The Dimensions of the Columns
a) The Columns of the Peripteros.
The 42 normal columns of the peripteros have a diameter of 100 fingers (6½ feet); the module is the geographic foot, so that the diameter is 1926.7 mm. The 4 corner columns have the same diameter, but the module is the trimmed wheat foot, so that 100 fingers are 1965.7 mm. The 4 corner columns have the same diameter, but the module is the trimmed wheat foot, so that 100 fingers are 1965.3 mm. Since the geographic foot is 25/24 of the Roman foot, and the trimmed wheat foot is 17/16 of the Roman foot, the diameter of the corner columns is 17/16 x 25/24 = 51/50 of that of the normal columns. This is in perfect agreement with Vitruvius rule (III,3,11):
We must therefore follow the rules of symmetry required by each kind of building. Then, too, the columns at the corners should be made thicker than the others by a fiftieth of their own diameter, because they are sharply outlined by the unobstructed air around them, and seem to the beholder more slender than they are. Hence, we must counteract the ocular deception by an adjustment of proportions.
The diameter of the corner columns is 102 fingers of geographic foot.
The columns of the peripteros have 20 flutings as is usual with columns of the Doric order. This means that after the column drums have been turned out on a lathe as cylinders, the circular section was changed by cutting it into a polygon with 20 faces, and ikosagon. Each face of the column corresponds to 18° of the circumference. In order to calculate the dimensions of an ikosagon, it is necessary to know the angular functions of 9°. The most important datum is the cosine, which is 0.98769. The ancient practice was to reckon the cosine of 9° as 80/81, using the mnenomic number 0.98765... This means that the distance between opposite faces of the columns was reckoned as 98.765... fingers. In order to obtain the width of the faces it was enough to multiply by 5 the semi-diameter expressed in feet, which is 3 1/8 and take the result as fingers, that is, 15 5/8 fingers. This follows from the fact that the width of the faces is reckoned by 2 x sine 9° = 0.31287, which can be considered equal to 5/16 = 0.31250. The division by 16 was easy, since the diameter was calculated in 16ths of foot, that is, fingers.
I have calculated the diameter of the normal columns as 1926.7 mm.; Balanos reports a diameter of 1928 mm. According to my reckoning the distance between opposite faces was 80/81 x 1926.7 mm. = 1902.9 mm.; Magne reports a distance of 1904 mm., and Penrose a distance of 1903.5 mm on the east front, of 1905.3 mm. on the west front, and of 1905.0 mm. on the north flank. The differences among these figures indicate how much we need a detailed report on the dimensions of the columns one by one. Balanos reports that by a careful examination of a single column, he found that diameter may vary of as much as 2 or 3 mm., when tested in different directions. Given the penury of available data, it is impossible to ascertain whether these differences were planned, or were the result of imperfection in workmanship.
According to my calculations the 4 corner columns had a diameter of 1985.5 mm. and a distance between opposite faces of 1941.0 mm. Magne reports that the diameter of the corner columns is 1968 mm.; Penrose reports that the distance between the opposite faces is 1944.0 mm. in the southeast column and of 1945.2 mm in the northeast column.
Concerning the distance between the bottoms of opposite flutings, Balanos reports a distance of 1834 mm., whereas Penrose reports a distance of 1832.8 for the northeast column, of 1835.2 mm for the northwest column, and of 1835.2 mm for the southwest column. It would seem that the distance was reckoned as 931/3 fingers or 1834.2 mm., the flutings being 31/3 fingers deep. Apparently the fluting of the normal columns was deeper, being 3½ fingers, sot hat the distance between the opposite bottoms of the fluting was 93 fingers or 1791.8 mm.; Balanos reports a distance of 1792 mm.
b) The Columns of the Cella
The reports about the columns of the cella, of which there were 6 on each front, are most contradictory. According to Magne, the columns have the same diameter on the two porches. But Hans Riemann charges that most likely Magne measured only the columns of the west porch and wrote down a figure for the columns of the east porch by assuming without any test that the latter were identical with the former; given the proven carelessness of Magne, this accusation may be credible. According to Penrose the columns of the east porch, of which at present there remains only one, were thinner. Balanos, who spent some forty years of his life handling the stones of the Parthenon, does not help in solving this controversy, since in the text he states that the columns of the two porches were identical, but in the plates attached to it he pictures the surviving column of the east porch as thinner. He explains that, in the case of the columns of the cella, he measured only the distance between opposite bottoms of the flutings, since the fillets between the flutings are too damaged. I shall limit my interpretation to the columns of the west porch.
According to Vitruvius (IV,4,2), the diameter of the columns of the cella must be 9/10 of that of the peripteros. In the Parthenon this rule was followed by making the diameter of the columns of the cella equal to 90 fingers, but the module of foot is the English foot which is slightly shorter than the geographic foot used as module for the columns of the peripteros. In the case of the columns of the cella probably there was used sexagesimal reckoning, taking 1½ fingers as the unit. It is to be noted, however, that these columns, too, are of the Doric order with 210 flutings. Reckoning sexagesimally the distance between opposite faces may be taken as 59¼ units, which would make cosine 9°-0.9875002, instead of 0.98769.
According to my calculation the columns of the eastern porch had a diameter of 1715.2 mm.; Penrose reports a diameter of 1716.6 mm. The distance between the bottom of opposite flutings was 1610 mm. according to Balanos and 1610.3 mm according to Penrose. Apparently the distance was reckoned as 84½ fingers or 1610.3 mm, with flutes 2¾ fingers deep.
According to Penrose the columns of the eastern porch had a diameter of 1,646.5 mm. and a distance between the bottoms of opposite flutings of 1544.1 mm.; but according to Balanos the latter was 1535 mm.
c) The Columns of the Naos
The columns of the Naos have completely disappeared, since they were removed when the Parthenon was transformed into a Christian church. But it has been possible to ascertain their bottom diameter by observing its impression on the blocks of the stylobate.
The columns were of the Doric order with 18 flutes. Hence, each face corresponded to 20° of the circumference. Because of this they were computed sexagesimally, since cosine 10°, which is 0.98481, can be most easily computed as 59/60=0.98333. They had a diameter of 60 fingers of Roman foot (geometric form) or 1114.4 mm.; Penrose reports a diameter of 1114.4 mm.
The 2 corner columns were extraordinarily large in relation to the normal columns; according to Penrose they had a diameter of 1,947.1 mm. Most likely they had a diameter of 60 units of 7/4 fingers of Roman foot or 1950.0 mm. This is the unit that is obtained by constructing from the Roman foot a royal cubit of 28 fingers and then dividing it into 16 fingers; there are Egyptian measuring rods that are so constructed and divided.