ARCHITECTURE. 
line D C at E ; on G as a centre, with a radius GE, de- 
fcribe a circle cutting DC on the oppofite fide of the cen¬ 
tre at F ; divide FE in fix equal parts at 4, 6, G, 5, 3 ; 
then on E as a centre, with a radius D B, defcribe an arc 
BC cutting DC at C; on F, with a radius F C, defcribe 
the femicircle CAK, cutting CD at K; 0113, with a 
difiance 3K, defcribe a femicircle KL; on 4 as a centre, 
with the radius 4L, defcribe a femicircle LM; on 5 as a 
centre, with a radius 5 M, defcribe a femicircle MN; 
lafily, on C, with a radius 6 N, defcribe a femicircle N E, 
•touching the centre at E, and the figure will be comple¬ 
ted. This method will alfo defcribe an elliptical volute 
to a given height, but not to any given width, this being 
only a preparation to the following: 
To defciibe. an Elliptical Volute to any given Height and Pro¬ 
jectionfrom the.Centre. —Divide the given height LM,fg.^, 
into twenty-three equal parts as before, taking the centre 
E ten from the bottom, or thirteen from the top ; through 
N the firfi divifion above E draw N F, cutting the diago¬ 
nal line EO at F ; on E as a centre, with a radius E F, 
defcribe the dotted circle, or through E draw P Qjit right 
angles to the diagonal line O E ; make E P and E Q^each 
equal EF; on F as a centre, with the diftance LF, de¬ 
fcribe an arc LH, cutting EH at right angles to L-M at 
H ; from E make E G equal to the diftance the projection 
of the volute is intended to be from the centre, divide GH 
into fix equal parts, and fet one of the parts to I; make 
EK and ER each equal to the fum of the two lines EF 
and G I, through the points KPRQ^; complete the pa¬ 
rallelogram A BCD, whofe tides A B, DC, are parallel to 
PQ^and AD, BC parallel to K R; draw the diagonals 
A C and B D, and divide each of them into fix equal parts; 
then, on B as a centre, with the radius B L, defcribe the 
arc Lb, cutting AB produced at b\ on A as a centre, 
with the radius A b, defcribe the arc be, cutting A D pro¬ 
duced at c ; on D as a centre, with the radius Dr, de¬ 
fcribe an arc cd, cutting C D produced at d\ on C as a 
centre, with a radius Cd, defcribe an arc de ; on 5 as a 
centre, with a radius 5?, defcribe an arc ef-, on 6 as a cen¬ 
tre, with the radius 6 f defcribe an arc f g ; on 7 as acen- 
tre, with the radius 7g, defcribe an arc gh ; on 8 as a cen¬ 
tre, with the radius 8 k, defcribe an arc h i; proceed in this 
manner, beginning the third revolution at 9, and ending 
at 12; lafily, defcribe an ellipfis touching the laft centre 
of the third revolution E, being its centre; and its tranf- 
verfe and conjugate axis being in the fame ratio as the 
length or height of the volute is to its width, it will com¬ 
plete the figure. If due attention be paid to the figures 
projefled on the Plate, it is impofiible to miftake any part 
of the operation. 
To PROJECT, SETOFF, or DRAW, the 
FIVE ORDERS. 
Suppofe it be required to projeiff or fet off the Tufcan 
Order : for this purpofe make a fcale to the diameter of 
the column at the bottom ; firfi divide it into fix equal 
parts, and divide the firfi of thefe into ten; each of thefe 
parts is called a minute ; then every member of the order 
is fo many minutes of this fcale, either in height or pro¬ 
jection. * The operation is as follows : draw an axis or 
perpendicular through the middle of the column; on 
this line fet off till the heights, or on any other line paral¬ 
lel to it; then make another line parallel to the axis at tlie 
difiance of twenty-five minutes, which allows five minutes 
on each fide for the diminution at top ; from this line fet 
off the projections, as figured in jig. 1, of the annexed 
Plate ; for example, the projection of the top fillet E is 
forty-two minutes, and the projection of the next fillet G 
is thirty-two minutes and a half; then proceed to defcribe 
the cima recta, and all the other members unto the bafe, 
which is fet oft' from the outer extremity of the column, 
that is, thirty minutes from the axis. 
