RAILWAY CONSTANTS. 19/ 



Mrsi Report on the Determination of the Mean N'umer'ical 

 Values of Railway Constants. By Dionysius Lardnbr, 

 LL.D. F.R.S., 8}c. 



It will be in the recollection of the Members of the Mechani- 

 cal Section of the British Association, that the circumstance out 

 of which this inquiry arose, was the discordance of opinion 

 which prevailed ainong the members of the Section, including 

 several engineers and other practical men, on the subject of the 

 amovmt of the resistance to the tractive power offered by trains 

 on railways ; this resistance being variously estimated at six, 

 seven, eight, nine, and even ten or twelve pounds per ton of the 

 gross load. 



The resistance to the motion of a train of wagons or coaches 

 on a level and stx-aight line of rails arises from the following 

 causes : 



1°. The friction of the axles with their bearings. 



2°. The resistance to the rolling motion of tlie tires on the rails. 



3°. The friction of the flanges with the rails bi'ought into oc- 

 casional contact with the latter by the lateral oscillation of the 

 carriages. 



4°. The resistance of the air. 



If the line of rails be curved, another source of resistance arises 

 from the pressure and consequent friction of the flanges of the 

 outer wheels on the rails, which combined with the effects of 

 the conical form of the tires, is in fact the force by which the 

 direction of the motion of the train is continually changed. 



If the line be inclined at any given angle to the horizon, the 

 resistance will be modified by the gravitation of the load in a 

 manner which is easily inferred from the elementary principles 

 of mechanics. 



The practical importance of ascertaining the proportion in 

 which the whole resistance is distributed among these several 

 sources is evident. It is only by determining this that the en- 

 gineer can be guided in the selection of means for reducing 

 that resistance ; and the importance of reducing it will be un- 

 derstood, when it is considered how large an item in the expen- 

 diture of railway companies is locomotive povver, and that the 

 amount of this power is, ceteris paribus, in the exact proportion 

 of the resistance of the loads which it draws. 



The first question to which the present inquiry has been di- 

 rected was, to determine what the total resistance which is pro- 



VOL. vii. 1838. 



