vent spalling. One of the spans, at the time I saw the aqueduct, was (in my opinion,) in imminent danger of falling, in consequence of this. I am confident that two trusses, instead of four, would have been sufficient to support the trunk of this aqueduct, especially if another arch-piece had been added to the depth of the curved ribs, and the height of the trusses made a little greater. This additional height would, moreover, have added to the convenience of passengers on the roofs of the boats, who are now obliged to stoop in passing through the aqueduct. As the use of but two trusses would, of course, increase the clear width between them, to admit the tow-path, the girders might be trussed by a heavy arch-piece, which would insure abundant strength. A considerable diminution of expense would attend such an arrangement.

As to the piers of this aqueduct, they are, as before stated, but seven feet thick on top, or part of the span; or not quite one-half as great as the proportion of those used in the Trenton bridge, which is the boldest one cited by Tredgold, in his table of stone piers for wooden bridges.

I am by no means prepared to advocate the breakwater starling, (so called,) used in this aqueduct, and in many large bridges in the country. I have known them to pitch very heavy blocks of ice upon the roof, and outside footways of the bridges to which they were attached. This never occurs with semi-circular starlings, and as I have never known one of the latter shape to be injured when built with care, I consider it preferable to the other-though I think something like a semi-ellipse still better. My own practice is to batter the fronts of the starlings two inches to a foot, and work them into one inch to a foot, as they approach the sides of the piers. Experience has given me every reason to be satisfied with this shape. In very exposed situations, there would be no objection to increasing the front batter to considerably more than two inches to a foot.

The foundations of the piers of the aqueduct do not appear to have settled in the least, or to have undergone any derangement; still, even in the face of this precedent, I should certainly prefer the foundation to be laid at the depth of a few feet below the bottom, in structures so important as this. There are, however, several bridges across the Alleghany, in the vicinity of the aqueduct, and all their piers are founded in this manner, (some of them, indeed, having but one course of timbers in their platforms,) which is strong evidence of the sufficiency of the plan, on a gravel bottom, even when exposed to tremendous freshets.

Viewed as a whole, this aqueduct, for which, I am under the impression, there was no precedent, certainly reflects the highest credit

on Mr. Lothrop, for boldness and mechanical skill.* There are others, of much the same kind, on the canal; all, I believe, designed by him. The general arrangement of the timbers is not original with him, having been long before practised, in very many instances, in common bridges; but the application of it to the purposes of so extensive an aqueduct, was certainly a very bold step; and its entire success is proof of an intimate knowledge of what he undertook.

I look upon this arrangement of timbers as the best yet devised for large spans. It certainly admits of many improvements in its details, and from some experiments of my own on the subject, I am under the impression that considerable modifications in some of the more important parts, might be made with advantage. I may take occasion, in some future paper, to allude to them.

The curved rib, it is well known, is stronger in the centre than at any other point; or, in other words, a load, which, applied between the centre and one of the piers, would destroy the rib, might be supported, with perfect safety, in its centre. But the truss which is conneeted with the ribs, is weaker in the centre than at any other point; its resistance to a load acting at any point, being, as in the case of a single piece of timber, proportional to the rectangle of the distances from the point at which the load is applied to the points of support. Therefore, the combination of the curved rib with the truss, secures a more uniform degree of strength throughout the whole span, than could be attained by either one, used separately.

But besides this, another very important consideration attends the combination of the curved rib with the truss, viz.: that each not only contributes its own share to the support of the load, but actually increases the power of resistance of the other—that is, the two combined will support a greater load than they could separately, were the load divided between them. A curved rib, when employed by itself, is very weak at the haunches, and readily yields to a load applied there; but if proper means be adopted for preventing the rib from changing its form, its strength is wonderfully increased, indeed to such an extent that actual crushing of the timber must take place before the rib will yield to its load. Without this precaution, its flex

* We think it proper to remark here, that in the sixth volume of the London Repertory of Arts, p. 220, is detailed at length, the specification of a patent taken out in England, in 1796, by Mr. James Jordan, for constructing aqueducts and bridges, with curved ribs of timber, or iron, and suspending therefrom, by iron rods, the floor or trunk, as the case may be. The celebrated bridge over the Delaware, at Trenton, commenced in 1804, is, in its general outline, almost a precise copy of the plate illustrating Jordan's patent, in the Repertory of Arts, and is, in principle, unquestionably, an infringement of that patent. Mr. Jordan also gives a plate of a projected aqueduct, precisely the same in its essential principles as that which forms the subject of the above paper.

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ibility will permit it to bend, and fall through between its abutments, under a load many times less than that necessary to crush it. Such a change of form, or bending, is prevented by the truss, and thereby so great an accession of strength is imparted to the rib, that if we could conceive of the truss acting only in this capacity of a stiffener to the rib, without itself sustaining any portion of the load, still the strength of the bridge would be increased many fold. I have seen curved ribs of 200 feet span, bend, and fall into the river, between their abut

ments.

The highest known freshet of the Alleghany, rose to about the floor line of the canal trunk; the weather boarding of the outside formed a kind of dam, against which, trees, barns, houses, &c., accumulated, until they formed a wide field of drift on its upper side. A large concourse of people stood on the banks of the river, expecting to see the whole structure lifted off from its piers, and floated away; but it stood perfectly firm, and I believe sustained no injury whatever.

