tablished between quantities not else to be
dealt with; it may be fairly said that geometry plays towards mechanics
much the same part that the fire of the founder plays towards the metal
he is going to cast. If, in analysing the phenomena of the coloured
rings surrounding the point of contact between two lenses, a Newton
ascertains by calculation the amount of certain interposed spaces, far
too minute for actual measurement; he employs the science of number for
essentially the same purpose as that for which the watchmaker employs
tools. If, before writing down his observation on a star, the astronomer
has to separate from it all the errors resulting from atmospheric and
optical laws, it is manifest that the refraction-tables, and
logarithm-books, and formulae, which he successively uses, serve him much
as retorts, and filters, and cupels serve the assayer who wishes to
separate the pure gold from all accompanying ingredients.

So close, indeed, is the relationship, that it is impossible to say
where science begins and art ends. All the instruments of the natural
philosopher are the products of art; the adjusting one of them for use
is an art; there is art in making an observation with one of them; it
requires art properly to treat the facts ascertained; nay, even the
employing established generalisations to open the way to new
generalisations, may be considered as art. In each of these cases
previously organised knowledge becomes the implement by which new
knowledge is got at: and whether that previously organised knowledge is
embodied in a tangible apparatus or in a formula, matters not in so far
as its essential relation to the new knowledge is concerned. If, as no
one will deny, art is applied knowledge, then such portion of a
scientific investigation as consists of applied knowledge is art. So
that we may even say that as soon as any prevision in science passes out
of its originally passive state, and is employed for reaching other
previsions, it passes from theory into practice--becomes science in
action--becomes art. And when we thus see how purely conventional is the
ordinary distinction, how impossible it is to make any real
separation--when we see not only that science and art were originally
one; that the arts have perpetually assisted each other; that there has
been a constant reciprocation of aid between the sciences and arts; but
that the sciences act as arts to each other, and that the established
part of