A constant width for the dado is also common to all the orders in that it always lines up with the projection of column bases. This projection is the same for all the orders, as was established in the third chapter and as will be further explained in what follows. PERRAULT 82 Chapter VIII The Diminution and Enlargement of Columns TJLn.HE TWO most important requirements in architecture are durability and the appearance of durability, which, as we have already said, produce one of the principal constituents of beauty in buildings. All architects have made columns more slender at the top than at the bottom, and this is what we call diminution. Some have made them a little thicker near the middle than at the bottom, and this is what is called enlargement [enflement}?2 Vitruvius would have the diminution of columns vary according to their height in feet and not according to their height in modules. Accordingly, a column of fifteen feet must be diminished by the sixth part of the diameter at its base and one of fifty feet by only one eighth. For other columns of medium height, he makes the diminution proportional. But we find that these rules have not been observed at all in antiquity. The diminution of the columns of the Temple of Peace and of the portico of the Pantheon, of the Roman Forum, called the Campo Vaccino, and of the Basilica of Antoninus does not differ at all from the diminution of the columns of the Temple of Bacchus, which are only one quarter the height of the others. There are even some very large ones, such as those of the Temple of Faustina, of the Portico of Septimius, of the Temple of Concord, and of the Baths of Diocletian, whose diminution is greater than that of others that are half their size, such as those of the Arches of Titus, Septimius, and Constantine. In fact, these small columns, which are less than fifteen feet high, have a smaller diminution than the sixth part that Vitruvius gives them, since they diminish by only about a seventh part and one half. Furthermore, even in the largest, although they exceed the fifty feet of Vitruvius, we find a greater diminution than that prescribed for them, for they also diminish by as much as a seventh part and one half, instead of by only one eighth, as they should according to Vitruvius's rule. Nor are the differences between the orders what determine variations in diminution, since both small and large diminutions are present in various works of all the orders. The Tuscan column must be excepted, however, since Vitruvius gives it a diminution as large as a fourth part. Nevertheless, some Moderns have not followed Vitruvius in this, and Vignola gives it a diminution of only one fifth. In Trajan's Column, the only Tuscan work remaining from antiquity, the diminution, being only a ninth part, is much smaller still. Therefore, in order to maintain a mean between these extremes, I give the Tuscan column a diminution of a sixth part, rather PART ONE: THINGS COMMON TO ALL THE ORDERS than only a seventh part and one half, which the columns of the other four orders have. It would appear reasonable, were diminution to be altered according to the orders, to make diminution less rather than more in orders where columns are shortest in proportion to their thickness, because it is in these that diminution is most apparent. Nevertheless, since the diminution that Vitruvius gives the Tuscan column has been followed by most architects, I believe that deference to custom,33 which is one of the chief laws of architecture, demands that this diminution be somewhat increased in the Tuscan Order. I have put in the following table the different dimensions of the various orders, together with their diminutions, in order to show by these examples that the Ancients varied diminution neither according to the different orders nor according to different column heights. Diminutions vary within the same order and for the same column height and, moreover, are the same in different orders and for different column heights. One may see in the table, for example, that the Doric column of the Theater of Marcellus and the Doric column of the Colosseum, which are about the same height, have very different diminutions, one being twelve minutes, the other four, and that the Ionic column of the Temple of Fortuna Virilis and that of the Colosseum, which are also the same height, have divergent diminutions of seven and ten minutes respectively. On the other hand, in the column of the Temple of Fortuna Virilis and in that of the Portico of Septimius the diminution is the same, although the former, which is Ionic, measures only twenty-two feet and the latter, which is Corinthian, measures as much as thirty-seven feet. Now of all the diminutions that have been given to all columns, examples of which are listed in the table, I have taken the mean, adding the size of the smallest diminution to the size of the largest and taking half of their sum, which comes to about eight minutes. If we add the size of the smallest diminution, which is that of the Doric column of the Colosseum at only four and one-half minutes, to the size of the largest, which is that of the Doric of the Theater of Marcellus at as much as twelve, half of these sizes, which together make sixteen and one half, is eight and one quarter. Similarly, if we add the size of the smallest diminution of the columns that remain, which is six and one eighth in the column of the Basilica of Antoninus, to the largest of ten and one half in the column of the Temple of Concord, half of these two sizes, which together make sixteen and five eighths, is eight and five sixteenths. Now this dimension of eight minutes, which makes almost exactly a seventh part and one half of the diameter, is one fifth of my small module, or four minutes, taken from either side of the column. I have not listed the diminutions of the Moderns because they are the same as those of antiquity, which vary from author to author and from order to order. 83 PERRAULT 84 TABLE OF THE DIMINUTION OF COLUMNS Height Diameter Diminution of Shaft feet inches feet inches minutes Theater of Marcellus 21 0-0 3 0-0 12-0 Doric Colosseum 22 lo-V-z 2 8-Y4 4-'/a Temple of Concord 36 0-0 4 2-'/2 io-Y2 Ionic Temple of Fortuna Virilis 22 IO-O 2 II-O 7-Y2 Colosseum 23 o-o 2 8-3/4 I O-O Temple of Peace 49 6 3- 5 8-0 6-