109 
Information respecting Rail-Roads . 
and as, by Mr Wood’s conclusions, 
“=i’ and {=^o’ thenW=8E ’ 
or the proper load for an engine on a level is eight times the 
weight of the engine. 
If we wish to know at what inclination the engine would re- 
tain only half its power, we may make W — 4E ; then sin i = 
or the ascent will be 1 foot in 250, or about 21 feet per 
mile. In this case, two engines would perform the work of 
one on a level. The use of two engines on such slopes, one 
acting in front of a train of waggons, and the other behind 
them, has been proposed by Mr Stephenson of Newcastle-upon- 
Tyne ; and where the inclinations are of considerable length, 
would form a most convenient method of surmounting them. 
If, in the general formula, we make sin i = and use the 
lower signs, we will find that, at that inclination, one engine 
will travel down with forty-four times its weight, or eleven 
times the load which it could drag up the ascent. By the 
same formula, if the effort of a horse, at any velocity, be repre- 
sented by i of his weight, he will, on a level, drag twenty 
times his weight ; and the inclination at which his load, with 
the same velocity, ought to be one-half, or only ten times his 
weight, is The effort of a horse in carrying a load, is as- 
sumed to have, to his power of traction, the ratio of 3 : 1 ; or 
S1 ^ 1 is substituted for sin i in the first member in the equation. 
This is on the supposition, that the friction of the carriages is as 
small as that which is created on rail-roads. If the friction 
on a common road amount to five times that on a rail-road, 
the load, in the same circumstances, will, on a level, be four 
times the weight of the horse ;* and the inclination, diminishing 
the load to one-half, will be — or 1 foot in 47 nearly. Hence 
4o.o j 
we see the necessity of diminishing the rate of ascent on public 
roads more than is generally done, as well as improving the 
surface. 
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