DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.4327#0065
APPENDIX No. II.
ON THE ENTASIS AND HEIGHT OF THE COLUMN OF THE TEMPLE
AT PEIENE.
The height of the columns of the temple of Athene can
only be obtained mdirectly from the measurements of the
fallen drums. The fragments of no particular column
could be put together with certainty, and Mr. Pullan was
only able to find about one-fourth of the original number,
and of these the stones from the lower parts of the column
formed by far the largest proportion.
The plan which first presents itself in an attempt to
recover the original height is to superimpose one upon
another drums which have like dimensions in their top and
bottom beds respectively, but this is soon discovered to
give no satisfactory solution. Mr. Pullan found the flutes
generally so much worn that he was obliged to take the
measurements within the flutes, and an additional element
of uncertainty is thus introduced, for no column has ever
so perfect a contour within the flutes as it has upon their
edges. It thus happens, as will bo seen from the subjoined
measurements of the drums, that many of these stones,
Avhilst they have like measurements on their top and bottom
beds, vary very much in length, so that it is possible by
this process to arrive at results quite discordant one from
another. The measurements of the drums, however, seem
nevertheless cajoable of affording a very close and reliable
result when fully discussed, and I have from them deduced
a value in which I have great confidence. Mr. Pullan
fortunately measured all the drums which were unbroken,
and for the lower three-quarters of the column, at least,
they are sufficiently numerous to enable us to get rid of the
accidental errors, both of workmanship and of measurement,
and to determine a very close approximation to the original
character of the entasis, and from it to deduce the heights.
If the shaft of a column were to diminish without entasis,
and therefore should be truly conical, it would only be
necessary to measure a sufficient number of drums and we
could obtain the rate of diminution, and as the upper and
lower diameters are supposed to be known, and in fact in
this case are known, the height would at once follow. But
in the case of Priene, as of all good examples of ancient
Greek architecture, the contour of the shaft is a curved
line, and the question thus becomes more complicated;
nevertheless it may be completely capable of solution if
there be a sufficient number of drums of all diameters.
This is nearly the case at Priene but not quite, as those
near the top of the column are rather scanty, but I consider
that this deficiency may be got over in a satisfactory
manner and a close determination arrived at.
To understand the method about to be followed, let it
be first assumed that the shape of the entasis is known as
well as the amount of diminution and the vertical height.
Divide the given horizontal quantity, that is to say the
whole difference between the upper and lower semi-dia-
meters, into a number of equal parts, say not less than eight,
and plot these distances down along a base line. Then draw
perpendicular lines through the points so obtained to meet
the curved outline of the column and join the intersections.
These last straight lines will then form part of a polygonal
figure, the height of which will by construction be that of
the column exactly, and each of the sides will show the
rate of diminution of the column between the corresponding
horizontal diameters plotted down upon the base line.
That is, would show the angle of inclination of the shaft of
the column between those points.
The same result would follow if the horizontal sub-
divisions were not exactly equal; but to make a good
approximation to the shape of the column they must be
sufficiently numerous and properly distributed.
Conversely if the angles of inclination corresjwnding to
given horizontal differences were given or determined we
could draw the proposed polygonal figure, and should then
discover both the form of the entasis and the height of the
column, and it is on this method that the following cal-
culation is founded. For convenience, the differences of
diameter instead of semi-diameter are used in what follows,
but that does not affect the result:
Table I.
Diameters within
the flutes.
Height of
Drum.
Diameters within
the flutes.
Height of
Drum.
Top.
Bottom.
I
Top. 1 Bottom.
I
]
feet.
3-25
feet.
3-35
feet.
2-72
23
feet.
•54
feet.
•58
feet.
2-85
2
•32
•35
1-55
24
•55
•57
1-80
O
o
•32
•35
1-60
25
•55
•63
2-30
4
•34
•35
2-32
2G
•55
■58
3-20
5
•35
•3G
2-73
27
•55 -G2
3-24
6
•39
■41
235
28
•55 -58
3-38
7
•40
•46
2-71
29
■56
•59
2-47
8
•40
•48
2-36
30
•56
•60
2-79
9
•41
•42
2-01
31
•56
•59
2-92
10
•42
•45
2-18
32
•56 -59
3-54
11
•45
•48
2-89
33
•57 -62
2-77
12
•45
•50
2-52
34
•57
•58
2-78
13
•45
•49
2-64
35
•57
•61
3-95
14
•4G
•52
3-46
36
•58
•63
3-23
15
•48
•49
3-23
37
•58
•60
3-54
1G
•48
•51
2-71
38
•58
•68
415
17
•48
•53
2-67
39
•59
•64
2-63
18
•50
•50
1-69
40
•59
•63
2-71
19
•49
•52
2-49
41
■59 -60
3-25
20
•52
•57
3-50
42
•59 -65
3-50
21
•53
•58
2-80
43
•60 -63
2-82
22
•53
•58
3-38
44
•61
•71
3-88
ON THE ENTASIS AND HEIGHT OF THE COLUMN OF THE TEMPLE
AT PEIENE.