It is my intention to endeavor, through the medium of the Journal, to supply, in some measure, a deficiency that exists in all our works on carpentry, in that department which treats of the spanning of large openings. The best mode of doing this will, probably, be to present to the reader a series of papers, descriptive of existing structures, with such comments as may happen at the time of writing, to be suggested by the particular example under consideration. This paper may be looked upon as the first of the series, and I shall endeavor to follow it up, as my leisure permits, by other interesting examples of such works as have come under my own immediate notice. In some future paper I shall enlarge more fully upon the several individual timbers composing such a truss as that employed in this aqueduct. The subject of wooden bridges, of large spans, is a very interesting and important one, and one of considerable intricacy. Its importance has of late been much enhanced, by the discoveries of preservatives of timber from decay. Should an equally effective preservative against fire be discovered, which, under the present rapidly increasing discoveries in chemistry, is not at all improbable, we should have much less reason than at present to regret our national want of fine stone bridges.

Athens, Tennessee, May, 1842.

Mode of Tracing a Curve of very large Radius, adopted in the Survey of the Northern Boundary of the State of Delaware, in

1701.

Professor JOHN F. FRAZER has deposited at the Hall of the Franklin Institute, in Philadelphia, some interesting documents, concerning the original demarcation of the curvilinear boundary, dividing the northern part of the State of Delaware from the conterminous States of Pennsylvania and Maryland. These documents consist,

I. Of the original warrant by William Penn as "Proprietary and Governor of Pennsylvania and the counties annexed;" bearing date the 28th day of the 8th month, 1701, and directed to Isaac Taylor, of the county of Chester, in the province of Pennsylvania, and Thomas Pierson, of the county of Newcastle, "in the territories;" instructing them to accompany the magistrates of each county, or any three of them, within the space of forty days after date, and in their presence to admeasure, and survey, a circular boundary line, struck by a radius of twelve miles, from the town of New Castle, as a centre; the line to be well marked, and to consist of "two-thirds of a semi-circle of twelve miles radius."

II. Of a duplicate record of the official proceedings of the appointed surveyors, and the field notes of the survey, made pursuant to the aforesaid warrant, in the presence of six magistrates-three of the province of Pennsylvania, and three of the "annexed territories," now the state of Delaware.

By this document it appears that the centre of the arc of the circle, or the point of beginning the radial line, was established by the magistrates "at the end of the horse dike next to the town of New Castle," thence by various courses, rectified to a due north line, the surveyors ran off the radius of twelve miles, terminating at a white oak tree, in a sinuosity of the Brandywine Creek; and as it will probably be more interesting, we subjoin an extract from the official memoir, in which the surveyors (in their own language,) give a brief account of their operations, in first tracing a radius of twelve miles, due north, and then marking out the required segment of 120°, by uniform angles of deflection from primary chords, as is at this day practised upon railroads, and similar works.

Extract from the Surveyor's Memoir.

"The 26th day of the 9th month we did begin, in the presence of the said justices (Cornelius Empson, Richard Halliwell, John Richardson, Caleb Pusey, Philip Roman, and Robert Pyle, Esquires,) at the end of the horse dike, and measured due north twelve miles, to a white oak, marked with twelve notches, standing on the west side of

Brandywine Creek, in the land of Samuel Helm; and from the said white oak we ran eastward, circularly, changing our course from the east southward, one degree at the end of every sixty-seven perches, which is the chord of one degree to a twelve miles radius; and at the end of forty-three chords we came to the Delaware river, on the upper side of Nathaniel Sampley's old house, at Chichester; and then we returned to the said white oak in Israel Helm's land, and from thence we ran westward, changing our course one degree from the west southward, at the end of every sixty-seven perches, as before, until we had extended seventy-seven chords, (which being added to the forty-three chords, make two-third parts of the semi-circle to a twelve mile radius,) all which said circular line being well marked with three notches on each side of the trees, to a marked hickory, standing near the western branch of Christiana Creek. Surveyed the 4th day of the 10th month, 1701, by us.”

(Signed)

ISAAC TAYLOR,
THOS. PIERSON.

To elucidate more fully the principles involved in this demarcation, we subjoin a diagram (on a scale necessarily distorted,) showing three of the chords assumed at random from the eastern part of the survey.

a

b

Uniform length of each chord-nat. sin. 4° x 12 miles, rad. x 2 or .008726 x 3840 perches x 267.01952 perches, say 67 pers., which is the chord of 1° of a circular arc, of the radius fixed; as is correctly stated in the surveyors' memoir.

Angles of deflection,
e bc, fcd, &c.
uniformly 1°.
26th day of the 9th

The surveyors began their field labors on the

month, 1701, and closed them on the 4th day of the 10th month, having occupied but nine days in the work; running, within that time, twelve miles of radius, and twenty-five and one-eighth miles of chords of the curve-in all upwards of thirty-seven miles, or more than four miles surveyed and measured each day, at an average.

When we consider the care required in tracing the chords by rectified courses, and the obstacles which the face of the country must then have presented, this was rapid work; and it stands forth in striking contrast to the vast length of time, which similar geodesic operations are at this day made to consume.