DOI Page / Citation link:
https://doi.org/10.11588/diglit.4327#0067
58
APPENDIX.
of measurement are smaller in proportion to the derived
diminution. In order to arrive at this adjustment I have
calculated a table on the supposition that the drums are
entitled to preference in proportion to their lengths, and
obtain these ratios for their denominators, namely:
In group 1 for 89-60 . . . 97-3
■>
2
3
4
5
6
7
79-20
82-00
74-20
72-60
65-31
53-95
81-3
77-0
73-4
68-8
64-6
53-7
As however the errors of measurement are probably not
more than one-fourth of the inequalities of workmanship in
the interior of the flutes, I have taken one-fourth of the
range between the two tables, and the denominators of the
fractions in Column C, Table IV. then become
Table VI.
1 .
91-50
5 .
71-65
2 .
79-72
6 .
65-13
3 .
80-75
7 .
53-89
4 .
73-85
But there is also another correction required. The
groups of drums must necessarily admit some from the
pronaos and posticum, which were less numerous than
those of the peristyle in the proportion of 1 to 7|, and
they were also rather smaller in diameter, namely, the
lower full diameter was 4*160 instead of 4*230. This
dimension would exclude these drums from groups 1 and 2,
but in the third and subsequent groups they would be
liable to enter, and must be eliminated, on the considera-
tion that for every 7^ drums in group 3 one may have
belonged to the interior order having a rate of diminution
proper to group 1 or 2: that in group 4 there is an element
of the same nature, having the diminution proper to group
3, and so on. This problem admits of easy solution, and
the result is the set given in Table V.
We may now build up the column in this manner,
namely :
The base..... 1*770
The mean height of lowest drum . 4*209
•0420 X 91-50 . . . 3-843
79-72 . . . 2-950
80-10 . . ' . 5-206
72-93 . . . 6-053
71-35 . . . 4-745
64-26 . . . 5-077
53-40 . . . 3-818
34-17 . . . 0*833
The mean height of the topmost drum 2*268
The capital..... 1*570
0370
X
0650
X
0830
X
0665
X
0790
X
0715
X
0245
X
42*342
desirable to test the result above given by another method.
Let us therefore consider the first six groups only as esta-
blished, and then proceed as follows. Reckoning the shaft
proper from the top of the apophysis, the diameter within
the flutes is 3*826 and the height of the mean lower drum
above this point is 3*549, and therefore to the No. 5
point of Table IV. 26'356, with a diminution of -329
(namely, 3-826 - 3-4971), but the total diminution to
the bottom of the apophyge of the capital is -569. The
object will now be to draw a straight line from the bottom
of the shaft which shall represent the chord of the entasis,
which we have already traced for about two-thirds of its
extent. This done, I assume that the column had an entasis
proportional to that of the Erechthcum. Less than this
very delicate curvature would have been unlikely, whilst
it could not have been much more pronounced without
strong disagreement not only with the places derived
from the sixth, seventh, and eighth groups, but also with
the general sequence of the curvature given by the first
five points, which can hardly be questioned..
The horizontal distance between the chord and the
figure we have traced through the first five groups which
would be required to produce an entasis proportional to
that of the Erechtheum is 0*63; let this be added to the
*329 already stated as the diminution up to the No. 5
point (of Table IV.), making it "392, and the following
simple proportion will obtain:
s the
total height of shaft 26*356 »
•569 - -392 ' fr°m
which res
quantity 38-26 ; then the total column
will be—
Base
1-77
Apophysis
Shaft .
•65
. 38-26
Apophyge
Capital .
•70
1-57
42-95
As however the last two groups are not based on a suffi-
cient number of drums to be implicitly received, it will be
The two methods are, to a great degree, independent of
each other, and combine to point out that the height must
have been very nearly if not exactly ten diameters, which
would be 42-30, and I consider that the limits of error do
not admit the possibility of any other definite proportion
of diameters, or of halves or quarters of diameters.
There is a peculiarity to be noticed in the form of the
entasis as thus determined, namely, that the principal
amount of curvature is found towards the top of the shaft,
whereas in the Attic examples it occurs either near the
base or towards the middle. If, as has been done in The
Principles of Athenian Architecture, an hyperbola were
chosen to represent the curvature of this entasis, its vertex
would be above the capital. In all other ancient examples
known to me, this maximum curvature occurs either below
the shaft, as in the case of the Parthenon, or in some part
of the shaft itself.
