RAILWAY CONSTANTS. 201 



To reduce this to experiment it is onlj' necessary to attach to 

 an engine a train of loaded wagons, and so to adjust the load 

 and the engine that the latter shall be just capable of drawing 

 the former up the less steep plane with a slow uniform motion. 

 Let it then be taken to the steeper plane, and let such a number 

 of wagons be detached as will enable the engine, all things being 

 as before, to draw the remainder slowly and uniformly up the 

 steeper plane. If then for L' in (1) be substituted the former 

 load, for L the latter, and for h and A' the gradients of the two 

 planes, the numerical value of/ will be obtained by the fomnula 

 (1), and this will be the ratio of the friction to the load for the 

 wagons or carriages, which were detached to enable the engine 

 to draw the load up the steeper plane. 



It is evident that this experiment may be varied by altering 

 the tractive power of the engine, which may be done within 

 practical limits, by vaiying the pressure of steam in the boiler, 

 and the extent to which the regulator is opened. This will 

 produce a corresponding variety in the values of L and L', and 

 in this way various experiments may be made on the same pair 

 of planes. 



In this mode of experimenting it is not necessary that the ac- 

 tual pressure of steam on the pistons be known. All that is 

 indispensable is, that on both planes the tractive power of the 

 engine be the same. 



The equality of the tractive power would be more satisfac- 

 torily insured if the pressure of steam in the cylinders could be 

 measured and recorded, but no means have yet been contrived 

 for accomplishing this in locomotive engines. The pressure of 

 steam in the cylinders, however, depends on, 1°, the pressure 

 of steam in the boiler; 2°, the extent of the opening of the 

 regulator or steam valve; 3°, on the velocity of the piston. 

 These will be the same, if in both cases the motion of the engine 

 be slow and uniform, the regulator be equally open, and the 

 steam-guage show the same pressure. 



The limits of error depend on the practicability of trimming 

 the load so as to accommodate it to the same tractive power of 

 the engine. If the train on the less steep plane consist of a 

 great number of wagons, this may be done very nearly by 

 casting off a certain number of them on the steeper plane ; but, 

 if necessary, the load of the wagons remaining may be trimmed 

 by the addition or subtraction of weights. 



On the Grand Junction Railway, between Madeleyand Crewe, 

 there is a succession of three planes which are well adapted for 

 this method of experimenting : proceeding from Crewe, the first 

 ascends at the mean inclination of 1 in 330, the second at 1 in 

 260, and the third 1 in 178. 



