S6B 
Eteam Engine. 
called a dead pull. If M exceeds W, then will V be- 
come negative, and instead of the animal advancing 
with the load, the load will compel him to move back- 
wards and no useful work can be accomplished. 
Now these circumstances may be expressed algebrai- 
cally, by the general formula M oc (U — ^V)^, in which 
the exponent n can only be determined by means of ju- 
dicious and numerous experiments, where the magnitude 
of M should be ascertained for many variable values of 
V between the terms V=U, and V=o. From this theo- 
rem, following the common rules for the maxima and 
minima of quantities, it may readily be found that in or- 
der to have the useful w^ork done the greatest possible, we 
we must increase or decrease the weight till V becomes 
U 
when the performance will be denoted by 
72+1 
n 
n 
— — — xWU And if the value of V thus exhibited 
72+1 
(t2+1) 
be once ascertained experimentally, we need never be ap- 
prehensive of a material loss by a small variation from it % 
for by a well known property of those quantities which 
admit of a proper maximum and minimum, a value as- 
sumed at a moderate distance from either of these ex- 
tremes will produce no sensible change in the effect. 
In some of the actions of men, such as dragging a boat 
along a canal, See. the value of n in the preceding theo- 
rems has been found to be nearly =2. And the draught 
of horses is conformable to a law not widely different^ 
The best experiments which have yet been made on this 
point with regard to horses drawing in nearly rectilinear 
paths, lead us to conclude that n is then very nearly 
in the expression M OC (U— V)” Assuming therefore, 
for the utmost w^alking velocity of a horse, the value 
VoL IL 3 A 
