Of course we do not want all these measures for a single arch, but it
often happens that some of them are attainable more easily than others;
some are often unattainable altogether, and it is necessary therefore to
have expressions for whichever we may be able to determine.

V _p_ or V _a_, _a b_, and _d c_ are always essential; then either _a c_
and V _c_ or _c c_ and _c p_: when I have my choice, I always take _a
b_, V _p_, _d c_, _c c_, and _c p_, but _c p_ is not to be generally
obtained so accurately as the cusp arcs.

The measures of the present arch are:

Ft. In.
_a b_, 3 ,, 8
V _p_, 4 ,, 0
V _c_, 2 ,, 4-1/2
_a c_, 2 ,, 0-1/4
_d c_, 0 ,, 3-1/2

20. SHAFTS OF DUCAL PALACE.

The shortness of the thicker ones at the angles is induced by the
greater depth of the enlarged capitals: thus the 36th shaft is 10 ft.
4-1/3 in. in circumference at its base, and 10 ,, 0-1/2[103] in
circumference under the fillet of its capital; but it is only 6 ,,
1-3/4 high, while the minor intermediate shafts, of which the thickest
is 7 ,, 8 round at the base, and 7 ,, 4 under capital, are yet on the
average 7 ,, 7 high. The angle shaft towards the sea (the 18th) is
nearly of the proportions of the 36th, and there are three others, the
15th, 24th, and 26th, which are thicker than the rest, though not so
thick as the angle ones. The 24th and 26th have both party walls to
bear, and I imagine the 15th must in old time have carried another,
reaching across what is now the Sala del Gran Consiglio.

They measure respectively round at the base,

The 15th, 8 ,, 2
24th, 9 ,, 6-1/2
26th, 8 ,, 0-1/2

The other pillars towards the sea, and those to the 27th inclusive of
the Piazzetta, are all seven feet round at the base, and then there is a
most curious and delicate crescendo of circumference to the 36th, thus:

The 28th, 7 ,, 3 The 33rd, 7 ,, 6
29th, 7 ,, 4 34th, 7 ,, 8
30th, 7 ,, 6 35th, 7 ,, 8
31st, 7 ,, 7 36th, 10 ,, 4-1/3
32nd, 7 ,, 5

The shafts of the upper arcade, which are above these thicker columns,
are also thicker than their companions, measuring on the average, 4 ,,
8-1/2 in circumference, while those of the sea facade, except the 29th,
average 4 ,, 7-1/2 in circumference. The 29th, which is of course above
the 15th of the lower story, is 5 ,, 5 in circumference, which little
piece of evidence will be of