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The laws of numbers in physics are often only laws of
proportion. We transform them into laws of equation, because we
introduce numerical coefficients and choose the units on which they
depend so as to simplify as much as possible the formulas most in use.
A particular speed, for instance, is in reality nothing else but a
speed, and it is only by the peculiar choice of unit that we can say
that it is the space covered during the unit of time. In the same way,
a quantity of electricity is a quantity of electricity; and there is
nothing to prove that, in its essence, it is really reducible to a
function of mass, of length, and of time.
Persons are still to be met with who seem to have some illusions on
this point, and who see in the doctrine of the dimensions of the units
a doctrine of general physics, while it is, to say truth, only a
doctrine of metrology. The knowledge of dimensions is valuable, since
it allows us, for instance, to easily verify the homogeneity of a
formula, but it can in no way give us any information on the actual
nature of the quantity measured.


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