(200.)

In the autumn of 1838 a course of experiments was commenced at the suggestion of some of the proprietors of the Great Western Railway Company, with a view to determine various points connected with the structure and the working of railways. A part of these experiments were intended to determine the mean amount of the resisting force opposed to the moving power, and this part was conducted by me. After having tried various expedients for determining the mean amount of resistance to the moving power, I found that no method gave satisfactory results except one founded on observing the motion of trains by gravity down steep inclined planes. When a train of waggons or coaches is placed upon an inclined plane so steep that it shall descend by its gravity without any moving power, its motion, when it proceeds from a state of rest, will be gradually accelerated, and if the resistance to that motion was, as it has been commonly supposed to be, uniform and independent of the speed, the descent would be uniformly accelerated: in other words, the increase of speed would be proportional to the time of the motion. Whatever velocity the train would gain in the first minute, it would acquire twice that velocity at the end of the second minute, three times that velocity at the end of the third minute, and so on; and this increase of velocity would continue to follow the same law, however extended the plane might be. That such would be the law which the descending motion of a train would follow had always been supposed, up to the time of the experiments now referred to; and it was even maintained by some that [Pg409] such a law was in strict conformity with experiments made upon railways and duly reported. The first experiments instituted by me at the time just referred to afforded a complete refutation of this doctrine. It was found that the acceleration was not uniform, but that with every increase of speed the acceleration was lessened. 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, and so on. 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. In effect, since the moving power which impels a train down an inclined plane of uniform inclination is that fraction of the gross weight of the train which acts in the direction of the plane, this moving power must be necessarily invariable; and as any acceleration which is produced must arise from the excess of this moving power over the resistance opposed to the motion of the train, from whatever causes that resistance may arise, whenever acceleration ceases, the moving force must necessarily be equal to the resistance; and therefore, when a train descends an inclined plane with a uniform velocity, the gross resistance to the motion of the train must be equal to the gross weight of the train resolved in the direction of the plane; or, in other words, it must be equal to that fraction of the whole weight of the train which is expressed by the inclination of the plane. Thus if it be supposed that the plane falls at the rate of one foot in one hundred, then the force impelling the train downwards will be equal to the hundredth part of the weight of the train. So long as the resistance to the motion of the train continues to be less than the hundredth part of its weight, so long will the motion of the train be accelerated; and the more the hundredth part of the weight exceeds the resistance, the more rapid will the acceleration be; and the less the hundredth part of the weight [Pg410] exceeds the resistance, the less rapid will the acceleration be. If it be true that the amount of resistance increases with the increase of speed, then a speed may at length be attained so great that the amount of resistance to the motion of the train will be equal to the hundredth part of the weight. When that happens, the moving power of a hundredth part of the weight of the train being exactly equal to the resistance to the motion, there is no excess of power to produce acceleration, and therefore the motion of the train will be uniform.

Founded on these principles, a vast number of experiments were made on planes of different inclinations, and with loads of various magnitudes; and it was found, in general, that when a train descended an inclined plane, the rate of acceleration gradually diminished, and at length became uniform; 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 former editions of this work having been published before the discovery which has resulted from these experiments, the average amount of resistance to railway trains, there stated, and the conclusions deduced therefrom, were in conformity with what was then known. It was stated that the resistance to the moving power was practically independent of the speed, and on level rails was at the average rate of about seven pounds and a half per ton. This amount would be equivalent to the gravitation of a load down an inclined plane falling 1⁄300, and consequently in ascending such a plane the moving power would have to encounter twice [Pg411] 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 1⁄300. 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.