The height of the columns of the temple of Athene can
only be obtained mdirectly from the measurements of the
fallen drums. The fragments of no particular column
could be put together with certainty, and Mr. Pullan was
only able to find about one-fourth of the original number,
and of these the stones from the lower parts of the column
formed by far the largest proportion.
The plan which first presents itself in an attempt to
recover the original height is to superimpose one upon
another drums which have like dimensions in their top and
bottom beds respectively, but this is soon discovered to
give no satisfactory solution. Mr. Pullan found the flutes
generally so much worn that he was obliged to take the
measurements within the flutes, and an additional element
of uncertainty is thus introduced, for no column has ever
so perfect a contour within the flutes as it has upon their
edges. It thus happens, as will bo seen from the subjoined
measurements of the drums, that many of these stones,
Avhilst they have like measurements on their top and bottom
beds, vary very much in length, so that it is possible by
this process to arrive at results quite discordant one from
another. The measurements of the drums, however, seem
nevertheless cajoable of affording a very close and reliable
result when fully discussed, and I have from them deduced
a value in which I have great confidence. Mr. Pullan
fortunately measured all the drums which were unbroken,
and for the lower three-quarters of the column, at least,
they are sufficiently numerous to enable us to get rid of the
accidental errors, both of workmanship and of measurement,
and to determine a very close approximation to the original
character of the entasis, and from it to deduce the heights.
If the shaft of a column were to diminish without entasis,
and therefore should be truly conical, it would only be
necessary to measure a sufficient number of drums and we
could obtain the rate of diminution, and as the upper and
lower diameters are supposed to be known, and in fact in
this case are known, the height would at once follow. But
in the case of Priene, as of all good examples of ancient
Greek architecture, the contour of the shaft is a curved
line, and the question thus becomes more complicated;
nevertheless it may be completely capable of solution if
there be a sufficient number of drums of all diameters.
This is nearly the case at Priene but not quite, as those
near the top of the column are rather scanty, but I consider
that this deficiency may be got over in a satisfactory
manner and a close determination arrived at.
To understand the method about to be followed, let it
be first assumed that the shape of the entasis is known as
well as the amount of diminution and the vertical height.
Divide the given horizontal quantity, that is to say the
whole difference between the upper and lower semi-dia-
meters, into a number of equal parts, say not less than eight,
and plot these distances down along a base line. Then draw
perpendicular lines through the points so obtained to meet
the curved outline of the column and join the intersections.
These last straight lines will then form part of a polygonal
figure, the height of which will by construction be that of
the column exactly, and each of the sides will show the
rate of diminution of the column between the corresponding
horizontal diameters plotted down upon the base line.
That is, would show the angle of inclination of the shaft of
the column between those points.
The same result would follow if the horizontal sub-
divisions were not exactly equal; but to make a good
approximation to the shape of the column they must be
sufficiently numerous and properly distributed.
Conversely if the angles of inclination corresjwnding to
given horizontal differences were given or determined we
could draw the proposed polygonal figure, and should then
discover both the form of the entasis and the height of the
column, and it is on this method that the following cal-
culation is founded. For convenience, the differences of
diameter instead of semi-diameter are used in what follows,
but that does not affect the result:
Table I.
Diameters within
the flutes.
Height of
Drum.
Diameters within
the flutes.
Height of
Drum.
Top.
Bottom.
I
Top. 1 Bottom.
I
]
feet.
3-25
feet.
3-35
feet.
2-72
23
feet.
•54
feet.
•58
feet.
2-85
2
•32
•35
1-55
24
•55
•57
1-80
O
o
•32
•35
1-60
25
•55
•63
2-30
4
•34
•35
2-32
2G
•55
■58
3-20
5
•35
•3G
2-73
27
•55 -G2
3-24
6
•39
■41
235
28
•55 -58
3-38
7
•40
•46
2-71
29
■56
•59
2-47
8
•40
•48
2-36
30
•56
•60
2-79
9
•41
•42
2-01
31
•56
•59
2-92
10
•42
•45
2-18
32
•56 -59
3-54
11
•45
•48
2-89
33
•57 -62
2-77
12
•45
•50
2-52
34
•57
•58
2-78
13
•45
•49
2-64
35
•57
•61
3-95
14
•4G
•52
3-46
36
•58
•63
3-23
15
•48
•49
3-23
37
•58
•60
3-54
1G
•48
•51
2-71
38
•58
•68
415
17
•48
•53
2-67
39
•59
•64
2-63
18
•50
•50
1-69
40
•59
•63
2-71
19
•49
•52
2-49
41
■59 -60
3-25
20
•52
•57
3-50
42
•59 -65
3-50
21
•53
•58
2-80
43
•60 -63
2-82
22
•53
•58
3-38
44
•61
•71
3-88