carriages resting upon the two rails, such an inclination as will produce upon the carriages a gravitating force towards the centre of the curve, equal in amount to that of the centrifugal force outwards, there will be no tendency in the carriages to upset, or to press the wheels against the rails. It is obvious that the smallest curvature should have a considerable radius: Mr. Wood states that a radius of 565 feet is less than ought to occur in any curvature on a railway. In going round a height, the radius ought to be considerably larger, in order to allow the engine driver to look out, so as to prevent collisions from trains travelling in either direction.

130. Of Gradients.—Gradients are inclinations of the road, and are obviously of two kinds, ascending and descending. 1. In the case of ascending gradients, in which the inclination exceeds a certain limit, additional power must be given to the engine, in order to overcome the increased effect of gravity. Various methods have been adopted for this purpose: a subsidiary locomotive engine is kept in readiness at the foot of the gradient, in order to assist the train on its arrival, as is generally adopted on the Liverpool and Manchester line; or a fixed engine is placed on the summit of the gradient, and communicates by a rope with the train at the foot of the plane; or the load is divided at the foot of the gradient, and the engine carries it up by two or more ascents, as has been occasionally done on the Rainhill inclination of the Liverpool and Manchester Railway. 2. In the case of descending gradients, the increased velocity arising from gravity must be checked by means of a break; this consists of a curved piece of wood, which fits the circumference of some of the wheels of the carriages, and is pressed upon them by a lever worked by the engine driver with more or less force, according to the declivity of the gradient, or the velocity with which it is desirable for the train to descend. The subject of gradients will be noticed again presently.

DIFFERENT KINDS OF FRICTION.

185

OF RESISTANCE ON RAILROADS.

131. Different kinds of Friction. In all locomotive engines, a certain degree of obstruction, or resistance, is caused by friction. There are two kinds of friction, the rubbing friction of the axles sliding within their chairs or bearings,* and the rolling friction of the circumference of the wheels upon the rails; but, as both these retarding forces are in operation at the same time, it is usual to comprehend both kinds under the general term friction or resistance. Until a recent period, almost the total amount of resistance to the progressive motion of an engine was referred to the mechanical obstructions above mentioned. The total amount of resistance has been variously stated by different authorities: on a well-constructed level, it has been generally estimated at the 240th part of the gross load; on inclined planes, the ordinary resistance is, of course, increased by the effect of gravity, and the power of traction must be proportionably increased. According to this mode of calculation, an ascent of one foot on a plane of 240 feet, would require the power of traction to be doubled; on an ascent of two feet in 240, the power must be trebled; on an ascent of three feet, it must be fourfold; and so on. Hence, it appears that a very slight inclination involves a very considerable increase of the power of traction: the

*The annexed figure represents the simplest form of axle, and plan of bearing. A represents an end view of an axle, which revolves in the direction of the arrow. B represents

a cast or wrought-iron chair, which is secured to the framing of the carriage by bolts, with a semicircular bearing for the axle to work in. The bearings are placed within, or outside, the wheels of the carriage. The lubricating matter C is placed against the axle, so as to keep up a continual supply, and ensure a uniform action.

A

B

Fig. 74.

186

M. PAMBOUR'S CALCULATIONS.

Rainhill inclination, on the Manchester railway, rises one foot in 96, and would, accordingly, require the amount of ordinary traction to be increased fourfold. But this mode of calculation has recently been called in question.

132. M. Pambour's Calculations.-In 1834, M. Pambour instituted a series of valuable experiments upon the Liverpool and Manchester Railway, in order to determine the amount of friction, or resistance to traction, in locomotive engines as at present constructed. The portion of the line selected was on the Sutton Plane, which is a uniform inclination of nearly 1 in 100; at the bottom of the plane, the line is nearly level. His plan was to start the carriages from a given point on the plane, to allow them to run down the plane, and to be brought to rest by their friction on the level part of the line below. Stakes were set up at intervals of 330 feet; the distances, and corresponding descent of level from the starting point to the different stakes, in feet, were carefully noted. The details of these experiments are described in the Traité des Machines Locomotives of M. Pambour. The conclusions at which he arrived, are as follow. 1. The average resistance of the carriages, without the engine and tender, is about 8 lbs. per ton of the gross weight of the carriages and load. 2. The average resistance of locomotive engines, in good order, is about 15lbs. per ton of their weight. 3. The resistance of the engine is increased by the load at an average of about 1 lb. per ton. In these experiments, the average resistance of the single carriages was estimated at the 206th, that of the carriages in trains at the 262d, part of the weight. These results are considered by Mr. Wood as too favourable; they may, however, be taken as approximate estimations for locomotive engines as at present constructed.

