Given the chord _c_ of a circular arc, and the vertical height _h_, to
find the diameter _d_ of the circle.
Set the height _h_ on B to half the chord on D, and over 1 on B read _x_
on A. Then _x_ + _h_ = _d_.
EX.—_c_ = 6; _h_ = 2; find _d_. Set 2 on B to 3 on D, and over 1 on B
read 4·5 on A. Then 4·5 + 2 = 6·5 = _d_.
Given the radius of a circle _r_, and the number of degrees _n_ in an
arc, to find the length _l_ of the arc.
Set _r_ on C to 57·3 on D, and over any number of degrees _n_ on D read
the (approximate) length of the arc on C.
EX.—_r_ = 24; _n_ = 30; find _l_.
Set 24 on C to 57·3 on D, and over 30 on D read 12·56 = _l_ on C.
Given the diameter _d_ of a circle in _inches_, to find the
circumference _c_ in _feet_.
Set 191 on C to 50 on D, and under any diameter in inches on C read
circumference _c_, in feet on D.
EX.—Find the circumference in feet of a pulley 17 in. in diameter. Set
191 on C to 50 on D, and under 17 on C read 4·45 ft. on D.
Given the diameter of a circle, to find its area.
Set 0·7854 on B to 10 (centre index) on A and over any diameter on D
read area on B.
When the rule has a special graduation line = 0·7854, on the right-hand
scale of B, set this line to the R.H. index of A and read off as above.
If only π is marked, set this special graduation on B to 4 on A.
On the C and D scales of some rules a gauge point marked _c_ will be
found indicating √((4)/(π)) = 1·1286. In this case, therefore, set 1 on
C to gauge point _c_ on D, and read area on A as above. If the gauge
point _c_′ is used, divide the result by 10. Or set _c_ on C, to
diameter on D, and over index of B read area on A. Cursors are supplied,
having _two_ lines ruled on the glass, the interval between them being
equal to (4)/(π) = 1·273 on the A scale. In this case, if the right hand
of the two cursor lines be set to the diameter on D, the _area_ will be
read on A under the _left_-hand cursor line. For diameters less than
1·11 it is necessary to set the middle index of B to the L.H. index of
A, reading the areas on the L.H. B scale. The confusion which in general
work is sometimes caused by the use of two cursor lines might be
obviated by making the left-hand line in two short lengths, each only
just covering the scales.
Given diameter of circle _d_ in _inches_, to find area _a_ in square
_feet_.
Set 6 on B to 11 on A, and over diameter in inches on D read area in
square feet on B.
To find the surface in square feet of boiler flues, condenser tubes,
heating pipes, etc., having given the diameter in inches and length in
feet.
Find the circumference in feet as above and multiply by the length in
feet.
EX.—Find the heating surface afforded by 160 locomotive boiler tubes
1¾in. in diameter and 12 ft. long.
Set 191 on C to 50 on D; bring cursor 1·75 on C, L.H. index of C to
cursor; cursor to 12 on C; 1 on C to cursor; and under 160 on C read
880 sq. ft. of heating surface on D.
If the dimensions are in the same denomination and the rule has a gauge
point M at 31·83 (= (100)/(π)), set this mark on B to diameter of
cylinder on A, and read cylindrical surface on A over length on B.
To find the side _s_ of a square, equal in area to a given rectangle of
length _l_ and breadth _b_.
Set R.H. or L.H. index of B to _l_ on A, and under _b_ on B read _s_ on
D.
EX.—Find the side of a square equal in area to a rectangle in which
_l_ = 31 ft. and _b_ = 5 ft.
Set the (R.H.) index of B to 31 on A, and under 5 on B read 12·45 ft.
on D.
To find various lengths _l_ and breadths _b_ of a rectangle, to give a
constant area _a_.
Invert the slide and set the index of Ɔ to the given area on D. Then
opposite any length _l_ on Ɔ find the corresponding breadth _b_ on D.
EX.—Find the corresponding breadths of rectangular sheets, 16, 18, 24,
36, and 60 ft. long, to give a constant area of 72 sq. ft.
Set the R.H. index of Ɔ to 72 on D, and opposite 16, 18, 24, 36, and
60 on Ɔ read 4·5, 4, 3, 2, and 1·2 ft., the corresponding breadths on
D.
To find the contents in cubic feet of a cylinder of diameter _d_ in
inches and length _l_ in feet.
Find area in feet as before, and multiply by the length.
If dimensions are all in inches or feet, set the mark _c_ (= 1·128) on C
to diameter on D and over length on B, read cubic contents on A.
To find the area of an ellipse.
Set 205 on C to 161 on D; bring cursor to length of major axis on C, 1
on C to cursor, and under length of minor axis on C read area on D.
EX.—Find the area of an ellipse the major and minor axes of which are
16 in. and 12 in. in length respectively.
Set 205 on C to 161 on D; bring cursor to 16 on C, 1 on C to cursor,
and under 12 on C read 150·8 in. on D.
To find the surface of spheres.
Set 3·1416 on B to R.H. or L.H. index of A, and over diameter on D read
by the aid of the cursor, the convex surface on B.
To find the cubic contents of spheres.
Set 1·91 on B to diameter on A, and over diameter on C read cubic
contents on A.