564 



THE STEAM-ENGINE. 



comparatively small speed was gained in the same time when moving at fif- 

 teen miles an hour, and so on. In fact, the augmentation of the rate of accel- 

 eration 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 pro- 

 duced 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 downward 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 accelera- 

 tion be ; and the less the hundredth part of the weight exceeds the resist- 

 ance, 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 hap- 

 pens, the moving power of a hundredth part of the weight of the train be- 

 ing 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 re- 

 sistance to railway-trains had a dependence on the speed ; that this de- 

 pendence was of great practical importance, the resistance being subject to 

 very considerable variation at different speeds, and that this source of re- 

 sistance 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 wagons of equal weight. 



The series of experiments which have established these general conclusions 

 have not yet been sufficiently extended and varied to supply a correct practi- 

 cal estimate of the limit which it would be most advantageous to impose upon the 

 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 



