gers, at a high rate of velocity, by having more powerful engines it is perfectly practicable.

We must, in this case, however, either increase the diameter of the wheels propelling the engine, or cause them to make a greater number of revolutions than one, for each double stroke of the piston. For a velocity of twenty miles an hour, a wheel of five feet is generally used; suppose the length of the stroke of the cylinder sixteen inches, this will cause the piston to travel at the rate of about 270 feet per minute, which is quite as great a velocity as should be attempted. It follows, therefore, that we must either shorten the length of the stroke, which is attended with a great waste of steam, at each change of motion, or increase the diameter of the propelling wheels of the engine, to accomplish a higher rate of speed. If the latter is done, the increase should be in the ratio of the velocity; and, therefore, if the rate of travelling is to be thirty miles an hour, the diameter of the wheels should be seven feet and a half; and forty miles, ten feet; fifty miles, twelve feet and a half; and sixty miles, fifteen feet; or, which would amount to the same effect, smaller wheels increased in velocity by cog-wheels.

Mr. Harrison, of the Stanhope and Tyne railway, has a patent to effect the velocity by the latter method, which is to be tried on the Great Western railway; and Mr. Brunel is likewise increasing the size of his propelling wheels to ten feet in diameter.

We now give a table of the performances of several of the engines on the Liverpool and Manchester railway, as observed by M. Pambour, in his inquiries on the subject of the powers of locomotive engines, which can be compared with the preceding theoretical tables.

f-Theory of the Power of Engines on Inclined

Planes.

Having thus ascertained the load, which a locomotive engine can drag at different rates of velocity upon a horizontal railway; we now come to the effect of inclined planes, occurring on the line of road, to which all lines of railway are subjected. Considerable discussions have arisen upon this part of the subject, not only for the purpose of determining the absolute weight, which an engine is capable of dragging upon given inclined planes; but for the purpose of comparing the relative merits of different or competing lines of road with each other, where the planes or gradients were not the same in the intermediate parts of the road, but where the level of the two termini were the same. Professor Barlow, and Dr. Lardner, have been most prominent in this inquiry, and both these gentlemen have given theories on the subject. Without going into all the theoretical considerations of the question, which would extend our inquiries further than our limits will allow, we shall endeavour to consider the subject in its application to practice.

We have already seen, that the production of the steam does not vary materially from, but that it may be considered as, a constant quantity; and that the pressure in the cylinder, is always less than that in the boiler, and further, that this difference becomes greater as the velocity of the engine, is increased. Suppose then, that a locomotive engine travelling along a horizontal plane, arrives at the foot of an ascending plane; in addition to the friction and resistance of the load, the engine has then to overcome the gravity of the plane upon the whole train, engine and tender included; the

resistance R, is therefore increased, and the velocity, v, will be diminished, until the pressure in the cylinder becomes nearly the same as that in the boiler, when the motion will become uniform, and will be equal to that which the evaporating power of the engine will supply steam at that elasticity, which is competent to overcome the aggregate resistances.

In all ascending planes, therefore, we must add to the resistance, R, the effect of the gravity upon the load; and the gravitation of the load, has likewise the same effect upon the friction of the engine as that of the load, м; making, therefore, & equal the gravitation of the whole train, we have F+M+G=the friction of the engine, and n M+G=the resistance and friction of the train.

=

The resistance, R, upon ascending planes, will then be

D

= [F+ (¿ M + G) + n M+G+P, and, therefore, by applying this to the preceding theorems, we can readily ascertain the load which an engine can drag up any plane of a given inclination; or the rate of speed at which an engine will travel up such plane with a given load.

We come now to the effect upon descending planes, in this case, the gravitation of the load upon the plane diminishes the resistance, and, therefore, must be taken from it, and, consequently, R, will be = [F+(8 M-G)+ n M-G] del +P, from which, by adopting the theorems in the preceding section, we can determine the load which an engine will drag down any plane with a given inclination; or the velocity, which such engine will travel upon such plane with a given load.

This expression must, however, be taken subject to

certain limitations. We may suppose, that, in the case of an engine traversing a horizontal plane, the resistance, R, may be so diminished, that the velocity may become greater than it is prudent to keep up; in such a case, by closing the damper in the chimney, the production of the steam is diminished, until the velocity becomes uniform, and the limit of speed will then be that which it is deemed advisable in practice to attain. This operation becomes more apparent, in the case of a train descending a plane. Upon a horizontal plane, the production of steam being as the time, and not as the velocity, when the speed increases, the elasticity of the steam in the cylinders is reduced; and, therefore, the moving power is diminished, and, consequently, the motion at last becomes uniform, unless the resistance is so much diminished, that, before reaching that extent, the velocity becomes dangerous; when, by management, the rapidity of production of steam is also checked, until an uniform velocity is attained.

In the case of an engine and train descending a plane, the case is different. We may suppose the inclination to be such, that the gravitation diminishes the resistance of the engine and carriages, to so great an extent, that no steam is required, and gravity being a constant force, the motion then becomes an accelerated one; or the gravitation may be such, as to diminish the resistance to such an extent, as that, added to the force of steam acting on the pistons, the velocity becomes accelerated, and is allowed to increase until it reaches the limit of safety. Artificial means, or the brake, is then obliged to be resorted to, to check the further acceleration, and reduce the speed to a uniform and safe velocity. We shall take a case where the inclination is such, that the gravity will not urge the load down the plane, with sufficient velocity, but that a