On the Spiral Line. 163 
diili, taken from g,o0, 7,0, &c. every templet throughout the 
niche, the core excepted —The moulds z2x, fig. C, give the 
bevel, curvature, and convexity of the bricks in the core of the 
niche, which core is generally composed of about two bricks, 
(but sometimes of stone) and is always introduced on account 
of the bricks becoming so very thin at the back. Thus is the 
whole sufficiently and practically expiained. 
I]. On the Spiral Line. 
The construction of the screw round the cylinder (which is 
performed by a wedge bent round it), aad the evolution of the 
spiral line from the ccne, not being generally understoed among 
mechanics, I have been induced to lay before your readers the 
following simple illustrative diagrams. 
Fig, H represents an orthographical cylinder, and the semi- 
circle 1254 half its plan or circumference: this cylinder we will 
suppose is required to be cut into a screw. Todo this, the num- 
ber of revolutions or threads to be cut must first be determined: 
if there be four, five, or more worms, it will then require less 
power to turn the screw than if it were less vermiculated: here the 
screw has only two revolutions. ‘Io construct them, first draw the 
line a 8, at right angles to the cylinder, on which line set twice 
the circumference as shown by the figures 123 4,81234,&c. 
next erect the line 8, 9, perpendicular to the base line 8, “and 
_ place the height of the eylincer thereon: then from p produce a 
line to a; this will now represent the surface of the wedge, which 
wedge is ‘to be represented as furled round the cylinder in the 
following manner. First, draw the lines 1234, &c. perpen- 
dicularly up the surface of the cylinder, and on the wedge; next 
produce parallel lines fram the inclined points hh, and perpen- 
dicular to Sp, until they eross the evlinder: the points of in- 
tersection on’ the surface will then be the points through which 
the curve or thread must pass: this is the construction and a 
development of the screw. For, the spiral line, first form a cone, 
as at fig. L, of the same height and diameter at the base as the 
cylinder; then sct one leg of the compasses at the apex of the 
cone /, extending the other leg to r, and with the radius 2,7, 
describe the curve. 78; on this-curve set sixteen divisions, 
four heing eyual to the circumferehce of the base of the cone, 
and the sixteen equal to two revolutions round its base: next 
converge these lines towards ¢: this being done, take from the 
wedge of the cylinder the length of the lines 44, 4 A, &c. and set 
them on the lines 40, 41, &c. of the conic evolution: next 
L 2 set 
