RAILWAY CONSTANTS. 229 



From which it appears that the resistance in this case is very 

 nearly proportional to the squares of the velocities. 



By substituting for M and h in (25.) their values in these ex- 

 periments, we find that M A = 364 lbs. in the first two experi- 

 ments, and M A = 421 lbs. in the last three experiments. 



Hence it follows, that at the speed of 45*8 feet per second, 

 or 31'2 miles per hour the resistance of this train of four first- 

 class carriages, weighing 15'6 tons gross, was 364 lbs., and at the 

 speed of 49'45 feet per second, or 33"72 miles per hour, the re- 

 sistance of the same carriages loaded so as to amount to 18*05 

 tons gross was 421 lbs.; being in each case at the rate of 23^ lbs. 

 per ton. 



Since the effect of the wind must, in these experiments, have 

 rendered the resistance less than it would have been had the 

 atmosphere been calm, it may be inferred with certainty, that 

 the resistance of a train of four first-class carriages, carrj'ing 

 the weight of their usual complement of passengers at 33| miles 

 an hour on a level and straight railway in calm, weather, must 

 he greater than 421 pounds, or 23|^ pounds per ton. 



Consequently, for such a load moved at such a speed, the 

 angle of resistance, or the inclination which in its ascent would 

 double the resistance, and in its descent require no moving 

 power, is greater than g'^. 



If the weather had been calm when these experiments were 

 made, the distance which the train ran in each case before it 

 came to rest, after leaving the foot of the plane, would have 

 supplied means of obtaining a tolerable approximation to the 

 proportion in which the whole resistance ought to be assigned 

 to each of the two causes — that which is independent of the 

 velocity, and that which is proportional to its square. 



As it is intended to repeat these experiments in calm weather, 

 it may be worth while at present to investigate the formulae by 

 which such an approximation may be obtained. 



The symbols in (22.) and (25.) retaining their signification, 

 and h' expressing the gradient of the line extending from the 

 foot of the plane down which the train has been supposed to 

 have descended with a velocity rendered uniform by the resist- 

 ance, we shall suppose this uniform velocity to be expressed 

 by V ; and since the train is allowed to run until it is brought 

 to rest by the resisting forces, we shall have V = 0, and S = the 

 distance from the foot of the plana to the point where the traiji 

 stops. Making the reductions consequent on these conditions 

 the equations (22.) and (25.) become 



2ftgS _ „ ( h + h' \ 



M + M' VA+/y 



VOL. VII. 1838. Q 



