EXAMPLES. 338. 1. Reduce 15° 20′ 10′′ to seconds. 2. Reduce 37° 18' 32" to seconds. 3. How many seconds are there in 40° 28′ 21′′? 4. Reduce 24350′′ to higher denominations. 5. Reduce 74680′′ to higher denominations. COUNTING. 339. In counting certain classes of articles, the following denominations are used: Two things of a kind are frequently called a pair, six a set, and twenty a score; as, a pair of gloves, a set of chairs, a score of years. STATIONERS' TABLE. 340. Paper in the stationery trade is sold by the following 341. In printing books large sheets of paper are used which are folded into leaves according to the size of the book. The terms folio, quarto, octavo, etc., applied to printed books, are based on sheets about 17 X 22 in., and indicate the number of leaves into which a sheet is folded. 1. The following table shows the number of leaves and pages to the sheet (size 17 inches by 22 inches called Folio), and the sizes of the pages in standard books, the pages of course being always double the number of leaves: 2. Printing paper is made of many sizes, to suit the requirements of the printer. In book printing, paper about 24 × 38 inches, called Double Royal, is extensively used; but the size of the book is, nevertheless, based on the size of the paper called Medium, which is 18 X 23 inches. 3. A careful examination of the upper or lower inside edge of an open book will determine the number of leaves in a sheet, as each full-sized sheet is folded separately, and placed together side by side with the packs of other sheets, or collated" " before a book is bound. 342. Copyists are often paid by the folio for making copies of legal papers, records, and documents. In copying usually 100 words are considered the unit of measure or folio. 343. In type-setting, an em, the portion of a line formerly occupied by the letter m, then a square type, is used as a unit by which to measure and estimate the amount of printed matter. PRACTICAL PROBLEMS. 344. 1. How much must be paid for 4 gross of pencils at 3 cents apiece? 2. How many sheets of paper in 5 reams? 3. What will 1240 sheets of foolscap cost at 15 cents a quire? 4. How much must be paid for a quarter gross of pens at the rate of $16.80 for a great gross? 5. How much paper will be required to issue an edition of 3000 copies of a 12 mo. book of 300 pages, allowing a quire to a ream for waste? MEASURES OF HEAT. 345. Temperature, or Intensity of Heat, is measured by instruments called Thermometers. The principal kinds in common use are Fahrenheit's, the Thermométre Centigrade, and Réaumur's. The first named is the kind mostly used in England and America, though the Thermométre Centigrade, owing to its convenient decimal scale, is coming into general use for scientific purposes throughout the world. A comparison of the three different scales is shown in the following 346. To reduce from one Thermometer to another. Let F°, C°, R°, represent any number of degrees, Fahrenheit, Centigrade or Réaumur. It will be seen from the table that the difference between the melting point of ice and the boiling point of water is 180° F, 100° C, and 80° R. 1. On the Fahrenheit thermometer, the freezing point of water is 32°; seawater, 28°; strong wine, 20°; mercury, 39° below zero. The boiling point of alcohol is 167°; water, 212°; oil of turpentine, 560°; linseed oil, 600°; quicksilver, 660°. The melting point of butter, lard, and tallow is about 92°; spermaceti, 112°; beeswax, 142°; sulphur, 239°; tin, 442°; bismuth, 507°; lead, 617°; zinc, 773°; corper, 2200°; silver, 1832°; gold, 2518°; cast iron, 2800°. 2. The mean temperature of the blood is 99.5°. Iron red-heat in the dark is 752°; in twilight, 884°; in daylight, red-heat fully visible, 1077°. The heat of common fire is 790°. 