APPENDIX

these resting-places will form a scale of proportion, a series of

steps by which we may regulate degree of approach to and

departure from equality between any compared dimensions or

series of dimensions. On what principles are the resting-places to

be determined, the scales constructed ? I can only give results,

briefly and partially too.

First, The design itself will necessitate the adoption of certain

ratios from the requirements of purpose and plan.

Secondly, The variety of exigencies demand that the other

selected ratios should range pretty widely over the interval to be

divided, and give a choice of proportions verging towards inequality

as well as towards equality, yet with sufficient interval to preclude

confusing proximity.

Without pursuing the analysis further here, I must content

myself with stating that the scale by which the Parthenon is

regulated, commencing with the ratio I : 6, advances towards

equality by ratios preserving the common difference between their

terms of 5. Thus 1:6,2:7, 3:8,4:9, 5: 10, etc. As the

scheme advances, the differences become trifling, and the numbers

undesirably high, and the scale is made out by the ratios 4 : 5,

5 : 6, 6 : 7, etc., the common members of a primary series. Such

a scale is formed by the rejection of the innumerable other ratios,

some self-condemned by their high numbers, but others as not

required or as interfering with the effect of the most characteristic

ratios. Thus, the ratios 1 : 3 and 2 : 5 are most extensively and

importantly employed in the temple at Bassa:, but are absolutely

unknown in the Parthenon. Even of the members of the scale

admissible and admitted some are comparatively neglected, while

emphasis is given to a few by repetition in many instances, and

both rectilinearly and rectangularly, and in applications expressive

and important. Such predominance we shall find to be given

in the Parthenon to the ratios 4:9, 7:12, and 9: 14,—to the

first especially. It is to be assumed that the system of making

dimensions proportionate to each other, sometimes rectilinearly

and sometimes rectangularly, was adopted on the principle that

tiic mind and eye naturally take cognizance of both forms of

comparison, and feel satisfaction in both harmonies. What then,

it may be said, are their comparative values when they clash ? It

was the aim and study of the Greek architect of the Parthenon

that they should not clash ; and we shall have to admire the

dexterity and success with which he harmonised the two forms

of comparison, so that rectilinear proportions that fall out as

happily as if they had been exclusively considered, are found to

be compatible with, indeed to be the means of bringing about,

rectangular comparisons that are still more effective ; but I must

leave it for the examples to bring home the value of this principle,

and the skill evinced in employing it.

To the examples again I must trust for conveying due appre-

ciation of the strict and logical consistency with which the Greek

architect selected the terms of his comparisons ; that the length of

an apartment should be brought into proportion to its breadth,

may be obvious enough, but in the ramification of design divisions

are called for which must not be proportioned at random, but can

only be correctly referred by a shrewd eye for correlative function

and expression. Proportions, to be expressive, must correspond

with and so represent natural relations of analogy or antithesis,

and it was in the discernment or contrivance of these that genius

founded and perfected Greek architecture.

The terms to which a prerogative importance is allowed in

regulating other dimensions are, especially—

1. The breadth of the front, from which are derived,

2. The breadth of the abacus, and

3. The lower diameter of the column.

Put no subdivision of these into any moderate number of fixed

minutes or modules will explain their regulating power, which is

dependent upon variable proportion, upon the adoption of ratios

that may be taken from any part of the scale.

The designer of a Greek temple held it of importance to secure

a definite proportion of low numbers between the length and

breadth of the structure, as taken upon the grand stylobatc,

whether upon the topmost or on a lower step ; a horizontal

rectangular proportion. Thus the Parthenon has breadth and

length on top step as 4:9, the Theseum the same, but on the

lower step, and the temple at Bassa; also on lower step, has the

proportion of 2 : 5, and the temple at ^Egina that of a double

square-

Equally important, or even more so, was it that the full vertical

height of the front, from the pavement of the peribolus to the

apex of the pediment, should compare in a ratio of low numbers.

In several hexastyle temples, those of Theseus and Bassa? arc

examples, and, I may add, the western front of the Propylaea, the

height of the front is commensurate with the breadth, as 3:4,

In the Parthenon we shall find that, besides this grand ratio of

height and breadth, which there is 9 : 14, very accurate rectangular

proportions were obtained between other main divisions of the

elevation; the check upon multiplying these in every instance

was the stringent importance of certain rectilinear proportions

which were liable to interfere with them. Of these it appears,

from comparison of examples, that the greatest importance was

attached to making the height of the column exceed the joint

height of the other members, that is, stylobate, entablature, and

pediment, by a single aliquot, For example, the height of the

column may compare with the complementary height of the front

as 7:6, or as 6 : $, etc. etc. In other words, the height of the

column as compared with complement of height is the larger term

in what is technically called a super-particular ratio. The ratio

applied in the Parthenon is 10:9, in the Theseum 5:4, equiva-

lent to 10:8, The Sicilian builders never discovered or appre-

ciated this principle, and their effects suffer accordingly.

Thus much for the elevation of the front , but a further

arrangement was thought necessary or desirable in the Parthenon,

in order to harmonise the column as vertical member with the

joint horizontals, the entablature and stylobate, as seen on flank,

where from such frequented points of view the height of the roof

was not visible or brought into comparison. Accordingly the

joint height of the stylobate and entablature on the flank is just

equal to half the height of the column ; or say, height of column :

complement on flank : :2: I. With what exactness this is the

case will appear from the comparison of figures to be given

presently. The same ratio holds good in the like comparison in

the Theseum, where the entablature received an addition of height

from the cymatium, which, as discovered by Mr. Penrose, was

returned along its entire length.

It was a further established principle that the height of the

column should compare symmetrically with the horizontal spacing

of the columns; should, in fact, be just equal to the dimensions

from the centre or edge of one column to the centre or edge of a

third, measured upon the plan. In the Parthenon this symmetry-

is applied to three ordinary columns and the two intercolumns

included, and the same appears to be the case at Sunium. In

the east front of the Propylaea and in the temple at Bassa; an

angle column and columniation are included in the comparison,

which, in the latter case at least, introduces a difference from the

relative contraction o( the angle columniation. In the temple

at Rhamnus the dimension is taken from the outer edge of the

angle column to the centre of the third from the angle ; in the

Theseum we have a like division, but involving only ordinary

columns,

I apprehend that the introduction of these equalities of heights

with breadths was found to give repose to the effect of a long

range of columns, as a repetition of similar spaces and dimensions,

and the principle may be susceptible of wide application, as in