108 Rev. Mr Adamson on the extent of our 
timates, and in those of Mr Wood’s table, p. 239. the weight of 
the carriage is considered as part of the load, and this in gene- 
ral is rather more than one-fourth of the whole weight. 
These theorems express only the relation of the effort to the 
effect, on a dead level. On an ascent, not only must the resist- 
ance be increased, but wherever the moving power resides in a 
moving body, the effect of its effort must be diminished. Thus, a 
horse weighing 10 cwt. walking unloaded up an ascent of 1 foot 
in 33, would exert an effort nearly equal to that of dragging 
1 ton on a level rail-road. The weight of the moving body is 
peculiarly worthy of attention, when locomotive engines are em- 
ployed. In the theorems on this subject, as they are stated by 
Mr Tredgold, the weight of the engine is not admitted as part 
of the load ; but it bears too great a proportion to the whole 
load, to be safely neglected, and the introduction of it will be 
found to modify very greatly the practical conclusions to be 
drawn from the formulae. 
Let E represent the weight of the engine, and a be that frac- 
tional part of its weight representing the available friction 
which produces the progressive motion of the engine- wheels up- 
on the rails ; then E a will represent the engine’s force of trac- 
tion upon a level. 
Let i be the angle of inclination ; 
W the weight of the waggons and load ; 
/the friction at the axle of the waggons when the pres- 
sure is 1 ; 
n the diameter of the wheel when that of the axle is 1 ; 
then we have the general equation to express the relations of 
those quantities, , 
E (a qz sin i) = W 
The upper signs give the equation for ascending slopes, and the 
lower that required for descending slopes. W may be express- 
ed by a multiple of E, and in that case we shall be able to find 
the inclination at which any required proportion of the work 
done on a level may be performed. If sin i = o ; then 
-c „ _ w f 
