the resistance opposed to it on a level. As it was generally assumed that a locomotive-engine could not advantageously vary its tractive power beyond this limit, it was therefore inferred that gradients (as inclinations are called) ought not to be constructed of greater steepness than . It was supposed that in descending gradients more steep than this the train would be accelerated and would require the use of the brake to check its motion, while in ascending such planes the engine would be required to exert more than twice the ordinary tractive power required on level rails. As the resistance produced by the air was not taken into consideration, no distinction was made between heavy trains of goods presenting a frontage and magnitude bearing a small proportion to their gross weight and lighter trains of passenger-coaches presenting great frontage and great magnitude in proportion to their weight. The result of the experiments above explained leads to inferences altogether at variance with those which have been given in former editions of the present work, and which were then universally admitted by railway engineers. The tendency of the results of these experiments show 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 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.

(201.) The series of experiments which have established these general conclusions have not yet been sufficiently extended and varied to supply a correct practical estimate of the limit

gradients of railways; but it is certain that railways may be laid down, without practical disadvantage, with gradients considerably steeper than those to which it has been hitherto the practice to recommend as a limit.

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. These conclusions have been abundantly confirmed by the experiments made in last July with the Hecla engine above referred to. The line of railway between Liverpool and Birmingham on which the experiment was made extended over a distance of ninety-five miles, and the gradients on which the effects were observed varied from a level to thirty feet per mile, a great portion of the line being a dead level. The following table shows the uniform speed with which the train ascended and descended the several gradients, and also the mean of the ascent and descent in each case, as well as the speed upon the level parts of the line:

From this table it is apparent that the gradients do possess the compensating power with respect to speed already mentioned. The discrepancies existing among the mean values of the speed are only what may be fairly ascribed to casual variations in the moving power. The experiment was made under favourable circumstances: little disturbance was produced from the atmosphere; the day was quite calm. In the same experiment it was found that the water evaporated varied very nearly in proportion to the varying resistance, and the amount of that evaporation may be taken as affording an approximation to the mean amount of resistance. Taking the trip to and from Birmingham over the distance of 190 miles, the mean evaporation per mile was 3.36 cubic feet of water. The volume of steam produced by this quantity of water will be determined approximately by calculating the number of revolutions of the driving wheels necessary to move the engine one mile. The driving wheels being 5 feet in diameter, their circumference was 15.7 feet, and consequently in passing over a mile they would have revolved 336-3 times. Since each revolution consumes four cylinders full of steam, the quantity of steam supplied by the boiler to the cylinders per mile will be found by multiplying the contents of the cylinder by four times 336-3, or 1345.2.

The cylinders of the Hecla were 12 inches diameter, and 18 inches in length, and consequently their contents were 1.28 cubic feet for each cylinder: this being multiplied by 1345.2 gives 1721.86 or 1722 cubic feet of steam per mile. It appears, therefore, that supposing the priming either nothing or insignificant, which was considered to be the case in these experiments, 3.36 cubic feet of water produced 1722 cubic feet of steam, of the density worked in the cylinders, The ratio, therefore, of the volume of this steam to that of the water producing it, was 1722 to 3.36, or 512.5 to 1. The pressure of steam of this density would be 54.5 pounds per square inch.* Such, therefore, was the limit of the average total pressure of the steam in the cylinders. In this experiment the safetyvalve of the boiler was screwed down to 60 pounds per square

* See Table of Pressures, Temperatures, and Volumes, in appendix.

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 12 inch piston being 1227 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 o, 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