133. Dr. Lardner's Experiments.—In the autumn of 1838, a series of experiments was performed by Dr. Lardner, in order to determine the mean amount of the resisting force opposed to the moving power; the plan adopted, was to observe the motion of trains descending steep inclinations.

DR. LARDNER'S EXPERIMENTS.

66

187

Contrary to the opinion previously entertained, it was found. that the acceleration was not uniform, but that it actually lessened with increase of speed. Thus, if a certain speed were gained by a train in one second when moving at five miles an hour, a much less speed was gained in one second when moving ten miles an hour, and a comparatively small speed was gained in the same time when moving at fifteen miles an hour. In fact, the augmentation of the rate of acceleration appeared to diminish in a very rapid proportion as the speed increased: this suggested to me the probability that a sufficiently great increase of speed would destroy all acceleration, and that the train would at length move at a uniform velocity." It was found that the uniform speed thus attained, depended on the weight, form, and magnitude, of the train, and the inclination of the plane; that the same train on different inclined planes attained different uniform speeds, on the steeper planes a greater speed being attained. "From such experiments it followed, contrary to all that had been previously supposed, that the amount of resistance to railway trains had a dependence on the speed; that this dependence was of great practical importance, the resistance being subject to very considerable variation at different speeds, and that this source of resistance arises from the atmosphere which the train encounters. This was rendered obvious by the different amount of resistance to the motion of a train of coaches and to that of a train of low waggons of equal weight."

"The tendency

134. Compensating effect of Gradients.of the results of these experiments shows that low gradients on railways are not attended with the advantageous effects which have been hitherto ascribed to them; that, on the contrary, the resistance produced by steeper gradients can be compensated by slackening the speed, so that the power shall be relieved from as much atmospheric resistance by the diminution of velocity, as is equal to the increased resistance produced by the gravity of the plane which is ascended. And, on the other hand, in descending the plane,

188

GURNEY'S STEAM CARRIAGE.

the speed may be increased until the resistance produced by the atmosphere is increased to the same amount as that by which the train is relieved of resistance by the declivity down which it moves. Thus, on gradients, the inclination of which is confined within practical limits, the resistance to the moving power may be preserved uniform, or nearly so, by varying the velocity. The principle of compensation by varied speed being admitted, it will follow, that the time of transit between terminus and terminus of a line of railway laid down with gradients, varying from twenty to thirty feet a mile, will be practically the same as it would be on a line of the same length constructed upon a dead level; and not only will the time of transport be equal, but the quantity of moving power expended will not be materially different. The difference between the circumstances of the transport in the two cases will be merely, that, on the undulating line, a varying velocity will be imparted to the train, and a varying resistance opposed to the moving power; while, on the level line, the train would be moved at a uniform speed, and the engine worked against a uniform resistance."-Lardner On the Steam Engine, 7th edit., p. 408, &c.

LOCOMOTIVE ENGINES ON COMMON ROADS.

135. Gurney's Steam Carriage.-The resistance of carriages on turnpike roads has been made the subject of experiment by the Holyhead Road Commissioners, and has been estimated at not less than 72lbs. per ton of the gross weight. But the resistance on turnpike roads is not increased by curvatures in the same proportion as it is on railroads; and, hence, the increased power required by them is not so great proportionally on the former, as on the latter, kind of road. Further, it has been found that there is sufficient adhesion between the wheels of carriages and the surface of common roads, to propel a train of loaded carriages along them. These and other circumstances have