DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.2984#0125
112
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
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