ese
calculations be considered such--the feat, namely, of measuring the size
of the molecules themselves. Clausius was the first to point out how
this might be done from a knowledge of the length of free path; and the
calculations were made by Loschmidt in Germany and by Lord Kelvin in
England, independently.

The work is purely mathematical, of course, but the results are regarded
as unassailable; indeed, Lord Kelvin speaks of them as being absolutely
demonstrative within certain limits of accuracy. This does not mean,
however, that they show the exact dimensions of the molecule; it means
an estimate of the limits of size within which the actual size of the
molecule may lie. These limits, Lord Kelvin estimates, are about
the one-ten-millionth of a centimetre for the maximum, and the
one-one-hundred-millionth of a centimetre for the minimum. Such figures
convey no particular meaning to our blunt senses, but Lord Kelvin has
given a tangible illustration that aids the imagination to at least a
vague comprehension of the unthinkable smallness of the molecule. He
estimates that if a ball, say of water or glass, about "as large as
a football, were to be magnified up to the size of the earth, each
constituent molecule being magnified in the same proportion, the
magnified structure would be more coarse-grained than a heap of shot,
but probably less coarse-grained than a heap of footballs."

Several other methods have been employed to estimate the size of
molecules. One of these is based upon the phenomena of contact
electricity; another upon the wave-theory of light; and another upon
capillary attraction, as shown in the tense film of a soap-bubble! No
one of these methods gives results more definite than that due to the
kinetic theory of gases, just outlined; but the important thing is that
the results obtained by these different methods (all of them due to Lord
Kelvin) agree with one another in fixing the dimensions of the molecule
at somewhere about the limits already mentioned. We may feel very sure
indeed, therefore, that the molecules of matter are not the unextended,
formless points which Boscovich and his followers of the eighteenth
century thought them. But all this, it must be borne in mind, refers
to the molecule, not to the ultimate particle of matter, about which we
shall have more to say in another connection. Curiously enough, we shall
find that the latest theories as to the final term of the series are
not so