hey can be, consistently with their due
strength.

[Illustration: Fig. XLV.]

Let it be required to support the breadth of glass, _a_, _b_, Fig. XLV.
The tendency of the glass sustaining any force, as of wind from without,
is to bend into an arch inwards, in the dotted line, and break in the
centre. It is to be supported, therefore, by the bar put in its centre,
_c_.

But this central bar, _c_, may not be enough, and the spaces _a c_, _c
b_, may still need support. The next step will be to put two bars
instead of one, and divide the window into three spaces as at _d_.

But this may still not be enough, and the window may need three bars.
Now the greatest stress is always on the centre of the window. If the
three bars are equal in strength, as at _e_, the central bar is either
too slight for its work, or the lateral bars too thick for theirs.
Therefore, we must slightly increase the thickness of the central bar,
and diminish that of the lateral ones, so as to obtain the arrangement
at _f h_. If the window enlarge farther, each of the spaces _f g_, _g
h_, is treated as the original space _a b_, and we have the groups of
bars _k_ and _l_.

So that, whatever the shape of the window, whatever the direction and
number of the bars, there are to be central or main bars; second bars
subordinated to them; third bars subordinated to the second, and so on
to the number required. This is called the subordination of tracery, a
system delightful to the eye and mind, owing to its anatomical framing
and unity, and to its expression of the laws of good government in all
fragile and unstable things. All tracery, therefore, which is not
subordinated, is barbarous, in so far as this part of its structure is
concerned.

Sec. VI. The next question will be the direction of the bars. The reader
will understand at once, without any laborious proof, that a given area
of glass, supported by its edges, is stronger in its resistance to
violence when it is arranged in a long strip or band than in a square;
and that, therefore, glass is generally to be arranged, especially in
windows on a large scale, in oblong areas: and if the bars so dividing
it be placed horizontally, they will have less power of supporting
themselves, and will need to be thicker in consequence, than if placed
vertically. As far, therefore, as the form of the window permits, they
are to be vertical.

Sec. VII. But even when so placed, they cannot be trusted to support
th