Civil Engineering Reference
In-Depth Information
Of equal signii cance to these factors was the aspect. h e stone dome, unlike
the vault, was designed to present an external aspect. A tall “vertical feature” was
such a violent contrast to the overall horizontal lines of classical architecture as to
constitute an unpalatable shock. On the other hand the hemispherical form has
a restful disposition.
With these latter remarks in mind it is now appropriate to say something of
the protracted delay between the acceptance of the vault and the acceptance of the
dome in Graeco-Roman monumental building. h is manifestly has little to do with
masonry technology. h e stereotomy of a dome voussoir is more complicated than
that of a vault since the intrados and the extrados are curved in two dimensions (i.e.
horizontal as well as vertical), and the bed joints as well as the rising joints diverge
radially. However the incorporation of these features is simply by extension of the
features in setting out a vault voussoir. h e acceptance of the hemispherical dome
was governed entirely by questions of aspect not structure. h is change in aspect
was an image of a changed “world view”. Much has been written on this subject,
falling within the philosophy of history. A striking characterisation of the issue
is contained in Spengler's Decline of the West; while Baldwin Smith's h e Dome
rehearses all the ramii cations of symbol and image relating to the domical form.
h e delay in the introduction of the ashlar dome into the Classical World attended
on a change in society and its values away from the “dear city of Cecrops”.
It is now necessary to attempt some explanation of the second problem which
is endemic in the construction of domes: the adjustment between the circular
base of the dome and the square plan of the chamber over which it is set. h ere
are two circles which coincide at some points with the square: the inscribed circle
and the circumscribed circle. h e inscribed circle coincides with the square at
the mid points of the sides. h e diameter of this circle is thus the same length as
the side and the radius of the circle is half the length of a side of the square. h e
circumscribed circle coincides with the square at the angles and its radius is thus
half the length of the diagonal of the square. Since the ratio of the side of a square
to its diagonal is 1 : √ 2, the ratio of the radius of the inscribed circle to that of
the circumscribed circle is also 1 : √ 2 = 1 : 1.1414 or < 10 : 14 ~ 5 : 7. Neither
of these circles, however, makes the necessary adjustment. A dome raised on the
circumscribed circle oversails the chamber on all 4 sides, and a dome raised on
the inscribed circle leaves uncovered a considerable (triangular) space at each of
the four angles of the chamber.
h e problem is thus to cover these angle spaces in a way which facilitates tran-
sition into a dome raised on the inscribed circle. h is may be done more or less
hand over i st in a number of ways, but the rational (monumental) solution is to
occupy each of the angle spaces with a spherical triangle of masonry which “hangs
down” to a point in the angle of the chamber and is thus called a pendentive.
h e Dome
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300
290, 293
