The following Table will shew the result of the several preceding experiments, and the amount of deflection, for each ton of insistent weight, upon the different rails.

To compare the relative rigidity of parallel, with elliptic rails, it will be necessary to reduce all the experiments to the same length of bearing. With a view, therefore, of more clearly shewing the comparison, the following Table has been constructed, wherein the deflection shewn is, that which results from a length of bearing of thirty-six inches; those experiments only

being exhibited, which are, more particularly, capable of comparison, and the mean result of each experiment only is given.

On examining the above Table, and comparing the result with the different sectional areas of the two kinds of rails, it will be seen, that, with the same weight per yard, the elliptic rail is more rigid than the parallel; the two sections, which appear most nearly alike, being VII. and XI. in the elliptic, and XIV. and XVII. in the parallel rail. But it will be seen, on examining the section of these latter rails, that the lower flanch is much broader, than that which would give the greatest strength with the least material; and which is proved by the experiments in Table XVII. where the breadth of the rail was reduced, and, consequently, its weight, without producing any sensible effect, upon the rigidity. The conclusion, from these experiments, appears to be, that, by adopting the elliptic form, and thereby obtaining a

greater depth of iron, in the middle of the rail; a greater degree of rigidity is produced, in that form, with the same weight of material, than with a parallel bar, in the middle of the rail. In practice, however, it has been found, that the elliptic bars do not become injured, in the middle of the rail, but about nine inches from the bearing, or about one-fourth of the length between the bearings. This has been found to be the case, in the first rails laid down upon the Liverpool and Manchester railway, and, more particularly, upon other railways, which have come under our notice; where all the rails, which have broke, have failed about seven to nine inches from the bearing. This would shew, that, besides having to provide for a sufficient degree of rigidity, in the middle of the rail, the action of the carriages requires, that a greater degree of strength should be given to a railway bar, near the points of support, than is capable of sustaining the load, without injury; or, rather, that more than a uniform degree of strength should be given to that part of the bar. This, of course, extends only to a certain degree of additional strength, the above remarks applying to rails, either decidedly too weak, or of bad material; if stronger rails are used, which, we presume, will generally be done, no doubt, a saving of material, to a certain extent, may be accomplished, by the adoption of an elliptic form of rail.

Besides shewing the relative rigidity, of different sections of rails, these experiments are useful, in shewing the increase of effect between single lengths of rails, and long lengths, having several bearing points. In the first five Tables, the experiments will shew the result, between a single length of rail, and the whole combined. In those experiments, when said to be loose, the single division of the rail only, was fastened to its chairs at

each end, and those chairs fastened to the timber framing, by which the experiment was made; but when said to be fixed, all the chairs, of the several divisions of the rail, were fastened to the timber. The result exhibits a considerable increase of rigidity, and points out the advantage of long lengths of rails, and the necessity of adopting such a mode of fastening the rails to the chairs, as will effectually bind the whole together, and prevent the ends of the rail from rising out of the chair.

Having thus shewn, as well the relative, as the actual, rigidity of different sections of rails; it now becomes necessary to inquire, to what extent railway bars can be deflected, without producing an increase of resistance to the carriages passing along them.

§ 5.-Increase of Resistance, by the Deflection of Railway Bars.

When wrought-iron rails were first introduced, it was objected to them, that the resistance to the carriages was greater upon them, than upon cast-iron rails; experience, having proved that such was actually the case, on some railroads. The wrought-iron rails, when first laid down, were, however, much too weak for the strain which they were to sustain, and it was surmised, that the increase of resistance arose from the nature of the material, and not from the bending of the wrought-iron rails, from their deficient strength.

To ascertain, if, in the first place, any increase of resistance does actually exist, from the nature of the material, and, next, to what strain wrought-iron rails could be subjected, without increasing the resistance, the following experiments were made.

Two lengths of rails were laid down upon balks of wood, one of cast, and the other of malleable iron; both

of which were taken off the railway, in their working, and brightened, state; they were laid down, parallel with and close to each other, upon the same balks of timber, so that a pair of wheels resting on one could be readily lifted upon the other. Two wheels, joined together by an axle, and taken from one of the carriages in use, were then placed upon one of the lengths, and loaded on the lower side of the rim with weights, that could be varied at pleasure. The wheels, thus loaded on one point at the periphery, became like a pendulum; the centre of gravity, instead of being in the centre, was near the periphery. The wheels being placed on the rails, would, of course, only remain at rest, when the line of gravity, projected from the point resting on the rails, passed through the centre of the axle, joining the two wheels, and that part of the periphery which was loaded. When the wheels were rolled along the rails, until the line of gravity did not pass through the point of rest, but was several inches beyond it, and then let go, they, of course, vibrated backwards and forwards, until the resistance of the periphery of the wheels, upon the rails brought them to rest. This mode of experimenting was preferred, to trying the relative resistance by carriages; as, in experimenting with carriages, two species of friction are experienced, whereas, by this mode, there is no action, except that of rolling; and by lifting the wheels, alternately, from one kind of rail to the other, without altering the weight, the comparison upon cast and wrought iron became very delicate. A scale was used, to measure the extent of each vibration from the centre, and the observations were made by a telescope; and the number of oscillations were thus counted, while the extent of the vibrations was diminished each inch.