222 EIGHTH REPORT. — 1838. 



the inclined plane selected for the experiment may not have suf- 

 ficient length to allow the acceleration of the train by gravity to 

 continue till the velocity become uniform. It will therefore be 

 more convenient to dismiss the train with a considerable speed 

 from the top of the plane, which may be done by impelling it 

 by means of a locomotive engine towards the top of the plane, 

 and detaching the engine so that the train shall be started down 

 the plane with the velocity given to it by the engine. If this 

 velocity be less than that which balances the accelerating force 

 down the plane, the train will be accelerated until it attain the 

 limiting speed. If it be greater, then it will be retarded by the 

 air until it be reduced to the limiting speed. 



In the preceding investigation M^e have proceeded upon the 

 supposition that the air through which the train is moved is 

 quiescent. The effects of a wind of any considerable force would 

 generally be so complicated, that it would be difficult indeed to 

 introduce them into the calculation in such a manner as to give 

 results of any practical value. If the wind blow in the direction 

 of the motion, the velocity of the train through the air will be 

 the difference between the velocity of the train and the velocity 

 of the wind ; and if this was all the effect to be considered, the 

 investigation woidd not be attended with much difficulty ; for it 

 would only be necessary to consider in that case the velocities 

 expressed by Vand V in the preceding formula to, be the excess 

 of the velocity of the train above that of the air. But it should 

 be remembered, that besides the progressive motion of the train, 

 a part of the resistance which is assumed to vary in proportion 

 to the square of the velocity, is produced by the revolution of 

 the wheels. Now this part of the resistance is not affected by 

 the wind, and will be the same whatever be the state of the 

 atmosphere. Thus it is possible to suppose the velocity of the 

 train equal to the velocity of the wind, and therefore no resist- 

 ance whatever to be produced by the progressive motion of the 

 train. Nevertheless, in such a case, it is evident that the i-evo- 

 lution of the wheels would produce by the action of their spokes 

 the same resistance as if the atmosphere were calm. These con- 

 siderations appear to lead to the conclusion, that the diminution 

 of resistance to be expected from a wind blowing in favour of a 

 train, and the increase of resistance from a wind blowing against 

 it, will not be so great as it might be expected to be, if no effect 

 but the progressive motion were taken into account. 



But if a correct investigation of the effects of a wind either 

 directly favourable or directly adverse to the motion of a train 

 be attended with doubt and difficulty, the effects of every side 

 or oblique wind are still more so. An oblique wind would be 



