IOI 
A R C H I T 
which, from the axis towards the circumference, fetting 
off the interval C D, may be found any number of points, 
as a a a, &c. through wliich, if a curve be drawn, it will 
defcribe the fwelling and diminution of the column. 
Though this method be fufficiently accurate for prac¬ 
tice, efpecially if a conliderable number of points be found, 
yet, ftriftly fpeaking, it is defective, as the curve muft 
either be drawn by hand, or by applying a flexible ruler 
to all the points; both of which are liable to variations. 
Blondel, therefore, to obviate this objection, after having 
proved the curve palling from A to C, through the points 
a a a, & c. to be of the nature of the firft conchoid of the 
ancients, employed the inflrutnent of Nicomedes to de¬ 
fcribe it; the conftruCtion of which is as follows : having 
found the length of the fliaft, with the inferior and fiupe- 
rior diameters of the column, and the length of the line 
C D E, in fg. i. as before; take three rulers, either of 
wood or metal, as F G, I D, and AH; of which let F G 
and I D be fattened together at right angles in G. Cut a 
dove-tail groove in the middle of F G, from top to bot¬ 
tom; and at the point E on the ruler I D, (whofe dittance, 
from the middle of the groove in F G, is the fame as that 
of the point of interfeCtion from the axis of the column,) 
f x a pin ; then on the ruler A H fet off the dittance A B, 
equal to C D the inferior femi-diameter of the column, and 
at the point B fix a button, whofe head mutt be exactly 
fitted to the groove made in F G, in which it is to Aide ; 
and, at the other extremity of the ruler A H, cut a flit or 
channel from FI to K, whofe length muft not be lefs than 
the difference of length between E B and FI D, andw'hofe 
breadth muft be fufficient to admit the pin fixed at E, 
which muft pafs through the flit, that the ruler may Aide 
thereon. The inftrument being thus completed, if the 
middle of the groove in the ruler F G be placed exaCtly 
over the axis of the column, it is evident that the ruler 
AH, in moving along the groove, will, with its extremity 
A, defcribe the curve A a a C; which curve is the fame 
as that produced by Vignola’s method of diminution, fup- 
pofing it done with the utmoft accuracy ; for the interval 
A B, ab, is always the fame ; and the point E is the ori¬ 
gin of an infinity of lines, of which the parts B A , b a, b a, 
extending from the axis to the circumference, are equal to 
each other, and to D C. And if the rulers be of an inde¬ 
finite fize, and the pins at E and B be made to move along 
their refpeCtive ruler, fo that the intervals A B and D E 
may be augmented or diminifhed at pleafure, it is likewife 
evident, that the fame inftrument may be thus applied to 
columns of any fize. 
With regard to the generally-received opinion, that, in 
proportion as columns are elevated, the eye is deceived in 
the contour, and therefore they require a difference in the 
diminution to allow for this effeCt, it feems'proved by 
Perrault to be on moft occalions a miftake; for, if we 
judge by the rigour of optical laws, it muft be remem¬ 
bered, that the proper point of view for a column of fifty 
feet high is not the fame as for one of fifteen ; but on 
the contrary more diftant, in the fame proportion as the 
Vol. II. No.60. 
E C T U R E. 
column is higher ; and that confequcntly, the apparent re¬ 
lation between the low'er and upper diameters of the co¬ 
lumn will be the fame, whatever be its lize. For, if we 
fuppofe A, fig. 2. to be a point of view, whofe refpeCtive 
dittance from each of the columns fg, F G, is equal to t he 
refpeCtive heights of each, the triangles f Ag, F A G, will 
be fimilar ; and A f or A h , which is the fame, will be 
to Ag, as A F, or its equal A H, is to A G : therefore if 
d c be in reality to b c, as D F) is to B C, it will likewife be 
apparently fo ; for the angle d Ac, will then be to the angle 
b Ac, as the angle D A E, is to the angle BAG; and. if 
the real relations differ, the apparent ones will likewife 
differ. In this figure, the eye of the fpeclator at A, is 
fuppofed to be in a line perpendicular to the foot of the 
jfhaft; but, if the columns be proportionably raifed to any 
height above the eye, the argument will ftill remain in 
force, as the point of view muft of courfe be proportiona¬ 
bly more diftant; and even when columns are placed im¬ 
mediately on the ground, which feldom or ever is the cafe, 
the alteration oceafioned by that fituation is too trifling to 
deferve notice. When therefore a certain degree of dimi¬ 
nution, which by experience is found pleating, has been 
fixed upon, there will be no neceflity for changing it, what¬ 
ever be the height of the column ; provided the point of 
view is not limited. But in dole places, where the Ipec- 
tator is not at liberty to choofe a proper diftance for his 
point of light, the architect, if he inclines to be ferupu- 
loufly accurate, may vary; though it is in reality a matter 
of no importance, as the nearnefs of the objeCt will render 
the image thereof indiftinCt, and confequently any fmall 
variation will be imperceptible. 
By the following method alfo, columns may be dimi¬ 
nifhed with great eafe and facility, only by the help of a 
common meafuring rule, which every workman may make. 
Defcribe a femicircle, on the bottom of the column A B, 
as ftiewn at fg. i. in the annexed Plate ; from the top of 
the column draw the line E 4, parallel to the axis D C, 
or middle line of the column, cutting the femicircle at the 
bafe in 4 ; divide the arc A 4, into four, or any other num¬ 
ber of equal parts, and divide the height C D, into the 
fame number of equal parts ; as 1, 2, 3, through the divi- 
fions 1, 2, 3, 4, of the femicircle at the bafe, draw lines 
1 a, 2 b, 3 c, and 4 d, parallel to A B ; fet off thole parts 
from each fide of the axis, on the correfponding numbers 
on the fliaft ; then, by bending a thin lath or flip round 
pins or nails fixed in thefe points, it will give the con¬ 
tour, or curve of the column : and the reverie of this 
will be the edge of the diminifhing rule for working it by. 
Or, divide the height of the diminifhing rule A Ff, into 
any number of equal parts ; as four, at a, b, c, and divide 
the difference of the femi-diameter at the top and bottom, 
into the fame number, viz. four, and draw lines from each 
divifion parallel to the bafe, through 1, 2, 3, which points 
will produce a curve of a very regular and pleafing form, 
that may be drawn on the edge of the rule, or on the co¬ 
lumn itfelf, as is moft convenient for the workman. 
To project the Flutes and Fillets, and place them 
round the Column. 
To projeCt the flutes of the Doric column, let A B, 
fg. 2 and 3, in the annexed Plate, be the diameter of the 
column ; on which defcribe a femicircle into ten equal 
parts; (as the Doric column ufually contains twenty flutes, 
which are in general made fhallow, and without fillets;) 
through every two of the divifions draw the lines E 1, E 2, 
E3, E 4, &c. to E 10; between any two divifions, as 3 
and 4, defcribe an equilateral triangle, whofe vertex is C ; 
on E, with a radius E C, defcribe the quadrant MLKI 
H G, cutting the lines E A, E 1, E 2, E 3, E 4, See. in the 
points G H I K L M, which are the centres for the flutes; 
but, if the flutes are required to be deeper, make the dif¬ 
tance 5 D equal to one divifion on the arc; and proceed 
as ftiewn on the other quadrant, and from ab c, & c. draw 
perpendiculars to the bottom of the column, Jig. 3. The 
D d Ionic, 
