250 REPORT— 1841. 



ever, the velocity is accelerated or retarded between the two points of ob- 

 servation, although the mean resistance is known, we cannot state whether 

 that mean resistance is due to the mean velocity, or to some other velocity 

 intermediate between the limits of the initial and terminal velocities, because 

 experience has not yet assigned the law of the corresponding increments of 

 resistance and speed. It will be sufficient for all practical, and even theo- 

 retical purposes, to assume the mean resistance as applying to the mean ve- 

 locity, remarking that the calculations are chiefly made from observations 

 where the initial and final velocities do not widely differ, thus reducing, as 

 far as possible, the limits of error. A more considerable source of error 

 arises from the difficulty of obtaining with precision the initial velocity, 

 owing to our inability to measure the time of passing from stake to stake 

 accurately to a small fraction of a second. To obviate this, a mean has been 

 taken from the observed times of traversing one or two spaces, preceding 

 and succeeding the post at which the actual velocity is required. The errors 

 are thus diffused over a larger space, and rendered less sensible. 



The carriages employed belonged either to the Grand Junction, or to the 

 Liverpool and Manchester Company. The former were first class, the latter 

 second class, but both kinds were closed at the top and sides, presented the 

 same transverse section, were loaded to nearly the same gross weights, and 

 in other respects were identical. It is next to impossible to obtain two car- 

 riages even of similar make, whose friction shall be exactly the same, and 

 accordingly a slight difference was observed, and it was found on the whole 

 that the mean friction of the Grand Junction carriages exceeded the mean 

 friction of the Liverpool and Manchester carriages, a fact which may be ac- 

 counted for by the latter having been in use for a longer period. 



We shall now consider the results afforded by the tables under the follow- 

 ing heads : — 



1 . The Evaluation of Friction proper. 



2. The additional resistance produced by increase of speed in trains of 

 different sizes. 



3. The effect of modifying the form of frontage, and of otherwise altering 

 the nature of the exterior surface of the train, as for instance, by closing up 

 the spaces between the carriages, ascertaining also the effect of the engine (as 

 regards its external configuration in diminishing the resistance). 



1. TJie Evaluation of Friction, properly so called. — On the 23 rd of August 

 1839, the weather being perfectly fine and calm, three Liverpool and Man- 

 chester first class carriages, weighing gross l^'S tons, were allowed to de- 

 scend the Sutton inclined plane from a state of rest, starting from a post 

 numbered 0, and urged only by the force of gravitation. The experiment 

 was repeated four times, and the train descended the plane from to 22 post, 

 a distance of 2420 yards, in the following times respectively : — 



1st. 4 m 28 s. 2nd. 4 m 25 s. 3rd. 4 m 23 s. 4th. 4 m 22 s. 



These results coincide so closely, that we may fairly consider the sum of 

 the resistances to have been the same in all cases, or at any rate to have de- 

 creased in only a very slight ratio, in proportion as the axles became better 

 lubricated by continued running. 



The fourth experiment is chosen as the subject of calculation, to determine 

 the resistance of the said carriages at very slow velocities. Five separate 

 computations are made from observations of the times of descent from No. 

 to No. 1, No. to No. 2, No. to No. 3, No. to No. 4, and No. to 

 No. 5 posts respectively. 



