67 S 
MECHANICS. 
weight, and not by the force of their mufcles. In four- 
footed animal?, the hinder feet is the fulcrum of the lever 
by which their weight adls againft the load ; and, when the 
animal pulls hard, it depreffes its chert, and thus increafes 
the lever of its weight, and diminifhes the lever by which 
the load refills its efforts. Thus, in fig. i, let P be the 
load, A D the line of fraction, and let us fuppofe F C to 
be the hinder leg of the horfe, and A E part of its body, 
A its chert or cenire of gravity, and C E the level road. 
Then AFC will reprefent the crooked lever by which 
the horfe afts, which is equivalent to the llraight one A C. 
But, when the horfe’s weight adls downwards at A, fo as 
to drag forward the rope A D and raife the load P, C E 
will reprefent the power of the lever in this pofition, or 
the lever of the horfe’s weight, and C F the lever by 
which it is refilled by the load, or the lever qf relillance. 
Now, if the horfe lowers its centre of gravity A, which it 
always does when it pulls hard, it is evident that C E, the 
lever of its weight, will be increafed, while C F, the lever 
of its refiftance, will be diminilhed, for the line of trac¬ 
tion A D will approach nearer to C E. Hence we fee the 
great benefit which may be derived from large horfes ; for 
the lever A C necelfarily increafes with their lize, and 
their power is always proportioned to the length of this 
lever, their weight remaining the fame. Large horfes, 
therefore, and other animals, will draw more than finall 
ones, even though they have lefs mufcular force, and are 
unable to carry fuch a heavy burden. The force of the 
mufcles tends only to make the horfe carry continually 
forward his centre of gravity, or, in other words, the 
weight of the animal produces the draught, and the play 
and force of its mufcles ferve to continue it. 
From thefe remarks, then, we may deduce the proper 
pofition of the line of traction. When the line of trac¬ 
tion is horizontal, as A D, the lever of refirtance is CFj 
but, if this line is oblique to the horizon, as Ad, the le¬ 
ver of refiftance is diminilhed to Cf, while the lever of 
the horfe’s weight always remains the fame. Hence it 
appears that inclined traces are much more advantageous 
than horizontal ones, as they uniformly diminifti the re¬ 
fiftance to be overcome. Deparcieux, however, has in- 
veftigated experimentally the mod favourable angle of in¬ 
clination 5 and foun,d that, w hen the angle AF made by 
the trace A d and a’horizontal line is fourteen or fifteen 
degrees, the horfes pulled with the greatell facility and 
force. This value of the angle of draught will require 
the weight of the fpring tree bar, to which the traces are 
attached in four-wheeled carriages, to be one half of the 
height of that part of the horfe’s breaft to which the fore 
end of the traces is connedled. 
When feveral horfes are yoked in the fame carriage, 
as reprefented in fig. 3, and when the declivity changes, 
the length of the traces has a confiderable influence 
upon the draught. From the point E, where the traces 
are fallenc-d to the horfe next the load, draw E R to the 
fame point in the fecond horfe R, and let R' be another 
pofition of the fecond horfe; it is required to find the 
difference of effect that will be produced by placing the 
fecond horfe at R or at R', or the comparative advan¬ 
tages of fhort and long traces. From R', the point where 
the traces are fixed, draw R'F'E; and from E draw 
Emn parallel to the declivity DA. Take EF=EF' 
to reprefent the power of the horfe in the diredlion of 
the traces, which will be the fame whether he is yoked 
at R or at R'; draw EA perpendicular to DA; Fn, 
F'm, parallel to EA; and Ftp, F f, parallel to En. 
