RAILWAY CONSTANTS. 215 



plane was staked out in distances of a hundred yards by 58 

 stakes, commencing from the lowest point and numbered up- 

 wards, and the inclination was ascertained to be at the rate of 

 1 in 178, with great uniformity, throughout the whole length of 

 5800 yards. 



The time of passing the stakes successively being observed, it 

 was found that the motion of the wagons was accelerated rapidly 

 at first, but gradually less and less, until at length all acceleration 

 ceased and a perfectly uniform motion was maintained to the 

 foot of the plane. 



The unfavourable state of the weather prevented the circum- 

 stances of these earlier experiments from being observed and 

 recorded with sufficient accuracy to render them fit to be taken 

 as the basis of any exact calculation of resistance, but more 

 than svifficient evidence was obtained from them that no prin- 

 ciples of calculation could be applied to the motion of trains on 

 railways with any view to accurate results, or even to a rough 

 approximation in which the increase of resistance due to the 

 increase of velocity is not allowed for. 



The problem which now presented itself for solution was the 

 motion of a train of wheeled carriages subject to resistances 

 which have some dependence on the velocity. All the investi- 

 gations which have been hitherto made respecting friction are 

 in accordance in showing that the amount of this resistance is 

 independent of the velocity; and unless it be maintained that 

 the friction of carriages on railways differs from all the varieties 

 of friction to which experimental inquiry has been directed, it 

 must be admitted that the part of the resistance to railway car- 

 riages which depends on friction is independent of the velocity 

 of the motion. 



The problem of the resistance opposed by fluids to solids 

 moving through them has been investigated by Newton, and by 

 the most eminent of his successors, Bernoulli, Euler, and the 

 principal mathematicians of the last century. Their researches, 

 however, so far as regards the resistance of elastic fluids, are 

 more remarkable for profound mathematical skill than for prac- 

 tical usefulness, most of them being founded on conditions in- 

 applicable to the actual motion of bodies through the air, and 

 I leading to results more or less in discordance with expei'ience. 

 I The earliest experiments on the resistance of the air to bodies 

 1 moving through it which are entitled to attention, are those of 

 i Robins, made about the middle of the last century. These were 

 [subsequently repeated and to some extent varied by Borda, 

 jwho published the results of his inquiry in the Memoirs of the 

 lAcademy of Sciences of Paris, in 1763. 

 I p2 



