninth, it will bear 45,000 lbs. and at a sinking of one fourteenth, it will bear 30,000 lbs. and at a sinking of one thirtieth, it will bear only 15,000. Thus we see the effects of greater or less curve. Another purpose to be answered by the line and balances, is to find what position the chain would naturally take when supporting a bridge. We know it forms no part of a true circle, nor what is called the catenarian curve; the latter is formed by the weights being equal along the curve line, but in the case of a bridge, the weights are equal along the horizontal line.

EXAMPLE.

To find the proportions of the several parts of a bridge of one hundred and fifty feet span, set off on a board fence or partition one hundred and fifty inches for the length of the bridge, draw a horizontal line between these two points representing the underside of the lowest tier of joists-on this line mark off the spaces for the number of joists intended in the lower tier, and raise perpendiculars from each, and from the two extreme points, then fasten the ends of a strong thread at these two perpendiculars, twenty-three

inches and one quarter above the horizontal line-the thread must be so slack that when loaded, the middle of it will sink to the hori zontal line; then attach equal weights to the thread at each of the perpendiculars and mark carefully where the line intersects each of them. The distances between those marks on the curve line, is the length of each link for its respective place; and the distances from each of these marks to the horizontal line is the length of each suspender for its proper place.

It will sometimes be convenient to have a pier so nigh the abutment, that a part of the bridge can be attached to the chain as it descends to the ground to fasten. In one case, where the elevation of the chain at the pier is but twenty feet, there is forty feet attached to the chain, and ten more to reach the abutment. these cases, the line and balances determine every thing.

In all

In a bridge of but one arch or space, it must be considered a grievance, that the chains, including the branches, must be nearly twice as long as the bridge. I have just been trying on a space of 400 feet between two piers how much of the bridge can be attached to the chain as it descends to the bank to fasten; and it appears that about 170 feet may be attached to each end in this way. The two ends will and must be exactly in the position of a half bridge as far they go, the end of the chain taking nearly a horizontal direction, may be et into the bank as far as may be thought proper. Here then is a bridge of say 740 feet, with scarcely any mason work but two piers, and the chains very little longer than the bridge. Suppose a shorter space to be divided in this way, say 300 feet, the middle space would be about 175: the chains would then need to be but a little more than half as strong, and not much more than half as long.

The spaces or spans may be different in the same bridge, and the suspenders must be longer in the short spaces, for although with equal weight on all the spaces the curve would be in propor tion to he span. But the large spaces having more weight of bridge to support, must have more than its proportion of curve and the short spaces less, in order that the tension may be equal on all the spaces.

In a bridge of two or more sp ces or spans a load on one will tend to sink it and raise the rest; to resist this tendency the framing

must be bound down to the stone work; for this purpose let four pieces of iron for each pier be made long enough to reach quite through the pier, and with strong eyes at each end turned up some inches, let two of these pieces be built in each end of the pier, say ten feet down in the stone work, so that the eyes may barely appear on the face of the work, and one brace of the framing can be fastened down to each eye.

If there should be a large space and a number of lesser ones, or should it be necessary to raise the chain at a draw-gate, lay off your plan on some convenient scale as before directed, employ the line and balances, fixing whirls at every bearing, to equalize the tension. In this way the position of the chain will be ascertained at every place, and likewise the length of the suspenders for their respective places; and I venture to say that this plan and this only, of ascertaining the proportions, can be safely depended on.

It is a matter worth knowing, what is the tension of the branches, compared with that of the main chain. It is evident if there were only two branches, and they should open so as to form an angle of 120 degrees, (that is one third of the circle) each of the branches would then be equally tense with the main chain; but whatever angle the branches form in spreading to receive the stones, the tension can be ascertained by the line and balances.

It may be inquired whether all parts of the chain are equally tense when supporting the bridge? I answer that the tension is about an eleventh less at the middle of the bridge than at the ends. I have ascertained this by taking a line to represent the chain that supports one half the bridge only, and extending it over two pullywhirls, one at the centre of the bridge and the other at the corner where the chain is supported, and loading it horizontally equal as in the case of a bridge. It is evident that the weight at the upper whirl must be greater than that at the lower; and the difference between the two, shows the difference of tension between the middle of the bridge and the two ends.

The spreading of the branches, unless very considerable, increases the tension less than I could have thought. In the length of branches that I have proposed the increase of tension is not worth notice. I have just been trying with a small line and balances, the longest branches two feet three inches, and the shortest fourteen

and a half inches, spread to fourteen and a half, and in that case the whole increase of tension in all the branches, appeared to be only one-seventh more than if they had all drawn in a straight line with the main chain. By these experiments it is probable that many of those concerned will be relieved from groundless fears. I have found great difficulty in obtaining permission to let the ends of the chains open each a foot or two off the direct line, so as to make the passage to and from the bridge more free, and remove the chains out of danger.

I know the young mathematician, with mind half matured, would smile at my mode of testing the relative force and effect of the several ties and bracings of any piece of framing: but the well informed, will not so lightly treat any information obtained or supposed to be obtained by actual experiment. If the process is before him, he will carefully ponder all the parts, and discover where the defect lies before he rejects the conclusions drawn therefrom.

SHAPE OF THE LINK.

It is plain that the bars in the middle of the link draw in a direct line, and it is easy to tell the strength: but is impossible to get the links fitted into each other as close and full as could be wished; to remedy which and to be secure in this point, it will be necessary to have those parts of the link made considerably larger. To accomplish this, nine or ten inches of each end of each bar is left a quarter of an inch larger than the rest, and two such bars make one link. As there is but one link of the chain to each space between the joists, there will not be much iron expended in this way. It is thought best not to round the inside of the links at the ends where they sit in each other, as there is no friction in the chain when in use. Every link will be so wide, that the side of the next one can turn freely in it, and the other side turn round its end, for the workmen will find it convenient to hang up the last made link of the chain, so that the lower end of it may be nearly on a level with the fire and anvil. In this way he will be able to turn up three sides of the one he is closing in, and will find no difficulty in shaping the work to his mind. This wideness of the link must always be filled up with the thickness of the end of the next. A link of inch and half bar will require to be more than two inches and a half wide,