rely upon the size of the blocks, and the mode of fixing them, being such as that no displacement will take place, or contrive such a joint as will allow of a block being displaced, without destroying the parallelism of the rails. We have gone, somewhat largely, into this part of the subject, when treating on the plan of setting the blocks; but we find, in practice, that it is extremely difficult to form such a foundation for the blocks, as will not occasionally yield, and produce the displacement of the rails. The plan of half-lapped joints, if the principles on which that plan is based could be fully carried into effect, in practice, would, to a very considerable extent, remedy, if not entirely remove, the evil; but there are great obstacles, in working out that theory, in practice. In the first place, in forming a half-lapped joint, by simply cutting or splitting the rail into two equal parts at the ends, the middle rib and base are so reduced in thickness, that, in practice, we find them laminating, or becoming crushed; it is, therefore, essential, in the construction of such a rail, either that the middle rib and base should be entirely set to one side, so as to preserve a sufficient thickness of iron to resist the pressure; or, that a portion of iron should be welded upon the end of the half lap, to form an adequate base to prevent its being crushed. These, and especially the latter, it will be seen, increases the cost of the rails, and therefore, in some cases, may be considered an important objection; and, in the next place, it is difficult, unless very great pains are taken, in the construction of the ends of a half-lapped joint, to form it in such a manner, as that, when a block is displaced, one end shall not be raised above that of the other ; as it requires to be to be a little rounded at the extreme end of the half lap. There can be no doubt,

however, if the funds of any railway company will allow of the more perfect mode of manufacturing this description of rail; and it be the intention to form a perfectly smooth line of railway, that the plan of forming the joints, in such a manner, effects that object better than rails with square ends. Sometimes, instead of making the half lap parallel, the ends of the rails are cut diagonally; but this forms a joint, with all the objections of the crushing at the ends, and does not completely obviate the shocks, by one end being raised above the other.

In considering the subject of the best form of joining the ends of the rails, we must not omit taking into account, the effect of the expansion and contraction of the rails, by the variation of temperature. We have seen, in § 6, Chap. III., that this amounts to about the fifteenth part of an inch, in a rail fifteen feet in length. Supposing the chairs and blocks to remain firm, this will be equal to the thirtieth part of an inch, at each end of every rail; and therefore, if the rails were laid down at the maximum degree of temperature, the open space between the ends, with a square joint, would amount to the fifteenth part of an inch; and would, therefore, present a shock to the carriage wheels in passing. In this case, the extent, which the half-lapped ends of the rails of that description of joint would have to slide against each other, would be the same distance, or the fifteenth part of an inch, when the temperature was at the lowest. This is, supposing the ends of the rails to be allowed to slide within the chair.

On referring to Chapter II., it will, however, be seen, that almost all the modes of fastening the rails to the chairs, is upon the principle of their being immoveably

keyed thereto, and, therefore, when perfect, no allowance is made for the variation of length, by the increase or diminution of temperature. This seems to imply, that it is the universal opinion of engineers, that no regard should be paid, in forming the joints, to the effect of the expansion or contraction. In laying down the railway however, the practice is, to keep the ends of the rails about a sixteenth of an inch separate; if the rails are laid in the medium temperature of the year, we find that in summer, the ends become quite close together, and in winter, they again open; although the principle of keying, is that of an immoveable joint.

According to the experiments of Barlow, a bar of iron is extended the one ten thousandth part of its length, by every ton of direct strain, per square inch of section. Now, suppose the railway bar to be of a sectional area equal to five square inches, this would be five tons per one ten thousandth part of an inch extension; and as we see the contraction between the maximum and minimum temperature, is equal to the fifteenth part of an inch, or, in a fifteenth feet bar, equal to the two thousandth part of the length of the bar, or five times that which the strain of one ton would effect; we find, therefore, that the strain upon each chair by the keys, if firmly fixed, would be equal to twenty-five tons. Any mode of keying the rails to the chairs, upon the principle of firmly securing the one to the other; would, therefore, impose such a strain upon the chair and rails, as would have considerable effect in breaking the former, and of diminishing the tensile force of the latter. In practice, therefore, when such a mode of keying is adopted, and when a space of about one sixteenth of an inch is left between the rails, it appears that the expansion in summer extends the ends, so as to become quite close, and,

if then keyed, we are convinced, that the rails are permanently lengthened by the action of the key, and the motion of the wheels upon the rails; and that the action of the temperature operates more in expanding, than in contracting, the rail; and hence, we find, in summer, the rails twist and bend as they become lengthened by the expansion, and in winter, the ends become partially opened by the contraction, but not to the extent which the temperature would produce, if there were not a certain degree of compression acting upon them previously. No doubt, the imperceptible, slow, but powerful effect of the heat, added to the tremour and motion occasioned by the wheels; produces a working of the keys, and they thus yield and become loose, and allow the rail to accommodate itself to the expansion or contraction, produced by the variation of temperature.

If, therefore, in practice, we find a constant motion in the joints of the rails, by the action of the weather, and that no plan of keying hitherto adopted, can or, perhaps, ought to produce an immoveable joint; it would appear, that the only mode of preventing the shocks and blows incident to the opening of the joints, and to produce a perfectly smooth railway, would be to have recourse to the adoption of half-lapped joints, so that they could slide longitudinally, to counteract the effect of the expansion and contraction. But to produce such a joint, which would not crush or yield to the pressure of the wheels, it is necessary, we find, to incur a considerable expense in its formation. At the same time, we think it right to observe, that in a well-constructed railway, with large blocks, well laid, and with heavy rails, a comparatively smooth and level railway can be formed with square joints; and that on almost all the modern railways, such a joint is used.

§ 15.-On Curves, on the Line of Railway. Where the line of railway is perfectly straight, it is scarcely necessary to observe, that the rails should be laid perfectly horizontal, or in a plane with the gradient of the line longitudinally, and perfectly level transversely; but where there are curves on a line, the level transversely will require some consideration. That property in all bodies to continue their motion in a straight line, gives to the carriages upon railways, a tendency to move in a tangential direction; and hence, on approaching a curve or change in the direction of the line of railway, the carriages have a tendency to move in the direction of the tangent to the curve; and they are only kept upon the rails, or along the line of the curve, by the action of the flanch of the wheels, against the side of the rails. The wheels, which act against the rails, are the flanches of the wheels, which travel on the outside rails of the curve, and their flanches act against the inside of those rails.

All the wheels now used on railways, especially where curves occur on the line, are constructed, so that the outside rim is conical, or is enlarged in diameter next the flanch; when, therefore, the carriages are passing round a curve, the wheels being connected together by the axle, forms, as it were, a conical roller, running upon the rails with different radii; the larger radii being on the outside curve of the rail. This increase in the diameter of the wheel, running on the outside, compensates, to a certain extent, for the increased length of the outer curve of the rail; and if the radius of the curve, is not less than the line which the two wheels of unequal radii would describe, the wheels will travel along the line of the curve without rubbing against the flanches. But, if the curve is more acute than such a