broad that any sizes may be in proportion. The quality of proportion in
design is always assumed to be a _pleasing_ relationship of sizes. It
thus becomes necessary to determine what relationship of sizes will be
most pleasing.

The use of equal masses in a design is monotonous. The eye finds variety
of size more interesting. But to determine what form of variety is most
interesting we must find, if possible, the ideal area relationship
between masses in a design. This problem has of necessity been solved by
the designers of all nations and all periods, and it is interesting to
note that the result has everywhere been practically the same.

Let us arrive at the expression of good proportion by the simple means
of dividing a rectangle into two parts which will have the most
interesting relationship. This rectangle is A in Fig. 8. B shows a
division into equal parts, the result being uninteresting and
monotonous. In C the division gives a feeling that the lower part is too
large; it is crowding the upper and the result is not pleasing. The
relationship in D is so nearly equal that the division seems to have
been an inaccurate effort to locate the center. Somewhere between the
division point in C and that in D will probably be the best point.
Repeated trials will locate the point about as in E, which will be found
to lie about two-fifths of the distance down from the top. This will
give the upper area in E an area of 2 and the lower an area of 3. Hence
the relationship or proportion is said to be as 2 is to 3. By the term
"good proportion," or merely the word "proportion," in speaking of
design this ratio of 2 to 3 is assumed.

[Illustration: Fig. 8. The division of a rectangle, A, to secure spaces
of interesting relationship. Equal division in B. Overbalanced effect in
C. Too nearly equal in D. More interesting in E, where the relationship
of spaces is as 2 is to 3.]

It is interesting to note that when a space has been divided into the
ratio of 2 to 3, the relationship of the smaller to the larger is
practically the same as the relationship of the larger to the original
whole. Or, mathematically, if the original, having an area of 5, is
divided into parts of 2 and 3, then 2 is to 3 as 3 is to 5,--a ratio
which is approximately true.

The student of architecture finds the most careful consideration of
proportion in the relationship of spaces throughout all the
architectural orders. In printing, the designer must