RAILWAY CONSTANTS. 203 



tage, that the result is very slightly, perhaps insensibly, affected 

 by the resistance of air. The wagons whose friction is here ob- 

 served, being those thrown off in passing from the less to the 

 more steep plane, are preceded by others, before which the air 

 is driven. Besides, the motion being slow, the resistance of 

 the air to the motion of the wheels must be quite insensible, 

 and the motion on both plains being at nearly the same rate, 

 the same resistance, or nearly so, from the air is encountered. 

 For all these reasons the quantity F — F' in the formula (1.) may 

 be taken to represent the actual resistance from friction of the 

 wagons detached. 



In the course of the limited number of experiments which 

 this Committee have been enabled to make, however, they have 

 not yet obtained an opportunity of instituting any by this me- 

 thod, the provisions for which are not easily obtained in the 

 midst of the busy traffic constantly carried on upon the railways ; 

 and this difficulty has been increased by the circumstance that 

 there are vei*y few gradients on railways which fulfil the con- 

 ditions here required, and these few not always accessible. 



The method of determining the resistance by observing the 

 accelerated motion of carriages down inclined planes, and by ob- 

 serving the gradual retardation of their motion on a line where 

 the inclination is not such as to render gravity greater than the 

 friction, next demands attention. 



An extensive series of experiments having been formerly 

 made by M. de Pambour by this method, it will be convenient, 

 in the first instance, to notice the principles adopted by him and 

 the chief results at which he arrived. 



Let ^-^the accelerating force of gravity. 



Q = the angle which the plane makes with the horizon. 

 <^ = the accelerating force of the load moving down the 



plane. 

 T = the time of the motion counted from the moment 

 at which the load commences to move by gravity 

 from a state of rest. 

 V = the velocity it has acquired in the time T. 



d V 

 Then we shall have <p = -ryf, • 



M. de Pambour then infers that if the load which descends 

 the plane were free from friction, we should have 



^^sinfi = |^ (2.) 



and that if x express the space moved over in the time T, 