F. C. PENROSE.
APPENDIX.
of measurement are smaller in proportion to the derived
diminution. In order to arrive at this adjustment I have
calculated a table on the supposition that the drums are
entitled to preference in proportion to their lengths, and
obtain these ratios for their denominators, namely:
In group 1 for 89-60 . . . 97-3
■>
2
3
4
5
6
7
79-20
82-00
74-20
72-60
65-31
53-95
81-3
77-0
73-4
68-8
64-6
53-7
As however the errors of measurement are probably not
more than one-fourth of the inequalities of workmanship in
the interior of the flutes, I have taken one-fourth of the
range between the two tables, and the denominators of the
fractions in Column C, Table IV. then become
Table VI.
1 .
91-50
5 .
71-65
2 .
79-72
6 .
65-13
3 .
80-75
7 .
53-89
4 .
73-85
But there is also another correction required. The
groups of drums must necessarily admit some from the
pronaos and posticum, which were less numerous than
those of the peristyle in the proportion of 1 to 7|, and
they were also rather smaller in diameter, namely, the
lower full diameter was 4*160 instead of 4*230. This
dimension would exclude these drums from groups 1 and 2,
but in the third and subsequent groups they would be
liable to enter, and must be eliminated, on the considera-
tion that for every 7^ drums in group 3 one may have
belonged to the interior order having a rate of diminution
proper to group 1 or 2: that in group 4 there is an element
of the same nature, having the diminution proper to group
3, and so on. This problem admits of easy solution, and
the result is the set given in Table V.
We may now build up the column in this manner,
namely :
The base..... 1*770
The mean height of lowest drum . 4*209
•0420 X 91-50 . . . 3-843
79-72 . . . 2-950
80-10 . . ' . 5-206
72-93 . . . 6-053
71-35 . . . 4-745
64-26 . . . 5-077
53-40 . . . 3-818
34-17 . . . 0*833
The mean height of the topmost drum 2*268
The capital..... 1*570
0370
X
0650
X
0830
X
0665
X
0790
X
0715
X
0245
X
42*342
desirable to test the result above given by another method.
Let us therefore consider the first six groups only as esta-
blished, and then proceed as follows. Reckoning the shaft
proper from the top of the apophysis, the diameter within
the flutes is 3*826 and the height of the mean lower drum
above this point is 3*549, and therefore to the No. 5
point of Table IV. 26'356, with a diminution of -329
(namely, 3-826 - 3-4971), but the total diminution to
the bottom of the apophyge of the capital is -569. The
object will now be to draw a straight line from the bottom
of the shaft which shall represent the chord of the entasis,
which we have already traced for about two-thirds of its
extent. This done, I assume that the column had an entasis
proportional to that of the Erechthcum. Less than this
very delicate curvature would have been unlikely, whilst
it could not have been much more pronounced without
strong disagreement not only with the places derived
from the sixth, seventh, and eighth groups, but also with
the general sequence of the curvature given by the first
five points, which can hardly be questioned..
The horizontal distance between the chord and the
figure we have traced through the first five groups which
would be required to produce an entasis proportional to
that of the Erechtheum is 0*63; let this be added to the
*329 already stated as the diminution up to the No. 5
point (of Table IV.), making it "392, and the following
simple proportion will obtain:
s the
total height of shaft 26*356 »
•569 - -392 ' fr°m
which res
quantity 38-26 ; then the total column
will be—
Base
1-77
Apophysis
Shaft .
•65
. 38-26
Apophyge
Capital .
•70
1-57
42-95
As however the last two groups are not based on a suffi-
cient number of drums to be implicitly received, it will be
The two methods are, to a great degree, independent of
each other, and combine to point out that the height must
have been very nearly if not exactly ten diameters, which
would be 42-30, and I consider that the limits of error do
not admit the possibility of any other definite proportion
of diameters, or of halves or quarters of diameters.
There is a peculiarity to be noticed in the form of the
entasis as thus determined, namely, that the principal
amount of curvature is found towards the top of the shaft,
whereas in the Attic examples it occurs either near the
base or towards the middle. If, as has been done in The
Principles of Athenian Architecture, an hyperbola were
chosen to represent the curvature of this entasis, its vertex
would be above the capital. In all other ancient examples
known to me, this maximum curvature occurs either below
the shaft, as in the case of the Parthenon, or in some part
of the shaft itself.
F. C. PENROSE.