ground; were the purely practical questions out of which arose astronomy, mechanics, geometry.  Since then there has been a perpetual inosculation of the sciences and the arts.  Science has been supplying art with truer generalisations and more completely quantitative previsions.  Art has been supplying science with better materials and more perfect instruments.  And all along the interdependence has been growing closer, not only between art and science, but among the arts themselves, and among the sciences themselves.

How completely the analogy holds throughout, becomes yet clearer when we recognise the fact that the sciences are arts to each other.  If, as occurs in almost every case, the fact to be analysed by any science, has first to be prepared—­to be disentangled from disturbing facts by the afore discovered methods of other sciences; the other sciences so used, stand in the position of arts.  If, in solving a dynamical problem, a parallelogram is drawn, of which the sides and diagonal represent forces, and by putting magnitudes of extension for magnitudes of force a measurable relation is established 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