and
sounds can be expressed in terms of numbers, has certainly opened the
door to a new consideration of this subject of beauty in relation to
mathematics. And the result of such an inquiry, if it is being or has
been carried on, will be of much interest.

But there is something chilling to the artist in an array of dead
figures, for he has a consciousness that the life of the whole matter
will never be captured by such mechanical means.

The question we are interested to ask here is: are there particular
sentiments connected with the different relations of quantities, their
proportions, as we found there were in connection with different
arrangements of lines and masses? Have abstract proportions any
significance in art, as we found abstract line and mass arrangements
had? It is a difficult thing to be definite about, and I can only give
my own feeling on the matter; but I think in some degree they have.

Proportion can be considered from our two points of view of unity and
variety. In so far as the proportions of any picture or object resolve
themselves into a simple, easily grasped unity of relationship, a sense
of repose and sublimity is produced. In so far as the variety of
proportion in the different parts is assertive and prevents the eye
grasping the arrangement as a simple whole, a sense of the lively
restlessness of life and activity is produced. In other words, as we
found in line arrangements, unity makes for sublimity, while variety
makes for the expression of life. Of course the scale of the object will
have something to do with this. That is to say, the most sublimely
proportioned dog-kennel could never give us the impression of sublimity
produced by a great temple. In pictures the scale of the work is not of
so great importance, a painting or drawing having the power of giving
the impression of great size on a small scale.

The proportion that is most easily grasped is the half--two equal parts.
This is the most devoid of variety, and therefore of life, and is only
used when an effect of great repose and aloofness from life is wanted;
and even then, never without some variety in the minor parts to give
vitality. The third and the quarter, and in fact any equal proportions,
are others that are easily grasped and partake in a lesser degree of the
same qualities as the half. So that equality of proportion should be
avoided except on those rare occasions when effects remote from nature
and life are desi