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the foundations, they are built solid, and the remaining 50 feet hollow, the walls being only 2 feet in thickness, with one cross inner wall; by this means the centre of gravity of the piers is thrown lower, and the masonry economised. The width of the waterway is 12 feet; of which the towing-path covers 4 feet, leaving 71 feet for the boat as the towing-path is supported by iron pillars, the water fluctuates, and recedes freely as the boat passes.

There are 18 of these stone piers, besides the abutments; the span of the arches is 45 feet, and their rise above the springing 7 feet, and the total expense of its construction was 47,018.

This aqueduct almost rivals the works of a similar kind left us by the ancient Romans: the introduction of iron, however, for a watercourse, is a novelty with which they were unacquainted in this instance it has proved admirably well fitted for the purpose to which it is applied had the channel been constructed with stone or brick at this great elevation, it would have been less secure, as there would have been a constant danger of leakage.

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SKEW OR OBLIQUE BRIDGES.

One of the skew bridges on the London and Birmingham line, a fine erection of this kind, is 23 feet in height from the surface of the road below to that of the rails, making an angle of 32° with the road the direct span of the arch is 21 feet, and oblique span 40. The arch, which is 2 feet thick, is the segment of a cylinder, the internal radius of which is 12 feet, and the versed sine 5 feet. The angle of which the coursing joints of the soffite cross the axis of the cylinder is 53° 25', and the joints of the face of the arch all converge to a point 32 feet below the axis of the cylinder, and 45 feet below the crown of the arch.

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The Midland Counties Railway possesses another variety of skewed brick bridge, the span of which is 42 feet, and versed sine 11 feet;

the arch consists of six ribs, 2 bricks in depth, and 4 feet in thickness, the total breadth of the bridge, measured at right angles to the face, being 24 feet.

Manchester and Birmingham Railway. In Fairfield Street is a skew bridge, the oblique span of which is 128 feet, with a versed sine of 12 feet; the width from face to face is 31 feet.

Six ribs of iron abut on as many independent walls, and project before each other 13 feet; an ornamental stone parapet and cornice crown this viaduct, presenting a novel and agreeable appearance.

[graphic]

This bridge, executed after the designs of Mr. G. W. Buck, is remarkable for its acute angle, which is 241. The weight of the iron-work employed on the six ribs was 540 tons, and the whole was admirably secured together; the remainder of the viaduct is formed with brick arches of 45 feet span.

DIMENSIONS OF VIADUCTS IN VARIOUS RAILWAYS.

In the Grand Junction Railway, at Vale Royal, is a viaduct of stone over the river Weaver, in which are five arches, each 63 feet in span and 60 in height; the length of the viaduct is 456 feet. Where this railway crosses the Mersey and Irwell Canal there is a viaduct of stone having 12 arches; the two in the centre are 75 feet in span, and the remainder from 40 feet to 121.

In the Newcastle and Carlisle Railway, near Brampton, is a viaduct, which crosses the public road and the river Gelt, at the height of 80 feet above the bed of the river, over which it is carried in an oblique direction. The arches, which are three in number, are 33 feet in direct span, and are built at an angle of 45°.

In the Birmingham and Derby Junction Line, between Kingsbury and Tamworth, over the Anker, is a viaduct of 18 arches, each of 30 feet span, and one oblique arch of 60 feet span; its height above the river is 23 feet, and the cost was 18,000l. In the same line, between Tamworth and Burton-on-Trent, is a viaduct mile in length, built upon above 1000 piles, driven 15 feet below the bed of the river.

In the Newcastle and Shields Railway there is a viaduct over the Ouseburn of 9 arches, two of which at the ends are of stone, and the others are of timber, resting on stone piers; the three central arches have each a span of 116 feet, and two others 110; the total length of the viaduct is 750 feet, and its height above the water 180 feet. In the same line, the viaduct at Willingdon Dean has 7 timber

arches, five of which span 120 feet each, and the two exterior each 115 feet; the whole length is 1050 feet, and the height 82 feet.

In the Taff Vale Railway, near Quaker's Yard, is a viaduct crossing the Taff, the length of which is 600 feet, and the height above the river 100 feet, having 6 arches. In the same line, at the conflux of the Rhondda and Taff, is a viaduct having an arch of 100 feet span, and 60 feet in height.

In the London and Brighton Railway, across the valley of the Ouse, is a viaduct 1437 feet in length, and the height varies from 40 to 96 feet; it is formed of 37 brick arches of 30 feet span.

