364 Steam Engine. 
results of diflFerent experiments, it will always be necefe*sa^ 
ry to enquire what machine was interposed between the 
weight moved and the animal, in each case, that we may 
thence deduce the real velocity with which the animal mo» 
ved, from the velocity of the weight or load given by 
the observations. This is too frequently omitted in con-^ 
sequence of an implicit reliance upon a maxim, which, 
though highly useful under proper restrictions, is far 
from universal in its application. In the case before us, 
if we admit the maxim now alluded to, namely, that 
what is gained in power is tost in time, with regard to 
the machine through whose intervention the velocity of 
the weight is rendered different from that of the horse, 
it would be unsafe to adopt it in the appreciation of the 
varied energy of the animal when moving with different 
velocities. The reason of this is obvious. The ener- 
gy of the horse is obliged to be employed not only in 
overcoming the weight or resistance which opposes his 
progress, but in part in moving himself; for the parti- 
cles which constitute his frame possess weight and iner- 
tia, and therefore cannot be put into motion without efforb 
Hence it follows that there is a certain velocity, whicli 
may be denoted by U, with which, when the animal 
moves, his whole power will be employed in producing 
his own motion solely, without being able to move any 
other body. If a body whose mass is M be attached to 
the horse, so that he cannot move without giving an equal 
velocity to the extraneous body, the same effort being 
employed both in moving the animal and the n>ass at-^ 
tached ; the velocity V, with which they move must ne- 
cessarily be less. And if M be farther increased while 
the weight and energy of the horse continue the same, 
the velocity V will be still farther diminished ; and thus 
as M increases V will diminish, until when M arrives 
at a certain magnitude, W, the animal is unable to make 
any progressive motioiij and exerts his force at what 
