Paper and Its Uses/Problems

by Edward A. Dawe

PROBLEMS IN COST, WEIGHT, AND
QUANTITIES OF PAPER

To find the Cost of Paper.—The methods of calculation of cost will depend upon the number of sheets to the ream. If packed in 480's, and the quantity is stated in reams, quires, and sheets, the cost is obtained very easily. Paper at £1 per ream is 1s. per quire, ${\tfrac {1}{2}}$d. per sheet. Take 110 reams, 17 quires, 12 sheets, at 7s. 6d. per ream. At £1 per ream this equals £110. 17s. 6d.; and at 7s. 6d. this comes to ${\tfrac {3}{8}}$ of that sum = £41. 6s. 7d.; or reckoned at 110${\tfrac {7}{8}}$ reams at 7s. 6d., the same figures are obtained. When reams containing a larger number of sheets are concerned, the calculation is made on the number of reams plus the fraction of the ream.

Prices and Weights of Boards.—To obtain the price per 480 when the price per gross is given, multiply the figure by ${\tfrac {10}{3}}$. Per 500 is taken as 3${\tfrac {1}{2}}$ times the price per gross. When the price is given per 480, the price per gross is ${\tfrac {3}{10}}$ of that amount. If the price is given as per 500, the gross will cost ${\tfrac {2}{7}}$ of that amount. Weights are calculated on the same basis.

To Calculate the Weight of a Paper from the Size and Weight of another Paper.—A table of equivalent weights papers of regular sizes based on demy of certain weights is given on pages 144-45. To find the weight of other sizes, multiply the weight of the ream in pounds by the area of the new size in inches, and divide by the area of the size, the weight of which is known.

Example.—The weight of large post is required equivalent to double foolscap 30 Ib.

${\frac {30\times 21\times 16{\tfrac {1}{2}}}{17\times 27}}=22{\tfrac {11}{17}}=23$lb. large post.

If the table of equivalent weights be examined, it will be seen that the area of large post is 346 ${\tfrac {1}{2}}$ square inches, and that of double foolscap 459 square inches. For approximate purposes these may be taken as 350 and 460, and this shows large post to be practically three-quarters of the area of double foolscap. Other instances may be cited: demy 393¾ square inches, if taken as 400, renders royal as one-fourth extra, and double crown one-half above the demy weights. These figures are useful for quick calculation, but the first method is more exact and should be generally adopted.

To find the Number of Sheets which a Reel of Paper will Produce.—Weigh the reel and deduct the weight of the core or centre. Cut a piece the full size of the sheet, but if a trim is allowed, the sheet cut should be untrimmed size. Weigh the sheet on the sheet scale, read the weight in 500's, and divide the weight given into the net weight of the reel, and multiply the result by 500, this giving the number of sheets which will be produced.

Example.—Reel is 50 inches wide, weighs 740 lb.; the centre is 10 lb. in weight; to be cut to sheet 25 by 20 inches.

Sheet 25 by 20 inches = 25 lb. per 500.

740 – 10 = 730 lb. ÷ 25 = 730/25 x 500 = 14,600 sheets.

Alternatively a square may be cut by the demy template, weighed on the demy scale, the weight of the sheet equivalent to the demy weight calculated or obtained from table, and the number of sheets obtained as in above example.

Example.—Reel is 48 inches wide, weighs 640 lb. with 4 lb. centre; to be cut to 24 by 36 inches; demy = 21 lb. per 500 sheets.

640 – 4 = 636 x 500 x 17½ x 22½/24 x 36 x 21 = 6,901 sheets.

To find the Number of Copies of a Book that may be Obtained from a Given Quantity of Paper.—A publisher sends in twenty-seven perfect reams of quad crown for a crown octavo work of 216 pages. How many copies will be produced? A sheet of crown octavo = 16 pages, therefore quad crown = 64 pages.

27 x 500 ÷ 216/64 = 27 x 500 x 64/216 = 4,000 copies.

To find the Quantity of Paper required for an Edition of a Book of a Given Size.—An edition of a book of 400 pages demy octavo, 6,500 pages, is required. What quantity of double demy should be issued in perfect reams? A sheet of double demy will contain 32 pages; a ream will produce 500 copies.

Therefore, 6,500 x 400/32 x 500 = 162½ reams.

Or, 400 ÷ 32 = 12½ sheets per copy; 6,500 = 13 reams;
13 x 12½ = 162½ reams.

To Calculate the Weight of a Ream Containing a Larger or Smaller Number of Sheets.—Multiply the weight by the factor given below, or else add or subtract the fraction representing the difference in the number of sheets.

Table of Factors

Table of Factors.					Table of Fractions.[1]
To convert to	480	500	504	516	480	500	504	516
480	...	1.042	1.05	1.075	...	+ 1/24	+ 1/20	+ 3/40
500	.96	...	1.01	1.032	– 1/25	...	+ 1/125	+ 4/125
504	.95	.992	...	1.022	– 1/21	– 1/126	...	+ 1/42
516	.93	.969	.977	...	– 3/43	– 4/129	– 1/43	...

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1. Add or subtract the fraction of the weight of the ream as shown.