2. Reduce 80° C. to Fahrenheit. Solution: 80 +32= 176° F. 3. Reduce 50° F. to Réaumur. 4. Reduce 240° C. to Réaumur. 5. Mercury freezes at 39° below zero, or does it freeze Centigrade? ADDITION. 848. Addition of Denominate Numbers is the process of finding the sum of two or more similar compound denominate numbers. 349. Denominate numbers are added, subtracted, multiplied, and divided by the same general methods as are employed for corresponding operations in abstract numbers, except that in the latter we have the uniform scale of ten, while in compound numbers we have a varying scale. 350. 1. Add £3 58. 7d., £4 17s. 8d., £13 11s. 5d., and £9 6s. 13 11 5 9 6 10 31 1 6 EXPLANATION.-We write the numbers so that similar units shall stand in the same column, and begin at the right to add. The sum of the pence is 30d. = 2s. 6d. We write the 6d. in the pence column, and adding the 2s. to the column of shillings we obtain 41s. £2 1s. We write the 1s. in the column of shillings, and add the £2 to the column of pounds, obtaining £31 pounds which we write in the pounds column. Hence, the entire sum is £31 1s. 6d. EXAMPLES, 2. Add £18 16s. 5d., £23 178. 9d., £47 138. 8d., and £62 118. 11d. 3. Add 18 lb. 9 oz. 18 pwt. 12 gr., 13 lb. 7 oz. 15 pwt. 21 gr., 19 lb. 11 oz. 16 pwt. 15 gr. 4. Add 13 T. 15 cwt. 54 lb. 15 oz., 24 T. 12 cwt. 35 lb. 13 oz., 68 T. 17 cwt. 84 lb. 9 oz. 5. Add 5 yr. 7 mo. 12 da., 4 yr. 8 mo. 21 da., 3 yr. 7 mo. 25 da. 6. Add 14 cd. 121 cu. ft. 235 cu. in., 24 cd. 104 cu. ft. 670 cu. in., 35 cd. 94 cu. ft. 537 cu. in. 7. Find the sum of 12 mi. 132 rd. 3 yd. 2 ft. 5 in., 12 mi. 76 rd. 4 yd. 8 in., 5 mi. 92 rd. 2 yd. 1 ft. 7 in., 21 mi. 83 rd. 5 yd. 2 ft. 11 in. 8. Find the sum of 146 mi. 140 rd. 2 yd. 1 ft. 3 in., 150 mi. 80 rd. 3 yd. 1 ft. 10 in., 167 mi. 120 rd, 1 yd. 2 ft. 7 in., 187 mi. 200 rd. 5 yd. 1 ft. 4 in., 185 mi. 85 rd. 2 yd. 2 ft. 10 in., 147 mi 175 rd. 4 yd. 1 ft. 9 in., 275 mi. 190 rd. 2 ft. 8 in. SUBTRACTION. 351. Subtraction of Denominate Numbers is the process of finding the difference between two similar compound denominate numbers. 352. 1. From 11 oz. 9 pwt. 18 gr. take 6 oz. 14 pwt. 13 gr. oz. pwt. gr. 11 9 18 6 14 13 4 15 5 EXPLANATION.-We write the subtrahend under the minuend, placing similar units in the same column and begin at the right to subtract. 13 gr. from 18 gr. leave 5 gr., which we write under the grains. 14 pwt. cannot be subtracted from 9 pwt.; we will therefore take 1 oz. from 11 oz., leaving 10 oz., and add it to the 9 pwt. 1 oz. equals 20 pwt., which added to the 9 pwt. equal 29 pwt. Then 14 pwt. taken from 29 pwt. leave 15 pwt., which we write under the pwt. col6 oz. from 10 oz. leave 4 oz., which we write. Hence, the remainder is 4 oz. 15 pwt. 5 gr. umn. EXAMPLES. 2. From £124 11s. 7d., take £87 19s. 5d. 3. From £144 78. 9d., take £68 12s. 11d. 4. From 84 lb. 10 oz. 14 pwt. 17 gr., take 38 lb. 11 oz. 17 pwt. 20 gr. 5. From 240 T. 12 cwt. 70 lb. 13 oz., take 136 T. 9 cwt. 85 lb. 15 oz. 6. From 94 mi. 186 rd. 1 yd. 2 ft. 7 in., take 68 mi. 259 rd. 4 yd. 1 ft. 10 in. 353. To find the difference in time between two dates. 1. What is the difference in time from June 9, 1898, to Dec. 5, 1903? da. yr. mo. 1903 12 5 EXPLANATION.-We express dates by the number of the year, the month, and the day. Since the later date expresses the greater period of time, we write it as the minuend, and the earlier date as the subtrahend. We then subtract as in denominate numbers, considering 30 days 1 month, and 12 months 1 year. The remainder will be as correct as can be expressed in months and days. EXAMPLES. 2. Find the time from Feb. 6, 1884, to Sept. 14, 1891. |