The Principles of Vaulting.
Vaulting of spaces of other forms than the mere square--Apsidal
aisles, St. John’s Chapel Tower, and St. Bartholomew’s Church,
Smithfield--Chapter-house and crypt, Worcester--Round-arched
vaulting in its most normal form, as resulting from the _barrel_
vault and its intersections--Short digression on another simple
form of vault, the _dome_--“Domed up” vaults--“Welsh” groining--The
square or polygonal dome--The Round-arched style of the twelfth
century almost perfect--First introduction of the Pointed arch into
vaulting--Names of the parts of groined vaulting--Two specimens in
London of the apsidal aisle, one in the Round-arched, the other in
the Pointed-arched style--Vaulting a polygon with a central
pillar--_Ploughshare_ vaulting--The artistic sentiment and
character of early Gothic vaulting.
In my last lecture I explained the general principles of groined or
intersecting vaulting, and just carried on the subject through its
simplest case,--the covering of a square space, or any repetition of
square spaces, by the intersection of semi-cylindrical vaults; and I
just showed how, by emphasising the outlines of the squares so covered
by means of transverse ribs or angles, and by placing impost mouldings,
pilasters, columns, or colonnettes in the sustaining piers, such a mode
of covering a space might be readily made at once susceptible and
suggestive of architectural treatment.
Let us now proceed to consider the application of the same principles to
the vaulting of spaces of other forms than the mere square.
The next form, perhaps, in point of simplicity is an equal-sided
polygon,--say, for example, an octagon (Fig. 322). We must here suppose
eight cylindrical vaults crossing one another from the opposite sides of
the octagon; and it is clear that their intersecting lines will be the
diagonals or lines joining the opposite angles of the octagon, which
will coincide in position with the transverse ribs. The objection to
this form of vaulting is the low proportion of the arches produced by
these intersections, which, though more than twice and a half the width
of the side arches, only rise to the same height, or about one-fifth of
their span,--a defect which will be remedied by a development I shall
presently have to describe.[40] Just as the half-dome (as seen in the
chapel of the Tower of London)[41] forms a natural covering for an
apsidal termination of a barrel vault, so a portion of a polygon, thus
vaulted, would _appear_ to be the correlative apsidal termination of a
_groined_ vault.[42] A difficulty, however, at once presents itself in
the small height of the vault last described, which is not one-half of
the height of the semicircular vault which it would have to meet. How,
then, is this to be got over? How are the vaults proceeding from the
narrow arches of the sides of the octagon to be brought to range in
height with the wide vault which spans the whole space (Figs. 323 and
326)?
[Illustration: Fig. 322.]
[Illustration: Fig. 323.]
[Illustration: Fig. 324.]
The solution of this difficulty will be better considered by means of a
simple and more familiar case. The intersecting vault in its most normal
form is plain enough in its application to a square compartment, but
becomes difficult when applied to a space longer one way than the other;
yet oblong spaces continually present themselves as requiring to be
vaulted.
Mathematically this is readily met, and that with perfect accuracy, by
making one of the intersecting vaults _elliptical_ instead of _circular_
in its curvature; making, for instance, the narrower arch a semi-ellipse
with its longer semi-diameter vertical. This, however, is an unsightly
form, and was always rejected, though the natural mode of effecting the
object, and though it would give intersecting curves which would be
complete and in vertical planes.
The Roman builders solved the problem at the sacrifice of mathematical
accuracy, by what is called _stilting_ the narrower arch; that is,
raising its springing till its crown becomes level with that of the
wider arch. This is a practical solution of the difficulty, but is not a
very pleasing one, inasmuch as the line of intersection is most
uncouthly twisted, and, in point of fact, begins at considerable height
above the springing of the vault (Figs. 324, 325.)
[Illustration: Fig. 325.]
To go back, however, to our previous case of the apsidal termination of
a vaulted space, it affords a very fair solution of the difficulty by
which we were before encountered; for it is clear that the arches on the
sides of the octagon may be lifted up till their crowns become level
with that of the main vault; and, as the intersecting angles of a
polygonal groined vault coincide with its transverse ribs, we have
nothing to do but to raise from every angle a transverse rib similar, or
very nearly similar, to those of the main vault, and to make the smaller
vaults of the octagon to intersect upon them (Fig. 326). There will be a
little geometrical inaccuracy in the forms of these cells of vaulting;
but, as the angle ribs would assume correct lines, these inaccuracies
would not seriously offend the eye.
[Illustration: Fig. 326.]
There is, however, another method of meeting the difficulty; but before
describing it, I will say a few words on the treatment of other
difficulties resulting from the irregularities in form of spaces which
have to be vaulted.
Let us, as an example, suppose an aisle or corridor passing round such a
polygonal figure as we have been considering. It is manifest that its
compartments will have a form enclosed by unequal sides, or, to say the
least, one side will differ greatly in width from that opposite to it.
The stilting system before-mentioned is the most obvious method of
getting over the difficulty. It may be, that three of the arches
surrounding such a compartment may be about equal, and no great
difficulty would occur as to _their_ intersection; but the fourth,
being far narrower, would have to be stilted to raise its crown to the
level of the others, and its lines of intersection will consequently be
more or less disturbed.
