RAILWAY CONSTANTS. 221 



of the velocitj'', combined with a retarding force which is propoi*- 

 tional to the square of the velocity ; and such will be the actual 

 equations of the motion of a train of railway carriages if the 

 friction be independent of the speed, and the resistance of the 

 air, and any other retarding forces which act upon it, be as the 

 square of the speed. 



It will now be a matter for consideration, in what manner ex- 

 periments may be devised so as to enable us to determine the 

 values of the constants / and a. 



If a train descend an inclined plane by gravity with accelerated 

 motion, that part of the I'esistance which increases with the 

 speed will be continually augmented, while the accelerating 

 force of gravity will remain unaltered. At length, therefore, a 

 velocity will be attained which will render the resistance so 

 great that it will be equal to the accelerating force of gravity, 

 and then all acceleration will cease, and the train will move with 

 an uniform velocity. The condition under which this will take 

 place will be expressed by putting the value of rf V = 0, whicli 

 gives 



M(/a-/) -aV2 = 



•.•M/+«V^ = MA (25.) 



where V is the vmiform velocity attained in moving down the 

 gradient h. 



If the same train be moved down another gradient, h\ another 

 uniform velocity, V, will be attained, and we shall have the con- 

 dition 



From these two equations the values of a and / may be ob- 

 tained. 



M {h - h') 

 "= V^-V'^ (26.) 



J — ya __ y/2 •••... (27.) 



If, therefore, two inclined planes be selected sufficiently steep to 

 produce accelerated motion in the train, and if the same train 

 be allowed to descend them until it acquire an uniform velocity, 

 this will give values for V and V ; the inclinations of the planes 

 will determine h and h', and the weight of the train will deter- 

 mine M. The values of a and / may then be computed by the 

 above formulfe. 



In the practical application of this method there are some cir- 

 cumstances which will demand attention. It may happen that 



