inch above the atmospheric pressure, which was therefore the major limit of the pressure of steam in the boiler; but as the actual pressure in the boiler must have been less than this amount, the difference between the pressure in the cylinder and boiler could not be ascertained. This difference, however, would produce no effect on the moving power of the steam, since the pressure of steam in the cylinders obtained by the above calculation is quite independent of the pressure in the boiler, or of any source of error except what might arise from priming. The pressure of 54-5 pounds per square inch, calculated above, being the total pressure of the steam on the pistons, let 14.5 pounds be deducted from it, to represent the atmospheric pressure against which the piston must act, and the remaining 40 pounds per square inch will represent the whole available force drawing the train and overcoming all the resistances arising from the machinery of the engine, including that of the blast-pipe. The magnitude of a 121 inch piston being 122.7 square inches, the total area of the two pistons would be 245.2 square inches, and the pressure upon each of 40 pounds per inch would give a total force of 9816 on the two pistons. Since this force must act through a space of three feet, while the train is impelled through a space of 157 feet, it must be reduced in the proportion of 3 to 157, to obtain its effect at the point of contact of the wheels upon the rails: this will give 1875 pounds as the total force exerted in the direction of the motion of the train. The gross weight of the train being 80 tons, including the engine and tender, this would give a gross moving force along the road of about 23.4 pounds per ton of the gross load, this force being understood to include all the resistances due to the engine. This resistance corresponds to the gravitation of a plane rising at the rate of, and therefore it appears that such would be the inclination of the plane by the gravitation of which the gross resistance would be doubled, instead of such inclination being about, as has been hitherto supposed.

Since the remarkable and unexpected results of this series of experiments became known various circumstances were brought to light, which were before unnoticed, and which

abundantly confirm them. Among these may be mentioned the fact, that in descending the Madeley plane, on the Grand Junction Railway, which falls for above three miles at the rate of twenty-nine feet a mile, the steam can never be entirely cut off. But, on the other hand, to maintain the necessary speed in descending, the power of the engine is always necessary. As this plane greatly exceeds that which would be sufficient to cause the free motion of the train down it, the power of the engine expended in descending it, besides all that part of the gravitating power of the plane which exceeds the resistance due to friction and other mechanical causes must be worked against the atmosphere.

This estimate of the resistance is also in conformity with the results of a variety of experiments made by me with trains of different magnitudes down inclined planes of various inclinations.

(202.) In laying out a line of railway the disposition of the gradients should be such as to preserve among them as uniform a character as is practicable, for the weight and power of the engine must necessarily be regulated by the general steepness of the gradients. Thus if upon a railway which is generally level, like that between Liverpool and Manchester, one or two inclined planes of a very steep character occur, as happens upon that line, then the engine which is constructed to work upon the general gradients of the road is unfit to draw the same load up those inclinations which form an exception to the general character of the gradients. In such cases some extraordinary means must generally be provided for surmounting those exceptionable inclinations. Several expedients have been proposed for this purpose, among which the following may be mentioned: :

1. Upon arriving at the foot of the plane the load is divided, and the engine carries it up in several successive trips, descending the plane unloaded after each trip. The objection to this method is the delay which it occasions a circumstance which is incompatible with a large transport of passengers. From what has been stated, it would be necessary, when the engine is fully loaded on a level, to divide its load into two or more parts, to be successively

carried up when the incline rises 52 feet per mile. This method has been practised in the transport of merchandise occasionally, when heavy loads were carried on the Liverpool and Manchester line, upon the Rainhill incline.

2. A subsidiary or assistant locomotive engine may be kept in constant readiness at the foot of each incline, for the purpose of aiding the different trains, as they arrive, in ascending. The objection to this method is the cost of keeping such an engine with its boiler continually prepared, and its steam up. It is necessary to keep its fire continually lighted, whether employed or not; otherwise, when the train would arrive at the foot of the incline, it should wait until the subsidiary engine was prepared for work. In cases where trains would start and arrive at stated times, this objection, however, would have less force. This method is at present generally adopted on the Liverpool and Manchester line.

3. A fixed steam-engine may be erected on the crest of the incline, so as to communicate by ropes with the train at the foot. Such an engine would be capable of drawing up one or two trains together, with their locomotives, according as they would arrive, and no delay need be occasioned. This method requires that the fixed engine should be kept constantly prepared for work, and the steam continually up in the boiler.

4. In working on the level, the communication between the boiler and the cylinder in the locomotives may be so restrained by partially closing the throttle-valve, as to cause the pressure upon the piston to be less in a considerable degree than the pressure of steam in the boiler. If under such circumstances a sufficient pressure upon the piston can be obtained to draw the load on the level, the throttle-valve may be opened on approaching the inclined plane, so as to throw on the piston a pressure increased in the same proportion as the previous pressure in the boiler was greater than that upon the piston. If the fire be sufficiently active to keep up the supply of steam in this manner during the ascent, and if the rise be not greater in proportion than the power thus obtained, the locomotive will draw the load up the incline without further assistance. It is, however, to be observed, that in this case

the load upon the engine must be less than the amount which the adhesion of its working wheels with the railroad is capable of drawing; for this adhesion must be adequate to the traction of the same load up the incline, otherwise, whatever increase of power might be obtained by opening the throttlevalve, the drawing wheels would revolve without causing the load to advance. This method has been generally practised upon the Liverpool and Manchester line in the transport of passengers; and, indeed, it is the only method yet discovered which is consistent with the expedition necessary for that species of traffic.

In the practice of this method considerable aid may be derived also by suspending the supply of feeding water to the boiler during the ascent. It will be recollected that a reservoir of cold water is placed in the tender which follows the engine, and that the water is driven from this reservoir into the boiler by a forcing pump, which is worked by the engine itself. This pump is so constructed that it will supply as much cold water as is equal to the evaporation, so as to maintain constantly the same quantity of water in the boiler. But it is evident, on the other hand, that the supply of this water has a tendency to check the rate of evaporation, since in being raised to the temperature of the water with which it mixes it must absorb a considerable portion of the heat supplied by the fire. With a view to accelerate the production of steam, therefore, in ascending the inclines, the engine man may suspend the action of the forcing pump, and thereby stop the supply of cold water to the boiler; the evaporation will go on with increased rapidity, and the exhaustion of water produced by it will be repaid by the forcing pump on the next level, or still more effectually on the next descending incline. Indeed the feeding pump may be made to act in descending an incline, if necessary, when the action of the engine itself is suspended, and when the train descends by its own gravity, in which case it will perform the part of a brake upon the descending train.

5. The mechanical connexion between the piston of the cylinder and the points of contact of the working wheels with the road may be so altered, upon arriving at the incline, as to

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give the piston a greater power over the working wheels. This may be done in an infinite variety of ways, but hitherto no method has been suggested sufficiently simple to be applicable in practice; and even were any means suggested which would accomplish this, unless the intensity of the impelling power were at the same time increased, it would necessarily follow that the speed of the motion would be diminished in exactly the same proportion as the power of the piston over the working wheels would be increased. Thus, on the inclined plane, which rises fifty-five feet per mile, upon the Liverpool line, the speed would be diminished to nearly one fourth of its amount upon the level.