[Illustration: Fig. 327.--St. John’s Chapel, Tower of London.]
[Illustration: Fig. 328.--St. Bartholomew’s Church, Smithfield.]
The difficulty is, in early specimens, increased through the apse being
usually round instead of polygonal; though this does not very materially
alter the case. We have in London two excellent examples of this apsidal
aisle; that in the chapel of the Tower of London[43] (Fig. 327), and
that in St. Bartholomew’s Church in Smithfield (Figs. 328, 329),--the
former of an early, and the latter of a later type.
[Illustration: Fig. 329.--Plan of Apse, St. Bartholomew’s Church,
Smithfield.]
In both, the narrow arches are greatly stilted; and at first sight the
two may appear to be similarly treated; but on closer examination there
will be found to be much difference between them. In the Tower Chapel
the transverse ribs are made to increase prodigiously in width towards
the outer wall, so as to reduce the want of parallelism of the groined
compartments, a very unsightly expedient; and the capitals of the
columns are square, which makes the backs of the arches they support
nearly double the width they present in front: while at St.
Bartholomew’s, the ribs are of uniform width, and the capitals, instead
of being square, have their sides radiating from the centre of the apse,
so as to share with their arches the spreading of their outer side. The
difficulty is really increased in the later work, but is met by more
skilful workmanship. Somewhat similar to the case of the aisle round a
semicircular apse, is the case of vaulting a circular building with a
central pillar. In each, the main surrounding vault, if uncut by others,
would assume the form of a portion of an _annulus_ or _ring_. In the
aisle such a ring would be wide in the opening it surrounds, but in the
circular building its opening would be reduced to the diameter of the
central column or its capital.
This annulus, or curved vault, would become divided in plan into
triangular portions by the transverse ribs which would meet on the
central pillar and the cross vaults, proceeding from the surrounding
arches, would intersect with only the _outer portion_ of the vault, the
_inner portion_ which rests on the pillars being uncut by them, and
assume the form of a concave conoid, something like the flower of the
convolvulus.
[Illustration: Fig. 330.--Chapter-house, Worcester Cathedral.]
[Illustration: Fig. 331. Plan of Crypt, Worcester Cathedral.]
This form of vault is well seen in two instances in the Cathedral at
Worcester. The best known of these is the Chapter-house (Fig. 330), a
circular building, between 50 ft. and 60 ft. in diameter, whose
circumference is divided into ten parts, from which small ribs run
across to the central pillar. The intersecting cells of groining are at
present _pointed_, possibly the result of a subsequent alteration, and
simply intersect with the surrounding vault. In this case the central
conoid is broken into a polygonal form to give piquancy to its otherwise
too unbroken surface. This may be considered the father of our beautiful
polygonal chapter-houses, of which I shall have more to say as I
proceed.
The other instance I have alluded to at Worcester is in the crypt (Figs.
331, 332). In this, the case in question occurs not in a distinct form,
but in combination with an apsidal aisle on the one side, and a vaulted
span, with a central range of pillars, on the other; the last pillar
forming the central point of the semicircular apse, is exactly parallel
in position, and forms very similar groining to that of the
Chapter-house.
[Illustration: Fig. 332.--View of Crypt, Worcester Cathedral.]
The same problem, when applied to a polygon instead of a circle, is open
to two different modes of solution. In the one, the main vault is always
supposed to run from each _side_ towards the central pillar; in the
other, from each _angle_ towards the pillar. I shall, however, have to
go more minutely into this when I come to pointed-arch vaulting, to
which the last-named system more especially applies.[44]
Having now briefly touched upon the most prominent forms of round-arched
vaulting in its more normal form, as resulting from the _barrel_ vault
and its intersections, I will digress for a short time to consider some
of the conditions which relate to what I in my last lecture stated to be
the other most simple kind of vault--the _dome_. I do so, however, not
with any idea of treating at large on a form which should be made the
subject of a separate lecture, but merely to facilitate the explanation
of certain indirect influences which it exercised upon ordinary
vaulting.
A dome in its most typical form stands upon a circular wall; this,
however, is by no means a necessary condition. It may in reality cover a
square or polygonal space just as well; for, suppose a square or a
polygon inscribed within the base of a hemisphere, it is clear, from the
properties of a sphere, that vertical planes erected on the sides of
such square or polygon will cut the hemisphere in semicircles of the
diameter of those sides (Fig. 333). It follows, therefore, that the
walls of a square or polygonal building would intersect with a dome in
the form of semicircular arches standing on each of its sides; and,
consequently, that such a square or polygon will carry a hemispherical
dome, or rather the remainder of it left after cutting the base into a
square or polygon.
[Illustration: Fig. 333.]
For our immediate purpose we will limit the case to that in which the
inscribed figure is a _square_.
[Illustration: Fig. 334.]
[Illustration: Fig. 335.]
