110 Odservations on Inclined Planes. 
This formula may be applied where cars are used to draw onsale 
rope from a fixed engine by the force of gravity alone. In estimating 
the value of @ in this equation, half- the weight of the rope is to be 
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 k=weight of 
the rope, m=weight of the sheaves, p= weight of the aaa = 
r=weight of the ascending train; we have 
ke 
F=,(ktm+p+—--) Be kK. 
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 descenaame adh we 
find from the- a mentioned above, 
F=,,(A+m+p)..... L. 
The values of F aa Jf being known, we may ascertain the amount 
of resistance overeome by a aad engine, in drawing a train of cars 
up an inclined plane. Putting a= weight of the train, it is evident 
that the ‘resistance to motion will be “+F4f since F' and J include 
the resistance of friction and inertia of all the moving parts. “Hence, 
making t= time in minutes,. we have for the resistance R, moved 
one foot in one minute, : 
it 3 r=i(24F4y) ss M. 
And the horse power necessary to overcome this resistance a vit beh 
supposing p= number of pounds expressing the power of « one horse, 
, exits +F+y) bas Wow: 
If the engine be assisted by a descending train, we have, making 
d= difference of the weights of the ascending and Cesconeam trains, 
d ‘ 
oor=t (4a ry) we OZ — 
atl +F4+) weed Ss: 
In order to give examples of the application of the shove formu- 
le, we may — some of the experiments given by Mr. Wood. 
