110 Observations on Inclined Planes. 



a 2as 

 F=— — -/ E. 



This formula may be applied where cars are used to draw out the 



rope from a fixed engine by the force of gravity alone. In estimating 



the value of a in this equation, half the weight of the rope is to h& 



considered a part of the weight of the descending train. 



The values of F in equations D and E being found from the data 



given in the experiments of Mr. Wood, we find an approximate value 



of F, that may be used in any case in practice. Let /<;— weight of 



the rope, m=weight of the sheaves', p — weight of the rope-roll, and 



r=weight of the ascending train, we have 



2r + Ic\ 

 F = ^\{k-hm+p^-^^] K. 



This value of F may be used, when a fixed engine draws up a train 



of cars, while another train descending, draws out the rope. from the 



engine. When the engine is not assisted by a descending train, we 



find from the experiments mentioned abo^e, 



F = ^\{k+m-^p) L. 



The values of F and y" being known, we may ascertain the amount 



of resistance overcome by a fixed engine, in drawing a train of cars 



up an inclined plane. Putting a= weight of the train, it is evident 



a 

 that the resistance to motion will be --\-F-\-f, since F andjT include 



the resistance of friction and inertia of all the moving parts. Hence, 

 making ^=time in minutes, we have for the resistance R, moved 

 one foot in one minute, 



s fa \ 



R=lU+F+/) M. 



And the horse power necessary to overcome this resistance will be, 

 supposing p— number of pounds expressing the power of one horse, 

 s fa \ 



P=plU+F+/) N. 



If the engine be assisted by a descending train, we have, making 

 d= difference of the weights of the ascending and descending trains, 

 s (d \ 



P=fis+F+/). ^-^ 



In order to give examples of the application of the above formu- 

 la, we may quote some of the experiments given by Mr. Wood. 



