Part 14

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.