190 REPORT— 1877. 



a weight of 2 tons, as representing the average weight of luggage it conveys. The 

 Companies had the option of using either 4-wheel" or 0-wheel carriages. 



Subject to those conditions the trains varied considerably in gross weight, which 

 ranged from 130 tons to 195 tons in respect of the fifteen loaded vehicles, and from 

 200 tons to 260 tons when the weight of engine and tender was included, the 

 heaviest trains being those of the Great Northern, and London and North-Western 

 .Railways, as being made up of 6-wheol carriages, all the other trains being furnished 

 with 4-wheel carriages. 



All the comparative trials, class by class, were made, as nearly as circumstances 

 would permit, at the same timo and under the like conditions of weather, state of 

 rails, &c. 



The trains were started from a point near Newark, about three miles from the 

 signal-post at which the signal to put on brakes was given, in order that they 

 might acquire the requisite speed. Owing to the differences in weights of trains, 

 and to the different powers of' the engines applied to them, it was not possible to 

 ensure equal rates of speed at the time of signalling to stop ; but by computing 

 the vis viva of the train in each case and dividing this by the stopping distance, 

 the mean retarding force is obtained in each case as a coefficient of the weight of 

 the train. 



The Royal Commissioners were desirous that, if possible, some graphic mode of 

 presenting the results should be arranged, so that by a glance, and without the 

 need of reference to the Tables which would of course accompany our Report, the 

 relative efficiency of the different brakes might be seen. 



We accordingly devised the means of doing this by diagrams, of which the one 

 now before the Section is a specimen (Plate III.). 



We were led to this method of exhibiting the duty done by the following con- 

 siderations : — 



The work done from first to last in the act of stopping a train by brake-power, 

 or otherwise, is necessarily equal to the vis viva or accumulated work which the 

 train possessed at the moment of commencing the stop *. 



The vis viva which a train possesses at any moment is that which it would have 

 acquired in falling vertically through the height required to produce the assigned 

 velocity in a body falling freely from a state of rest under the action of gravity. 



Thus the vis viva destroyed in the act of stopping is represented by the weight 

 of the train lifted through the vertical height in question, the condition necessary 

 being that the vis viva can only be exhausted by the train rising on any given 

 gradient to the height due to its velocity. 



Supposing, then, that at a given point of its course the propelling power of a 

 train should be suddenly arrested, and that at the same point it should be made to 

 enter upon a rising gradient, it would continue to run (setting aside for the moment 

 the question of friction) until it reached a point on that plane the vertical elevation 

 of which shall be equal to the height which would suffice to produce the particular 

 velocity which the train had attained on reaching the foot of the gradient. 



If the gradient be a gentle one, the distance run before the train is brought to a 

 stop will be considerable, and in proportion to its increasing steepness so will the 

 run be shortened. 



Taking such gradient as a convenient measure of the forces applied to stop a 

 train, its effect is represented by the inclination of that gradient, taking its height 

 as that due to the initial velocity and its length as the distance traversed during 

 the stoppage. 



A diagram can therefore be constructed by setting off by scale, from a zero point 

 on the base line, a gradient the length of which shall equal that of the distance of 

 the stop and its height the vertical height through which a body falling from a 

 state of rest would attain the observed velocity of the train at the time of the 

 commencement of the stop. 



This becomes the measure of all the forces concerned in producing the stop, 



V 2 

 * Vis viva (in foot tons) =Mtt7t, M being the weight of train in tons, V its velocity 



in feet per second. 



