Recognising thus the true position of aesthetics, and holding that while the cultivation of them should form a part of education from its commencement, such cultivation should be subsidiary; we have now to inquire what knowledge is of most use to this end—­what knowledge best fits for this remaining sphere of activity?  To this question the answer is still the same as heretofore.  Unexpected though the assertion may be, it is nevertheless true, that the highest Art of every kind is based on Science—­that without Science there can be neither perfect production nor full appreciation.  Science, in that limited acceptation current in society, may not have been possessed by various artists of high repute; but acute observers as such artists have been, they have always possessed a stock of those empirical generalisations which constitute science in its lowest phase; and they have habitually fallen far below perfection, partly because their generalisations were comparatively few and inaccurate.  That science necessarily underlies the fine arts, becomes manifest, a priori, when we remember that art-products are all more or less representative of objective or subjective phenomena; that they can be good only in proportion as they conform to the laws of these phenomena; and that before they can thus conform, the artist must know what these laws are.  That this a priori conclusion tallies with experience, we shall soon see.

Youths preparing for the practice of sculpture have to acquaint themselves with the bones and muscles of the human frame in their distribution, attachments, and movements.  This is a portion of science; and it has been found needful to impart it for the prevention of those many errors which sculptors who do not possess it commit.  A knowledge of mechanical principles is also requisite; and such knowledge not being usually possessed, grave mechanical mistakes are frequently made.  Take an instance.  For the stability of a figure it is needful that the perpendicular from the centre of gravity—­“the line of direction,” as it is called—­should fall within the base of support; and hence it happens, that when a man assumes the attitude known as “standing at ease,” in which one leg is straightened and the other relaxed, the line of direction falls within the foot of the straightened leg.  But sculptors unfamiliar with the theory of equilibrium, not uncommonly so represent this attitude, that the line of direction falls midway between the feet.  Ignorance of the law of momentum leads to analogous blunders:  as witness the admired Discobolus, which, as it is posed, must inevitably fall forward the moment the quoit is delivered.