In the Tufcan Order, the column is feven diameters 
high, that is, feven times its diameter at the bafe, the en¬ 
tablature is one-fourth of the height of the column : but 
toj 
if the order has a pedefial, which is feldont the cafe, it 
will be one-fifth part of the entire order in height. To 
make this praCtice obvious to the reader, the following ex¬ 
amples will be ufeful : 
To find the Diameter efi the Tufcan Column, when that alone 
is to be executed. —Rule. Divide the height of the column 
by feven, and the quotient will be the diameter. 
Ex. 1. Suppofe it were required to execute the Tufcan 
column alone, to the height of twenty-two feet three inch¬ 
es; demanded the diameter of the column. 
7 ) 22 ■■ 3 
8 •• 2 y 
So that the diameter of the column is three feet two inche3 
and one-feventh part of an inch. 
To find the Height of the Tufcan Entablature, and the Dia¬ 
meter of its Column, the entire height of the column and enta¬ 
blature being given. — Rule. Divide the height by five, and 
the quotient will give the height of the entablature; fub- 
traCl tire height of the entablature laft found from the entire- 
height, and the remainder will be the height of the column; 
divide this remainder by feven, as before, and the laft quo¬ 
tient will be the diameter of the column. 
Ex. 2. Suppofe it were required to execute the Tufcan 
with its entablature, to the height of twenty-two feet one 
inch; demanded the height of the entablature, and the 
diameter of its column. 
5 ) 22 .. 1 
4 .. 3 height of the entablature 
7 ) 17 .. 8 height of the column 
2 .. 6f- diameter of the column. 
The diameter of the column being thus found, it will 
eafily be put in, as follows : Suppofe it were required to 
execute a column to two feet fix inches and. two-feventh 
parts of an inch ; take a rod of that dimenfion, and divide 
it into fix equal parts, and the firfi part again into ten, for 
minutes; then proceed for practice in the fame manner as 
if the drawing were to be on paper. 
To find the Diameter of the Column, the Height of the Entabla¬ 
ture, and Height of the Pedefial, when the whole is to be executed, 
to a given height. —Rule. Divide the entire height by five, 
and the quotient will be the height of the pedefial; fub- 
tract this height from the entire height, and the remainder 
will be the height of the column, with its entablature. 
Divide the remainder again by five, and the quotient will 
be the height of the entablature; fubtracl the quotient 
from the firfi remainder, and the laft remainder will be 
the height of the column; and this laft remainder, being 
divided by feven, will give the diameter of the column. 
Ex. 3. Let it be required to execute the Tufcan Order 
complete, with an entablature, column, and pedefial, to 
the height of thirty feet; demanded the height of .the 
pedefial, height of the entablature, and diameter of the 
coin mn 
5 ) 30 
6 feet, the height of the pedefial 
5 ) 24 height of the column and entablature 
4 .. 9^ height of the entablature 
7 ) 19 .. 2-| height of the column 
2 .. 8 s diameter of the column. 
To draw the Tufican Column to a given Height .—Divide the 
height into feven equal parts, as in the fecond example; 
one will be the diameter of the column, and a fcale where¬ 
by to proportion the other parts, as is illuftrated by fig. 2, 
in the annexed Plate. 
To draw the Tufcan Column, with its Entablature, to a given 
Height. —Divide the given height into five equal parts; al¬ 
low one for the height of the entablature; and then divide 
the remaining four into feven parts, of which one will be 
the diameter of the column, as ftiewn in fig. 3, of the an¬ 
nexed Plate. 
To 
