ARCHITECTURE, 105 
of the column, and let fall a perpendicular line from the top of the shaft 
upon this diameter, which will intersect the semicircle in some point; 
divide the arc thus obtained into any number of equal parts, and the upper 
two thirds of the shaft into as many equal horizontal stripes. If, then, perpen- 
diculars are erected on the various points of the arc, and prolonged until 
they strike the horizontal lines in the shaft, the points of intersection will 
mark the diameters of the reduced stripes. The other kind of reduction 
is that of a swelling of the column, that is, a reduction upwards and down- 
wards. After the proper diameter of the column (jig. 11) and the height of 
the column are determined, give this diameter to the shaft at one third 
of its height, and erect at its extremities perpendiculars extending to the 
base and to the astragal. Prolong the diameter at one third the height, 
sideways, giving it the length of two thirds the height, and half a diameter. 
Connect the highest and lowest points of the shaft, by straight lines, with 
the end of the prolonged diameter. From the axis of the shaft mark off on 
these lines half the length of a diameter, when the points thus obtained will 
be those of the upper and lower reductions. From the apex of the triangle 
formed by the two lines and the axis of the shaft, lines may then be drawn at 
will to any number of points on the axis, and semi-diameters marked off on 
the same, when all the points thus obtained will he in the curve of reduc- 
tion. The French architect; Blondel, regards the first conchoid of Nico- 
medes as the curve of reduction, and gives an instrument to draw this 
conchoid. 
The twisted columns found in the altar of St. Peter’s at Rome, in the church 
Val de Grace in Paris, and elsewhere, can only be regarded as abortive 
creations of a sickly fancy, and as exhibitions of a vicious style. In the former 
the chevalier Bernini sinned against good taste, and Le Duc imitated him 
in the latter. We give here the construction of such columns in order to 
show what trouble is taken to accomplish a paltry result (pl. 20, jig. 12). 
To draw the twisted column you must first make the ground plan (fig. 
13) where the smaller circle indicates the cylinder of the column. Divide 
this circle into eight parts, and from all the points draw parallels-with the 
axis of the column. The axis of the column you divide by horizontals into 
as many times eight parts as the column has twists (generally six, conse- 
quently into forty-eight parts). The points of intersection of these lines and 
of those which were drawn parallel with the axis from the smaller circle will 
then mark the course of a twisted line, which rests upon the small cylinder. 
From the points thus obtained mark off half the diameter of the column 
outwards, when the terminal points of these horizontals will mark the exterior 
contour of the spiral. 
8. Doors anp Winpows. We have already stated (p. 29) that the doors 
and windows must harmonize with the cornices and members of the order, 
and for this reason Vignola has sketched especial doors for each order, 
although their form and size are always dependent upon the general relations 
and particularly upon the size of the building itself. The Tuscan door is 
very simple, twice as high as broad, and framed with a cavetto and socle, 
while the lintel, whose upper surface is curved, and the jambs are adorned 
105 
