that is the force, in this case, is of the weight of the train. Hence it may be perceived how extremely dangerous high velocities are in curves of small radius.

3. When the radius is = 1 mile = as in example 2; then

FW.

5280 feet, and V the same

This force, except in curves of very small radius, is counteracted by the conical inclination of the tire of the wheels of the engine and its train. The inclination with the lateral play of the flanges of the 2 wheels of about an inch on each side, and the centrifugal force urging the train towards the outer rail, when moving in a curve, increase the diameter of the outer wheel and diminish that of the inner one, which causes the train to roll on a conical surface, thus necessarily producing a centripetal force to counteract the tendency of the train to leave the curve. However, in curves of very small radius, the centripetal force thus generated, does not sufficiently counteract the centrifugal force, a proper super-elevation of the exterior or outer rail being required for this purpose; for determining which Pambour has given in his work on Locomotive Engines, the following.

FORMULE FOR THE SUPER-ELEVATION OF THE EXTERIOR RAIL. Let V = velocity of the train, R = radius of railway curve, R': = radius of the curve that the train would describe in consequence of conical shape of the tire of the wheels, and the centrifugal force impelling the train outward, and enlarging the diameter of the outer, and diminish that of the inner wheel, gauge of rails, g force of gravity, and a super-elevation

e

=

of outer or exterior rail; then

for the same curve: thus for a velocity of 120 miles per hour, on a curve of a mile radius, we shall have

that is, the centrifugal force is, in this case, more than

of the whole weight of the train; while for curves of 1 mile radius, which are very common in railways, f=W, or nearly of the weight of the train. It must, therefore be evident that a velocity of 120 miles per hour, or even one of 90 miles per hour, must be extremely dangerous, especially on an embanked curve, should any accident throw the train off the line, which is often the case with the present velocities. Moreover, the resistance of the air, which varies as V2, must be considerably augmented by high winds opposed to the direction of a train of these great velocities; while its engine would require a power greatly superior to those

zow in use.

d being

=outer diameter of the wheels, A deviation of the wheels, and = the inclination of the tire.

n

Concise and, he trusts, clear demonstrations of the above formulæ are given by the author, in his Railway Engineering. By solving these formula for some of the usual cases, Pambour produces the following.

TABLE OF THE SUPER-ELEVATION TO BE GIVEN TO THE EXTERIOR RAIL IN CURVES.

The correctness of the above results is pretty generally conceded. It must, however, be considered, that it is extremely difficult, if not impossible, to realize in practice, the precise conditions and proportions determined by these important formula; as accidental depressions and enlargements of guage of part of the rails, as well as many other matters that cannot be subjected to calculation, will unavoidably derange these results.

The reader, who wishes for further information on these subjects, may consult Tredgold on the Steam Engine; Hann's Treatise on the Steam Engine; and Baker's Statics and Dy

namics.

APPENDIX.

RAILWAY VIADUCTS OR BRIDGES.

There are few parts of a railway which strike the eye so much as the viaducts and bridges, some of which form the masterpieces of our railway engineers. The dimensions of the chief specimens are here given.

TUBULAR AND OTHER IRON GIRDER BRIDGES.

The Britannia tubular bridge.-This structure, combining unparallelled magnitude, strength, and novelty, forms one of the viaducts of the Chester and Holyhead Railway. It crosses the Menai Straits, uniting the shores of the mainland of Wales and the Isle of Anglesea. It consists of two rectangular tubes, each 1513 feet in length, or of a mile, 26 feet in average depth, and 11 feet 8 inches in width, the internal depth and width being respectively reduced by the construction to 22 and 14 feet. Each tube has four spans, and consequently three piers or towers, exclusive of the abutments. The two middle

spans, in each tube, are each 460 feet, and the two end spans each 230 feet, exclusive of the widths of the towers, which support the tubes at a height of 102 feet above high water mark, the whole height of the middle tower being 200 feet above high water mark, or 230 feet from its foundation. The parts of the tubes forming the middle spans were 472 feet in length, previous to their being united, and weighed upwards of 1600 tons, and were raised to their present lofty position by hydraulic presses worked by steam engines, thus leaving the navigation of the Menai Straits uninterrupted.

"It is seldom," says Mr. G. D. Dempsey, "that the invention of works of new design and skilful mechanical arrangement is due entirely to one mind, any more than their construction is due to one pair of hands: hence great difficulty arises in assigning to each contributor his fair share of merit in their production. It must, however, be admitted, that to Mr. R. Stephenson alone we are in this instance indebted for the original suggestion; and with this admission, we have endeavoured to avoid any attempt to judge of the precise claims of the two eminent men, whose joint labours have produced the

Britannia and Conway Tubular Bridges. That these great works owe their design and construction to their joint labours is clearly evident, and, we respectfully submit, amply sufficient to justify the record of the two names of Robert Stephenson and William Fairbairn in an honourable and enduring association." The machinery for raising these immense tubes was designed and executed by Messrs. Easton and Amos.

The Conway tubular bridge, in the same line of railway, preceded the Britannia, having been raised in 1848. It consists of one span only of 400 feet, clear width: the height of the tubes above the level of high water is

inconsiderable, when compared with the Britannia tubes, being only 18 feet. The bridge thus consists of two tubes only, each weighing 1300 tons. It is erected close beneath the ancient wall of Conway Castle, its abutments being of strong masonry, the designs of which are in harmony with that of the castle.

IRON TUBULAR GIRDER BRIDGES.

The

The first tubular girder bridge designed and constructed by Mr. Fairbairn, was for the purpose of carrying the Blackburn and Bolton Railway over the Leeds and Liverpool Canal. span of this bridge is 60 feet, the two lines of rails being carried between three parallel girders. The cellular work in girders of this kind constitutes their great strength, combined with comparative lightness, the same kind of cellular work being introduced both in the top and bottom of the tubes of the Britannia and Conway Bridges.

The Gainsborough tubular girder bridge is the largest yet constructed of this kind. It forms the viaduct of the Manchester, Sheffield, and Lincolnshire Railway over the Trent; and consists of two spans, each 154 feet wide, with a central pier and abutments of masonry, and two end arches each 40 feet span. This bridge crosses the river obliquely