458 APPENDIX, 20

a c the length of the chord of the lower arc of the cusp, V c the length of the chord of the upper arc of the cusp (whether continuous or not), and c p the length of a perpendicular from the point of the cusp on a b.

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 ,, 4½

a c, 2 ,, 0¼

d c, 0 ,, 3½

20. P. 244.-SHAFTS OF THE 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. 4¹/3 in. in circumference at its base, and 10 ,, 0½* in circumference under the fillet of its capital; but it is only 6 ,, 1¾ 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 one. 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 ,, 6½

26th, 8 ,, 0½

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 ,, 4¹/3

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 ,, 8½ in circumference, while those of the sea façade, except the 29th, average 4 ,, 7½

* I shall often have occasion to write measures in the current text, therefore the reader will kindly understand that whenever they are thus written, 2 ,, 2, with double commas between, the first figures stand for English feet, the second for English inches.

[Version 0.04: March 2008]