200 EfGHTH RElPOttT 1838. 



stance, measured along the rails, between thfe same points. This 

 method would be unobjectionable if the resistance was, as M. de 

 Pambour and most others at that time supposed it to be, inde- 

 pendent of the velocity. But we shall show presently that, so 

 far from this being the case, it has a dependence on the velocity 

 which renders this method of experimenting altogether falla- 

 cious. 



The foUowuig method of experimenting, with a view to the 

 determination of the amount of the resistance due to friction, 

 occurred to the reporter as being subject to fewer objections than 

 any of the methods above mentioned. 



Let two inclined planes of diflferent acclivities be selected. 

 Let h = the gradient of the steeper plane, expressed by the sine 

 of its inclination, or the numerical ratio of its height to its 

 length. 



Let /i' = the gradient of the other plane, similarly expressed. 

 Let L = a load which an engine, with an observed pressure of 

 steam in the boiler, and the regulator open to an observed 

 point, is capable of moving up the steeper plane at a slow uni- 

 form rate ; and let L' = the load which the same engine, in pre- 

 cisely the same state, is capable of moving up the other plane 

 at a slow uniform rate. 



The resistance on each plane will be the sum of the gravity 

 of the load down the plane and the friction. Now if F repre- 

 sent the friction on the former, and F' on the latter, the resist- 

 ance on the former will be 



L A + F, 



and the resistance on the latter will be 



L' h< + F. 



Since these two resistances are balanced respectively by the 

 tractive power of the same engine in the same state, they must 

 be equal. Hence we have 



LA + F = L'/i' + F 

 •.• F'-F = LA-L'A' 

 F-F _ LA -L 7t 

 '•" L' - L ~ L' - L * 



But F' — F l)eing the difference between the friction of L' and 

 L, tlie first member of this equality will be the ratio of the fric 

 tion to the lead. If this be expressed by/, we shall therefore'; 

 have 



•^ ~ L'-L > ''^ 