Now, a dome cut in this manner by four planes is not a very sightly
form, and needs some embellishment (Fig. 334); but if a horizontal
circle be drawn within it by means of a cornice resting on the crowns of
the supporting arches, it assumes at once an agreeable form, and one
which has been largely used both in Byzantine and in modern
architecture (Fig. 335). My present purpose, however, suggests another
mode of giving sightliness to the squared dome. The lines drawn on its
surface may lie in vertical as easily as in horizontal planes, and by
making such lines pass through the angles of the square, touching the
dome throughout their length, and intersecting one another at its apex,
we obtain a form not wholly unlike a square groined vault; the great
differences being that the intersecting diagonals of a groined vault
assume elliptical curves, whereas these are semicircles; that in the one
they represent an actual angle, while in the other they are arbitrarily
drawn on an unbroken surface; and that the ridges or crowns of the vault
in one case are horizontal, while in the other they are raised and
circular. This mode of vaulting, though frequent in some parts of
France, is seldom found in this country.
[Illustration: Fig. 336.--Goring Church, Oxfordshire.]
There is, however, an instance of it in the vaulting beneath the tower
of Goring Church, Oxfordshire. (Fig. 336).
Though this is not really _groining_, but a disguised dome, there is a
ready process by which it may be, and continually was, converted into
genuine groining.
I have defined the barrel vault as the prolongation of an arch in a
direct line at right angles to its plane.[45] But an arch may be
prolonged in other than a straight line. Let us, in the previous
figure, suppose the arches which rise from the sides of the square to be
prolonged, not horizontally, but in a curve rising as it proceeds, and
so regulated that the semicircle as it moves forward retains its
vertical position, and is guided in its motion by the diagonal lines
drawn in the dome. This process at once generates a new form of vault
(Fig. 337). For each of the triangular gores of the dome we now
substitute a vault, of which every vertical section parallel to the side
of the square is a portion of a circle of the same diameter with those
raised on the sides, while the angles of the intersection of these newly
generated vaults are themselves semicircles. It is a perfectly accurate
geometrical figure, none of whose salient lines are other than portions
of circles, though the ridge or crown lines now become elliptical. It is
a most useful development, as being much stronger than the ordinary
groined vault. Oddly enough, it has--so far as I am aware--no suitable
name. It is usual to speak of such vaults as being “domed up,” but this
is a very rough description. When adapted to the pointed arch, it has
been called by Mr. Petit the Angevine vault. I know no better way of
describing it than as round-arched vaulting with a raised ridge (Fig.
338).
[Illustration: Fig. 337.]
[Illustration: Fig. 338.]
Now, though less obvious at first sight, the very same processes are
applicable either to an oblong, to a tapering four-sided figure, such as
the bay of the aisle of an apse, or even to one of the triangular
compartments of the apse itself, or of a circle.
For, in either case, we have only to cut out the required slice from a
hemispherical dome, to draw the diagonal lines from the angles of such
form to the apex, and then to substitute for the gores of the dome the
vault generated by the motion of the semicircle, produced by the plane
of the sides of the figure parallel to itself, and rising under the
guidance of the diagonal lines (Fig. 339). This process, it will at once
be seen, is capable of solving all the problems of irregular figures
which I have enumerated at an earlier stage in my lecture, without the
aid of stilting, and without giving intersecting curves, which deviate
from the vertical plane, while it avoids the use of the ellipse for any
prominent line (Fig. 340).
[Illustration: Fig. 339.]
[Illustration: Fig. 340.]
[Illustration: Fig. 341.]
The last case I have named--that of the triangular gore of an apse or
circle (Fig. 341)--also solves the difficult case I mentioned at the
beginning of this lecture as arising in the groining of a polygon, owing
to the excessive lowness of the arch formed by the intersecting angles.
These are now raised to the full height of a semicircle, while if half
of such a polygonal vault be used for an apse, it agrees in height with
the main vault without the use of stilting.
It may, however, be mentioned that, as stilting is sometimes most useful
in making room for windows, it was not superseded by this invention;
the two systems continuing to be used at pleasure, and sometimes a union
of the two, which, however, is so arbitrary as to defy definition. The
form last described for a vaulted circle is often used as a variety of
the dome by raising numerous small arches round its circumference, and
giving a sort of fluted or shell-like surface to the dome.
I think I have now described the principal varieties of round-arched
vaulting with two exceptions. The one is that in which the side vaults
of oblong compartments cut the higher and main vault at a level lower
than its crown. This is vulgarly known as “Welsh” groining, and though
not quite pleasing in effect, it is a very legitimate mode of covering
an oblong compartment. It is customary to obviate the unpleasing
coal-scuttle shape of the true line of intersection (Fig. 342) (such as
may be seen in St. Martin’s Church), by making them take the lines given
by vertical planes, and throwing the irregular geometrical curve into
the surfaces of the cells where it does not strike the eye, or perhaps
generating them by the motion forward of the side arch (Fig. 343). This
has been done in the Sistine Chapel, and Mr. Smirke has, I think, done
the same in our Great Exhibition Room. In a ceiling to be decorated with
painting, this form of vaulting possesses the great advantage of leaving
the central range unbroken by diagonal lines.
[Illustration: St. Martin’s-in-the-Fields, London.