248 REPORT— 1841. 



different acclivities, and observing the maximum loads which an engine can 

 draw up those planes whilst exerting an equal tractive power. 



At the time of the publication of their first Report the Committee had 

 made a number of experiments in accordance with the second method, — that 

 of observing the motion of trains down inclined planes of different degrees of 

 acclivity, noting whether the motion were accelerated, uniform, or retarded. 

 Althougli these preliminary experiments were limited in number, and tried 

 under rather disadvantageous circumstances as respected the weather, the fact 

 that resistance increased in a heretofore unsuspected degree, in proportion as 

 the speed of the train increased, was satisfactorily established. In what ratio 

 the increment tooii place, whether as the square or some other function of 

 the velocity, could not be determined, the results presenting some trifling 

 apparent discordances, in consequence of the varying effect of the wind which 

 prevailed at the time of the experiments. In pursuing their inquiries at a 

 subsequent period, the Committee have been more fully convinced of the 

 soundness of the principle which guided them in the selection of the method 

 they at first adopted, and they have accordingly continued to conduct their 

 experiments in a similar manner, repeating them with various sizes of trains, 

 at various velocities, on the Sutton incline of 1 in 89 on the Liverpool and 

 Manchester Railway, and on the inclines of 1 in 177, 1 in 265, and 1 in 330, 

 on the Grand Junction Railway. 



It is to be regretted that the weather was not on all occasions perfectly 

 favourable. In some instances, however, there was not a breath of wind to 

 disturb the results, especially when engaged at the Sutton incline plane. 

 Such results deserve great confidence, and are particularly valuable for de- 

 termining the amount of friction, properly so called. 



A few remarks are necessary on the principle of analysis, adopted with re- 

 gard to the observations which appear in a tabular form at the end of this 

 Report. The data given there or elsewhere in the Report are, — 



1. The coefficient of gravity on the inclination of the plane. 



2. The initial velocity of the train at some determinate point on that plane. 

 This may be either zero, as when the train starts from a state of rest, or some 

 positive quantity. 



3. The terminal velocity at some other detei-minate point on the same plane. 



4. The time elapsed in traversing the space intervening between those two 

 points. 



5. The space intervening. 



6. The force of gravitation, which in this latitude is known to be repre- 

 sented by 32^, the velocity in feet per second acquired by a body falling 

 freely in vacuo, at the end of the first second. 



1. The weight or mass of the train, exclusive of the wheels and axles. 



8. The weight or mass of the train subject to rolling motion, viz. the wheels 

 and axles. 



9. The radius of the wheels. 



10. The distance from the centre of the wheel to the centre of oscillation. 

 From these data, when accurately obtained, the resistance of the train can 



be determined with absolute precision, the method turning altogether upon a 

 comparison between a certain fixed and standard force, the force of gravita- 

 tion, and the observed force by which the train is impelled in its descent. If 

 a body move down an inclined plane without encountering resistance, its ve- 

 locity at any given depth below the level of the point where its motion first 

 commences will be always equal to the velocity it would have acquired by a 

 free vertical descent, through the same height. If, then, this standard velocity 

 be compared with the qbserved velocity of a body which has moved down a 



