other: usually a steep bank at the
river-side next the large arch; always, of course, a flat shore on the
side of the small ones: and the bend of the river assuredly concave
towards this flat, cutting round, with a sweep into the steep bank; or,
if there is no steep bank, still assuredly cutting into the shore at the
steep end of the bridge.

Now this kind of bridge, sympathizing, as it does, with the spirit of
the river, and marking the nature of the thing it has to deal with and
conquer, is the ideal of a bridge; and all endeavors to do the thing in
a grand engineer's manner, with a level roadway and equal arches, are
barbarous; not only because all monotonous forms are ugly in themselves,
but because the mind perceives at once that there has been cost
uselessly thrown away for the sake of formality.[57]

[Illustration: FIG. 34.]

204. Well, to return to our continuity. We see that the Turnerian bridge
in Fig. 32 is of the absolutely perfect type, and is still farther
interesting by having its main arch crowned by a watch-tower. But as I
want you to note especially what perhaps was not the case in the real
bridge, but is entirely Turner's doing, you will find that though the
arches diminish gradually, not one is _regularly_ diminished--they are
all of different shapes and sizes: you cannot see this clearly in Fig.
32, but in the larger diagram, Fig. 34, over leaf, you will with ease.
This is indeed also part of the ideal of a bridge, because the lateral
currents near the shore are of course irregular in size, and a simple
builder would naturally vary his arches accordingly; and also, if the
bottom was rocky, build his piers where the rocks came. But it is not as
a part of bridge ideal, but as a necessity of all noble composition,
that this irregularity is introduced by Turner. It at once raises the
object thus treated from the lower or vulgar unity of rigid law to the
greater unity of clouds, and waves, and trees, and human souls, each
different, each obedient, and each in harmonious service.

4. THE LAW OF CURVATURE.

205. There is, however, another point to be noticed in this bridge of
Turner's. Not only does it slope away unequally at its sides, but it
slopes in a gradual though very subtle curve. And if you substitute a
straight line for this curve (drawing one with a rule from the base of
the tower on each side to the ends of the bridge, in Fig. 34, and
effacing the curve), you will instantly see that the