Part 15

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.

WEIGHTS OF METALS.

To find the weight in lb. per lineal foot of square bars of metal.

Set index of B to weight of 12 cubic inches of the metal (i.e., one lineal foot, 1 square inch in section) on A, and over the side of the square in inches on C read weight in lb. on A.

EX.—Find the weight per foot length of 4½in. square wrought-iron bars.

Set middle index of B to 3·33 on A, and over 4½ on C read 67·5 lb. on A.

(N.B.—For other metals use the corresponding constant in column (2), below).

To find the weight in lb. per lineal foot of round bars.

Set R.H. or L.H. index of B to weight of 12 cylindrical inches of the metal on A (column (4), below), and opposite the diameter of the bar in inches on C, read weight in lb. per lineal foot on A.

EX.—Find the weight of 1 lineal foot of 2 in. round cast steel.

Set L.H. index of B to 2·68 on A, and over 2 on C read 10·7 lb. on A.

To find the weight of flat bars in lb. per lineal foot.

Set the breadth in inches on C to (1)/(weight of 12 cub. in.) of the metal (column (3), below) on D, and above the thickness on D read weight in lb. per lineal foot on C.

EX.—Find the weight per lineal foot of bar steel, 4½in. wide and ⅝in. thick.

Set 4·5 on C to 0·294 on D, and over 0·625 on D read 9·56 lb. per lineal foot on C.

To find the weight per square foot of sheet metal, set the weight per cubic foot of the metal (col. 1) on C to 12 on D, and

────────────┬──────────┬──────────┬──────────┬─────────── │ (1) │(2) │ (3) │ (4) │Weight in │Weight of │ (1)/(Wt. │ Weight of Metals. │ lb. per │12 cubic │of 12 cub.│ 12 │cubic ft. │in. │ in.) │cylindrical │ │ │ │ in. ────────────┼──────────┼──────────┼──────────┼─────────── Wrought iron│480 │3·33 │0·300 │2·62 Cast iron │450 │3·125 │0·320 │2·45 Cast steel │490 │3·40 │0·294 │2·68 Copper │550 │3·82 │0·262 │3·00 Aluminium │168 │1·166 │0·085 │0·915 Brass │520 │3·61 │0·277 │2·83 Lead │710 │4·93 │0·203 │3·87 Tin │462 │3·21 │0·312 │2·52 Zinc (cast) │430 │2·98 │0·335 │2·34 „ (sheet) │450 │3·125 │0·320 │2·45 ────────────┴──────────┴──────────┴──────────┴───────────

above the thickness of the plate in inches on D read weight in lb. per square foot on C.

EX.—Find the weight in lb. per square foot of aluminium sheet ⅜in. thick.

Set 168 on C to 12 on D, and over 0·375 on D read 5·25 lb. on C.

To find the weight of pipes in lb. per lineal foot.

Set mean diameter of the pipe in inches (i.e., internal diameter plus the thickness, or external diameter minus the thickness) on C to the constant given below on D, and over the thickness on D read weight in lb. per lineal foot on C.

┌────────────┬─────────────────────┬─────────────────────┐ │ Metals. │ Constant for Pipes. │Constant for Spheres.│ ├────────────┼─────────────────────┼─────────────────────┤ │Wrought iron│ 0·0955 │ 6·87 │ │Cast iron │ 0·1020 │ 7·35 │ │Steel │ 0·0936 │ 6·73 │ │Brass │ 0·0882 │ 6·35 │ │Copper │ 0·0834 │ 6·00 │ │Lead │ 0·0646 │ 4·65 │ └────────────┴─────────────────────┴─────────────────────┘

EX.—Find the weight per foot of cast-iron piping 4 in. internal diameter and ½in. thick.

Set 4·5 on C to 0·102 on D, and over 0·5 on D read 22·1 lb. on C, the required weight.

To find the weight in lb. of spheres or balls, given the diameter in inches. (W = 0·5236d^3 × wt. of 1 cub. in. of material).

Set the constant for spheres (given above) on B to diameter in inches on A, and over diameter on C read weight in lb. on A.