Then, fince the fecond horfe when at R pulls with a 
force reprefented by FE, in the diredlion F E, we 
may refolve this force into the two forces E n, F tp, 
one of which E n is folely employed in dragging the 
cart up the inclined plane DA, while the other E^ is 
folely employed in prelling the firft horfe E to the 
ground. Let the horfe be now removed from R to R', 
the diredlion of the traces becomes RF'E, and F'E= 
FE is the power exerted by the horfe at R' and the di¬ 
redlion in which it is exerted. But this force is equi¬ 
valent to the forces Em, E f, the firft of which adU 
diredlly againft the load, while the other prefles the 
horfe againft the ground. Hence we fee the difad- 
vantages of long traces, for the force which draws 
the load when the horfe is at R' is to the force when 
the horfe is at R, as Em to E n, and the forces which 
prefs the horfe upon the ground as E f to E tp, or as 
F’m to Fa. No w, E 0 = Fa_ FExfin.aEF; hence 
E<p=:FExfin. ( nEg '—FEg') (g'E being parallel to 
AB'), and E» = E Fxcof. (a Eg’ — F Eg 1 ). In like 
manner we have E/=FExfin. (a Eg’ —F'Er'), and 
Ew = EFx cof. {nEg' — F'Eg'). Now (in. FEg' — 
Rg RV R e 
fin.FEg=—, and fin. FEg' = —= but Rg 
= R'g' = BR —EQ = BR — BR X cof. nEg'=BRx 
(1—cof. nEg.) By fubftituting this value in the equa¬ 
tions which contain the values of E (p, E n, Ef, Em, 
and confidering that the angles FEg', F’Eg' are always 
fo fmall, that their arcs differ very little from their fines. 
we have F Eg \ 
B R X 1 — col. n Eg 
EK ’ 
and 
F'E y— bRxi—co(.2^Bff 
^^ ~ F R > 
ER' 
By fubftituting thefe values in the preceding equations, 
we have 
E £> = E FXfin. {nEg 
Ey«=EFxfm. (aEg 
En =E FXcof. (a Eg 
Em — E Fxcof. {nEg 
B 
RX 
1 — col. n 
Eg 
ER 
* 
B 
RX 
1 — col. n 
Eg 
ER' 
7 
B 
RX 
1 cof. n 
ER 
B 
RX 
1 — cof. n 
Eg 
ER' 
If A B is horizontal, and the declivity AD=f we dial! 
have nEgz=z 9 0 28', or in parts of the radius = 0-16522, 
and cof. nEg= 0*98638. Then, if EF = 2oo pounds, 
B R =2 3! feet, E R = 8 feet, and ER'= 12 feet, then we 
lhall have, from the preceding formulae, Eip=3i*7i6 
pounds, Ey r := 32-350 pounds, £22 = 197-470 pounds, and 
£02—197-404. Hence an additional length of four feet 
to traces eight feet long, prefles the horfe E to the' 
ground with an additional force of 32-250 — 31*716 = 
0-534 pounds, and diminifhes the effect of the other horie 
by 0-066 pounds. 
On the Pofition of the Centre of Gravity, and the Manner of 
difpojing the Load. 
If the axle-tree of a two-wheeled carriage pafs through 
the centre of gravity of the load, the carriage will be in 
eqwilibrio in every pofition in which it can be placed 
with refpedl to the axle-tree; and in going up and down 
hill the whole load will be fuftained by the wheels, and 
will have no tendency either to prefs the horfe to the 
ground or to raife him from it. But if the centre of 
gravity is. above the axle-tree, as it mull neceffarily be 
according to the prefent conltruCtion of wheel-carriages, 
a great part of the load will be thrown on the back of 
the horfes from the wheels when going down a fleep road, 
and thus tend to accelerate the motion of the carriage 
which the animal is driving to prevent; while, in afeend- 
ing deep roads, a part of the load will be thrown behind 
the wheels, and tend to raife the horfe from the ground, 
when there'is tbegreateft neceflity for fome weight on his 
back to enable him to fix his feet in the earth, and over¬ 
come the great refiftance which is occafioned by the fleep- 
nefs of the road. On the contrary, if the centre of gra¬ 
vity is below the axle, the horfe will be preffed to the 
ground in going up hill, and lifted from it when going 
down. In all thele cafes, therefore, where the centre ol' 
gravity is either on the axle-tree or diredlly above it or 
below. 
