THE EOYAL ARTILLERY INSTITUTION. 
143 
If the obstacle be J in. in height, e = 5° 14 '; if J in., e = 7° 24'; if 
l in., £ = 10° 28' 3 and if 1 in., e = 14° 50'. 
Thus, to make a carriage which has the ordinary field wheel pass an 
unyielding obstacle of only 1 in. in height, the horses have for the 
instant to put forth as much power as would be required to move the 
same carriage on an incline of about 15°. 
The smaller the carriage wheel, the worse it is for passing over an 
obstacle. Thus, suppose it be a wheel 3 ft. 4 ins. instead of 5 ft. in 
diameter which meets the obstacle J in. in height, and e becomes 12° 50' 
instead of 10° 28', while in the case of the obstacle 1 in. in height it 
becomes 18° 12' instead of 14° 50'. From this, setting aside the fact 
that the traction on the level is inversely proportional to the radius of 
the wheel, the evil of giving a carriage a low front wheel is evident. 
In the 9-pr. M.L.R. gun-carriage and limber, Mark II. (packed), 
AC' — 1*38 ins., 
C'B — 30 ins., 
W = 3032 lbs., 
W' = 920 lbs. 
Taking \x — *01, and inserting these values in equation (U), or—what 
is sufficiently near for all practical purposes—in the modification of it, 
‘ ^ ’ -, the traction of the carriage on the level in a direction 
C _D 
P = 
parallel to the ground is found to be equal to 1*426 lbs. 
This, in the usual direction of the traces—namely, at an angle of 6J° 
with the horizontal—amounts to 1*448 lbs. Now, as a matter of fact, 
far greater power than this is required to move the carriage on even 
the best road, and the apparent discrepancy is simply due to the imper¬ 
fections of the road and the wheels, which oppose a constant resistance 
to the motion of the latter; in fact—as mentioned in a former place— 
whether the carriage is on the level or on an incline, there is always an 
angle ^ depending in amount upon the nature of the road, to be taken 
into account. 
It is in consequence of this that the inclination of 6J° is given to the 
traces ; and giving this to the line of traction is as much as saying that 
the average obstacle to the motion of the carriage on the usual nature 
of road it has to travel over (whether level or inclined), is one whose 
height will give an angle e = 6^°. 
In this view, if in equation (B) y be made = o, and y' = e ( = /3), the 
true traction, under average circumstances on the level, will more 
nearly be arrived at. Thus 
P _A O', fx s/CB 2 (l+fx 2 ) (cos 3 e.W 2 + sin 3 e . W‘ 2 ) - AC 2 . fx 2 . cos 3 <• . W 2 
CB 2 (1 + /x 3 ) — AC 2 . [B 
+ 
CB 2 . (1 + fx 2 ) sin e(W+ TV) — AC 2 , fx 2 . sin e . W 
OB 2 (1 + ix 2 ) AC 2 . ix 2 
which, for all practical purposes, may be modified to 
