Abstract and bill the various papers according to value, the cheapest first.

The Abstract having been completed and checked, it has to be "reduced"; that is, the columns of figures must be added up, the deductions made, and the net totals reduced to the proper form for billing. For example, the excavation to trenches must be brought to cubic yards; the surface excavation to superficial yards; the common brickwork to rods of 1 1/2 B. thickness, the principal items of Founder and Smith and Plumber to hundredweights, the Plastering and Painting to superficial yards, and the Paper to numbers of pieces. The form in which each item should be billed has been already noted in the chapters on "Taking-off," and will be further dealt with in the following Chapter on "Billing."

As previously stated, 12 inches are always reckoned to the foot, whether it be a lineal, superficial, or cubic foot, as this is sufficiently accurate for all practical purposes. It is scarcely necessary to say that superficial feet may be brought to superficial yards by dividing by 9, and cubic feet to cubic yards by dividing by 27.

Brickwork is billed by the rod, which is 272 1/4 feet super. 1 1/2 bricks thick. The 1/4 foot, however, is always omitted in practice, and the number of superficial feet of reduced brickwork is divided by 272 to bring it to rods.

To bring either the superficial or lineal dimensions in the Founder and Smith's Abstract to hundredweights it is only necessary to remember that cast iron 1 inch in thickness weighs 37.50 lbs., wrought iron 1 inch thick 40 lbs., and steel 1 inch thick 40.83 lbs. per foot super., from which it will be quite easy to deduce the weight of any other thickness, or the weight per foot run of a bar of any size. For example, the weight of a 2 by 1-inch bar per foot run will be 1/6 of the weight of 1-inch metal per foot super., 2 inches being 1/6 of a foot. A 2 by 3/4-inch bar will be 3/4 the weight of 2 by 1 inch, and so on. The weight of round iron can, of course, be ascertained from the above, but it would be rather a tedious operation. It is best to take it from tables, or the weight of 1-inch diameter may be committed to memory, and then, remembering that the areas of circles vary as the squares of their diameters, the weight of any other size can be found. Rolled steel joists are almost invariably selected from stock sizes, and their weight per foot run should be ascertained from the trade list; but be careful to consult the proper list, as the weights of the same sections vary with different makers, and many makers supply two different weights of the same section.

Cast-iron Hollow Columns. Although these should be measured per foot super on the "Taking-off," the method of measurement and its reduction to weight will now be given.

Ascertain the width of the piece of metal forming the column, supposing it were unrolled and laid out flat, by means of the formula πd, d being the mean diameter (see Fig. 48) and π being taken as 22/7. Having ascertained the width, multiply it by the height of column, and you have the number of feet super. of cast iron of a given thickness. Add the cap and base plate (remember to deduct the hole in these) and the stiffeners measured as triangles.

Moulded caps, neckings, or bases should be judged and averaged as triangles, half-rounds, or other nearly approximating figure, their length being ascertained by the formula πd. The superficial dimensions of the various thicknesses of metal should now be reduced to weight in pounds and added together. Add 2 per cent. of the total for featherings (see Fig. 49), and reduce to hundredweights.

Paperhanger 84

Fig. 48.

Paperhanger 85

Fig. 49.

Where bolts are billed by weight, the weight of heads, nuts, and washers may be ascertained from tables.

The weight of lead in lbs. is readily found by multiplying the total under each thickness by its weight per foot super. See example of abstracting under "Plumber." The weights in lbs. of the various thicknesses are then added together and reduced to hundredweights.

The principal items of plastering and painting should be reduced to yards, and the squares in painting to dozens.

It now only remains to reduce the superficial feet of paper to numbers of pieces. A piece of English paper is 12 yards long and 21 inches wide, which gives 63 feet super. per piece. The usual practice is to allow one piece in seven for waste, which is equivalent to deducting 1/7 from each piece: thus 63 feet 0 inches minus 1/7 of 63 feet 0 inches = 54 feet 0 inches. Therefore to reduce superficial feet to pieces, divide by 54, and call any fraction of a piece one piece.

French papers are usually 9 yards long and 18 inches wide = 40 feet 6 inches super. Deduct A for waste, and this leaves a divisor of 34 feet 9 inches. Call this 35 feet.

The reduction of the Abstract should now be checked and ticked in red, and all will then be in readiness for Billing.