The London and Greenwich Railway is a continuous viaduct of more than 1000 brick arches, each 18 feet span, 22 feet in height, and 25 feet in width. It is 33 miles in length, and cost 266,3221. per mile.

The extension of the South-Western Railway through the metropolis, from the Nine Elms to Waterloo Bridge, is a continuous viaduct, like the last-mentioned one, in which are several strong and elegant oblique iron arches for the purpose of crossing some of the principal streets.

The student's attention should also be directed to the many magnificent railway bridges and viaducts of iron which have been erected of late years; such as the Britannia and Conway Bridges in North Wales; the High Level Bridge at Newcastle-on-Tyne; and the great Victoria Bridge in Canada by Mr Robert Stephenson; the Windsor, Chepstow, and Saltash bridges by Mr Brunel; the new Charing Cross Bridge by Mr Hawkshaw; and the Viaduct at Crumlin in Monmouthshire, by Messrs Kennard. Descriptions of these will be found in engineering works.

I shall conclude this section by recommending to those who wish for scientific and practical information of the first order on this subject, "The Theory, Practice, and Architecture of Bridges," by J. Hann and others; "Practical and Theoretical Essay on Oblique Bridges," by G. W. Buck, M. Inst. C.E.; "Treatise on the Equilibrium of Arches," by Joseph Gwilt, architect, F.S.A.; Cresy's "Encyclopædia ;" and a "Practical Treatise on the Construction of Oblique Arches," by J. Hart.

SECTION VII.

SUPERELEVATION OF EXTERIOR RAIL IN CURVES.

The superelevation of the exterior rail in curves, the radii of which are within certain limits, is absolutely necessary to counteract the centrifugal force caused by the velocity of the train, since all moving bodies have a tendency to continue their motion in a direct line. From this cause the carriages of a railway train are driven towards the exterior rail, and would finally be thrown off the rails,

were it not for the conical inclination of the tire and the flanges of the wheels.

Let wweight of the moving body or train, v = its velocity per second, R= radius of the curve, and g-force of gravity at the earth's surface; then, by Dynamics, the centrifugal force

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When R1 mile = 5280 feet, V = velocity = 60 miles per hour =88 feet per second, and g= 321 feet, then

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that is, the centrifugal force that urges the moving body to leave the curve, in this case, is of its weight.

This force is slightly counteracted by the conical inclination of the tire of the wheels, each pair of which are firmly fixed on the axle that turns with them. This inclination of the tire, together with the lateral play of the flanges of an inch on each side, and the centrifugal force impelling the carriages of the train, when moving in a curve, towards the exterior rail, enlarge the diameter of the exterior wheel, and diminish that of the interior, thus causing the train to roll on conical surfaces, which necessarily produces a centripetal force, the centre of which force is the vertex of the cone, of which the increased and diminished diameters of each pair of wheels are sections.

Let d be the outer diameter of the wheels, d the increment and consequently the decrement that the diameters of the exterior and interior wheels respectively receive, through the joint action of the centrifugal force and the inclination of the tire: then under these circumstances the respective diameters of the exterior and interior wheels will be

dx 8 and d-d

also if R' be the radius of a circle which the centre of the carriage would describe in consequence of the inclination of the tire of the wheels, and b the breadth of the road or gauge : then R' + b and Rb are the radii which would be respectively described by the exterior and interior wheels; and by similar triangles

d + ò: d- ô :: R' + 16: R'-1b,

whence d: 8: 2R: b, and

bd R= 2

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inclination of the tire, and ▲ the deviation of the

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Also w and v representing the weight and velocity of the train, as in (1), and g the force of gravity, the centripetal force corresponding to the radius R' will be

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Since the forces f and f' (1) and (3), act in contrary directions, they will hold each other in equilibrium when they become equal, and the train will cease to have a tendency to leave the curve ; this takes place when

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which is the deviation required to produce the equilibrium between the centripetal and centrifugal forces of the train. Therefore since R = R', i.e., the vertex of the imaginary cone of which each pair of wheels are sections will coincide with the centre of the curve, there will in consequence be no dragging of either of the wheels on the rail.

In practice, however, it is safer to neglect the effect of the coning of the tires, and to calculate the superelevation of the rail as if the tires were cylindrical.

The rule for this is as follows:-
:-

Let R =

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radius of curve in chains

breadth of gauge of the line in feet; or more properly, the distance from centre to centre of rails.

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