each horse walking at the rate of 24 miles an hour, 
whence as before, 
f= 818 (FF) = 6.72 (7.5—0)2 = 168 bb...) 
7.5 
When the work of a horse is estimated by the 
load which he draws in a cart or waggon, it gene- 
rally bears some relation to that load, according to 
the good or bad construction of the cart, and the 
more or less easy motion of the wheels. Though 
accurate experiments on the friction of wheel car- 
riages have never been made with due care on a suf- 
ficiently extensive scale, yet no great error can be 
committed in supposing the friction on the road with 
a carriage of the ordinary construction, on the usual 
roads, to be between 3 and 5; of the load. If, then, 
a horse draw a ton in a cart, which a strong horse 
will continue to do for several hours together, his 
action may be supposed the same as if he raised the 
twelfth part of a ton, or 186 lbs., perpendicularly 
against the force of gravity, as in the case formerly 
mentioned. To raise a weight of 186 lbs., at the 
rate of 23 miles an hour, may, from the considera- 
tion of the action of a horse in a cart, be taken as 
nearly the average work of a strong draught horse 
in good condition. This is somewhat less than the 
estimate of Desaguliers, and a little more than that 
of Mr. Bevan, and it would give— 
fT 44 (7-5 —v)? = 186 Ibs. ...... (F) 
The mean of all these co-efficients, 8, 6°72, and 
7°44, will be 7°17, or, for simplicity, about 7 in 
whole numbers nearly, which finally give— 
PEE (BOP = 1B M8 ceccodeae (G); 
where v is, as usual, one-third of the greatest velo- 
city (74), or 24 miles an hour for strong draught 
horses. Indeed 72 miles an hour will be nearly the 
greatest velocity of such horses as are generally used 
in waggons and heavy carts, though, for those 
breeds of horses which run in mail-coaches, it must 
be too small, since they generally go at the rate of 
10 miles an hour for one stage of 10 or 12 miles 
twice a-day, when they receive a good rest between 
them. From this circumstance, it is evident that V, 
or the greatest velocity, must vary according to the 
quality of the horse, in relation to the manner in 
which the animal may be crossed with the finer 
breeds, while F must likewise change its value 
somewhat indirectly as V, as it is well known that 
slow heavy horses, at a moderate pace, can exert 
greater force, while light horses, at a considerable 
velocity, exert less. It is not too much to estimate 
V at 15 miles an hour for the latter kind of horses, 
and F at 180 lbs. or 200 lbs., about one-half the 
former, for strong draught horses, and consequently 
f=180 (4=*)"=4 (5—v)2 =80 Ibs. ...() 
supposing v to be 3 of V (15) or 5 miles. . By this 
means, the relative effects at their maximum value 
will be easily found from formula (B) or 
fXv=1%5 XK 23 = 487% for cart-horses. 
fXv= 80X55 = 400 for coach-horses. 
So that the greatest effects by these different kinds 
of horses, when the most favourable velocity is com- 
bined with the best weight, are very nearly equal; 
and the greater strength of the draught horse is, in 
a great degree, counterbalanced by the greater velo- 
city of the coach-horse. 
To point out clearly the relative effects produced 
by these two kinds of horses at different velocities, 
the following table is given. Part I. for cart-horses, 
and Part Ii. for coach-horses. 
WHEEL-CARRIAGE. 
TABLE I. 
I. Cart-Horsks. II. CoacH-HorszEs. 
E E 
v : or t Ui or 
Form. (8). 7 xv | Form. (1). tf Xv 
Miles. Pounds. Effect. Pounds. Effect. 
0 394 0 180 0 
i 296 296 157 157 
2 212 424. 135 270 
24 175 437 125 312 
3 142 426 115 345 
4 86 B44 97 388 
5 44 220 80 400 
6 16 96 65 390 
vi 2 14 61 357 
74 0 0 44. 337 
8 a 39 312 
9 29 261 
10 20 200 
11 13 143 
12 a 84. 
13 3 39 
14 1 14 
15 0 0 
In this table, the first column contains the velocity 
of the horse in miles an hour; the second contains 
the force which a cart-horse is capable of exerting, 
in pounds avoirdupois, at the different velocities 
marked in the first column; the third, the effect or 
product of the velocity multiplied by the force in 
pounds which the animal can exert at that velocity. 
The second part, for coach-horses, contains two 
columns corresponding to those in Part I. for cart- 
horses. By inspecting this table, it will be found, 
by columns first and second, that a cart-horse works 
most advantageously when moving at a rate of be- 
tween two and three miles an hour, and exerting a 
force in pulling of between 150 lbs. and 200 Ibs., 
since the numbers in the third column are then 
greatest, and they decrease at both a greater and 
smaller velocity, and consequently the labour be- 
comes less effectual. Comparing column first with 
the two columns in part second, it appears that the 
most effective rate of a coach-horse is five or six 
miles an hour, when exerting a force of traction of 
between 60 lbs. and 100 lbs.; consequently, there is a 
loss of effect when coach-horses move either faster 
or slower than this rate. No doubt the mail-coaches 
move faster than this rate (almost double indeed), 
but then the horses can exert little force if they do 
not injure themselves, or, if they are compelled to 
exert considerable force, they are worn out in a few 
years if they run two stages exceeding eight or ten 
miles a-day. 
In order to illustrate this subject more fully, it 
will be necessary to have recourse to investigation 
Let f be the force exerted by the muscles of the 
animal, which is continued for a day, b the weight 
of the animal itself, s the space described in a given 
time, and v the velocity; then, by the principles of 
dynamics, v will vary as 4/ cL. (Hutton’s Course of 
Mathematics, vol. ii. § 133.) Now, the space s 
will be inversely as the duration of a day’s work, 
denoted by d, or s is as =) and, consequently, »v is 
as »/ a For a horse of average strength, Sf = 250 
a 
lbs. nearly, and 5 about 1000 lbs., or, in general, - 
the force exerted by the muscles will be about one- 
fourth of the weight of the animal’s body; and as f, 
s, and 6 are all constant, it follows that 
i 1 
v IS as Ja 
