67 
can judge whether a force varies or no are time and space. 
If we can ascertain that the portions of each of these, in which 
a certain amount of velocity is produced, are equal, we are 
entitled to say, in Mr. Spencer's language, that the force has 
persisted. Now, this is to be ascertained by measurement. 
Space is measured by a bar (we will suppose) of a certain 
length, and time by the vibrations of a pendulum or balance. 
If two portions of space are covered successively by the 
measuring bar, we say they are equal; and if two portions of 
time are occupied successively by a vibration of the pendulum 
or balance, we say they are equal. In doing so, however, we 
assume that the bar has not altered in length between the two 
space- measurements, either by extension or compression, or 
by gain or loss of matter; and that the force of gravity, or 
the elasticity of the springs (according as a clock or a watch 
is used), has not altered between the two time-measurements. 
What, then, is our ground for these assumptions? Not, 
surely, that such variations are inconceivable ; for I persuade 
myself that I, for my own part, can very well conceive them, 
if a sufficient cause were to occur ; but, in the first place, 
because we know of nothing to cause these quantities to vary, 
which makes it at least very probable that they did not vary 
between the two measurements ; and in the next place, because 
bars of different materials and different degrees of compres- 
sibility could not give (as they do) the same result in the 
successive measurements unless their length were invariable ; 
and the improbability, on any other supposition than that of 
the constancy of the forces, that a clock and a watch should 
give the same result in successive trials (the former being 
acted on by gravity, and the latter by forces quite independent 
of gravity, viz., the main and balance springs) is next to 
infinite. Greater still is the improbability that variations in 
both these standards of measurement (the space-standard and 
the time-standard) should take place together, and in such 
proportions that it should be impossible to detect the slightest 
difference in the total effect. 
32. It is by reasoning of this nature that I, for my own 
part, have convinced myself that force is persistent, and not 
from any inherent impossibility that it should be otherwise. 
I am reluctantly obliged to instance my own power (or rather 
powerlessness) of mental conception in th s matter, because 
when we are called upon to admit any proposition to be an 
axiom, the appeal is to each man's understanding, and to that 
alone. And unless I much mistake, I am not the only person 
in the world who cannot see the axiomatic character of the 
principle of the persistence of force. Granted a sufficient 
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