1 4.15 Rail-Roads. 



Hence we see tliat, though n moving force of 100 pounds 

 produces three times as great an effect upon a canal as upon 

 a rail-way at 2 miles an hour, this superiority of the water con- 

 veyance is lost if we adopt a velocity at 6 miles an hour; and 

 at' all greater velocities the same expenditure of power will 

 produce a greater effect upon a rail-way, than upon a canal, a 

 river, or the sea. 



This calculation proceeds on the hypothesis that the friction 

 increases in the simple ratio of the velocity. Such was the 

 opinion of Ferguson, Musschenbroeck, and some other writers ; 

 but the more recent and accurate experiments- of Coulomb 

 and Vince have overthrown this doctrine, and established 

 conclusions extremely different, of which the following is an 

 abstract * : — 



1. The friction of iron sliding on iron is 28 per cent of the 

 weight, but is reduced to 25 per cent after the body is in 

 motion. 



2. Friction increases in a ratio nearly the same with that of 

 the pressure. If we increase the load of a sledge or carriage 

 four times, the friction will be nearly, but not quite, four times 

 greater. 



3. Friction is nearly the same whether the body moves upon 

 a small or greater surface ; but it is rather less when the sur- 

 face is small. 



4. The friction of rolling and sliding bodies follows nearly, 

 but not precisely, the same law as to velocity ; and that law 

 is, that the friction is the same for all velocities. 



It is with this last law onlj* we have to do at present ; and 

 it is remarkable that the extraordinary results to which it leads, 

 have been, so far as we know, entirely overlooked by writers 

 on roads and rail-ways. The results, indeed, have an appear- 

 ance so paradoxical, that they will shock the laith of practical 

 men, though the principle from which they flow is admitted 

 without question by all scientific mechanicians. 



First. It follows from this law that (abstracting the resist- 

 ance of the air) if a car were set in motion on a level rail-way, 

 with a constant force greater in any degree than is required to 

 overcome its friction, the car xcot/ld jiraceed ivith a motion con- 

 tiniuilly accelerated, like a fallivii body acted upon by the force 

 (f gravitation ; and however small the original velocity might 

 be, it would in time increase beyond any assignable limit. It 



* Leslie's Elements, p. 188, &c.; Plaj fair's Outlines, i. 88, &c.; Journal 

 de Phi/sique, 1/85; Philosophical Transactions, 17S5. Dr. Brewster has 

 given the results of f'oulonih's experiments in a tabular form, in the article 

 '' Mechanics''' in his {',!ir\ clopa'dia. 



is 



