year being 10 days behind the solar year. In 1582 Pope Gregory corrected the error by striking 10 days out of the calendar, calling the 5th of October the 15th, and ordering that henceforth only those centennial years should be leap years which are divisible by 400. 3. The Gregorian calendar was soon adopted by most Catholic countries. Great Britain adopted the change in 1752, calling the 3d of September the 14th, the error having amounted to 11 days. Russia and the other countries of the Greek Church still adhere to the Julian calendar, their dates being now about 12 days behind ours. The two calendars are distinguished as Old Style and New Style, marked 0. S. and N. S. respectively. In the Old Style the civil or legal year commenced on the 25th of March, while the historical year commenced on the first of January, and dates between those days were marked with the number of both years; thus, January 30th, 1649, is frequently found written, Jan. 30th, 1648. The New Style made the civil year commence also on the 1st of January. EXAMPLES FOR PRACTICE 1. How many minutes in a leap year? Ans. 527040. 2. How many seconds in a solar year? Ans. 31556929.7. 3. How many leap years from 1800 to 1861? Ans. 15. 4. How many" in 1 quadrant and 12°? Ans. 367200". 5. How many days from June 15 to Dec. 9? Ans. 177. 6. How many days in the 16th century? Ans. 36525. 7. How many degrees in 17651 "'? Ans. 4° 54' 11". 8. In 6 S. 25° 56', how many minutes ? Ans. 12356. 9. How many minutes from 15 minutes past 9 A. M. to 20 minutes of 12 A. M. ? Ans. 145. 10. How many hours and minutes from 7 h. 25 min. A. M. to 3 h. 45 min. P. M. ? Ans. 8 h. 20 min. 11. In what time does a fixed point on the earth's surface pass through 60° 15' 30'' ? Ans. 4 h. 1 min. 2 sec. 12. How many lunar months of 29 da. 12 h. 44 min. 2.7 sec. in a solar year? Ans. 12.36+. 13. The average daily motion of Mercury is 4° 5' 32.42"; how long will it require to complete a revolution in its orbit? Ans. 87 da. 23 h. 15 min. 43.6- sec. 14. In the Julian calendar a year equals 365 da. 6 b.; in how many years was a day gained? Ans. 128.89+. 10. Venus revolves around the sun in 224 da. 16 h. 49 min. 7.98 sec.; what is its daily motion ? Ans. 1° 36' 7.67". 16. A steamer sailing due east at the equator changes her longitude 3' every 15 minutes; how many knots an hour is she making ? Ans. 12 knots. MISCELLANEOUS TABLES. 409. The following tables are frequently used, the first in counting certain kinds of articles, and the second in the paper trade. COUNTING. PAPER. 12 units = 1 dozen. 24 sheets = 1 quire. 12 dozen = 1 gross. 20 quires = 1 ream. 12 gross = 1 great gross. 480 sheets = 1 ream. 20 units = 1 score. I. Two things of a kind are frequently called a pair and six a set. II. Paper is sold at retail by sheets and quires, and at wholesale by reanis. BOOKS. 410. 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., as applied to printed books, are based on sheets about 18 x 24 in., about half the sizes now generally used, and indicate the number of leaves into which such a sheet is folded. A sheet folded in 2 leaves is called a folio, makes 4 pages. A sheet folded in 4 a quarto or 4to, makes 8 pages. A sheet folded in 8 an octavo or 8vo, makes 16 pages. A sheet folded in 12 a 12mo, makes 24 pages. A sheet folded in 16 a 16mo, makes 32 pages. A sheet folded in 18 an 18mo, makes 36 pages. A sheet folded in 24 a 24mo, makes 48 pages. etc. etc. NOTE.-Printing paper is made of many sizes, according to the requirements of the printer. In book printing 24x38 inches, called Double Medium, is perhaps used most largely. 411. Clerks and copyists are often paid by the folio for making copies of legal papers, records, and documents. 72 words make 1 folio, or sheet of common law. EXAMPLES FOR PRACTICE. 1. A cabinet-maker uses 48 screws a day; how many gross will be use in 4 weeks ? Ans. 8 gross. 2. The agent of a Liverpool steamer ships for the voyage 4128 eggs packed in 8 boxes; how many dozen in a box? dns. 43. 3. A weekly newspaper has 4750 subscribers; how much printing paper would it require in 1 year ? Ans. 514 reams, 11 quires, 16 sheets. 4. On taking an account of stock, a bardware 'merchant finds he has on hand 11 gross 3.75 dozen of white door knobs; what is the number of knobs ? Ans. 1629. 5. How much paper is required to issue an edition of 2000 copies of a 16mo. book of 416 pp., allowing 1 quire in a ream for waste ? Ans. 57 reams, 9 sheets. 6. A lady copies 11,700 words of common-law folios, at 10% per folio; what does she receive ? Ans. $16.25. 7. A chancery case contains 561,420 words; what does the copying cost at 12¢ per folio? Ans. $779.75. 8. A stationer, on making an inventory at the close of the year, finds that he has on hand 11 packages of Gillott's steel pens of a dozen boxes each, a broken package containing 10 boxes, and an open box containing 7 doz. 5 pens; if each box contains 1 gross, how many pens bas he on band ? Ans. 20,537 pens. THE METRIC SYSTEM. 412. In the Metric System we first establish the unit of each measure, and then derive the other denominations by taking decimal multiples and divisions of the unit. Any quantity consisting of several denominations is thus written and treated as an integer and decimal. 413. Names.-We first name the unit of any measure, and then derive the other denominations by prefixing words to the unit name. 414. The higher denominations are expressed by prefixing to the name of the unit, DEKA HECTO Kilo MYRIA 10000 415. The lower denominations are expressed by prefixing to the name of the unit, DECI CENTI MILLI ito Todo 416. Units.—The following are the different units, with the English pronunciation: Measure. Unit. Pronunciation. / Measure. Unit. Pronunciation. LENGTH, Meter, (meter.) CAPACITY, Liter, (leeter.) SURFACE, Are, (air.) WEIGHT, Gram, (gram.) VOLUME, Stere, (stair.) VALUE, Dollar, In 1795, France adopted a system of weights and measures based upon the decimal scale, called the Metric System. This has been adopted by Italy, Spain, Portugal, many parts of Spanish America, Belgium, Holland, Germany, Austria, Switzerland, Sweden, Denmark, Greece, Mexico, and Brazil. In 1864, the Parliament of Great Britain passed an act permitting its use throughout the United Kingdom wherever parties should agree to use it. In 1866 its use was authorized in this country by Congress, and to furnish a convenient standard of comparison, and render the public familiar with the new measures, the five-cent piece issued at this time was ordered to be made 5 grams in weight, and of a meter in diameter. The system has not yet come into general use in this country, but is employed in the natural sciences, and to some extent in the U.S. Coast Survey and other branches of the public service. The base of the system is the meter, which is 100 body of the distance from the equator to either pole, as determined with the greatest care by the measurement of an arc of the meridian. MEASURES OF LENGTH. 417. The Meter is the unit of length. It is the ten-millionth part of the distance from the equator to the poles, and equals 39.37 inches, or 3.28 feet. The standard meter is a bar of platinum deposited in the archives of Paris. TABLE.—10 millimeters (mm.)=1 centimeter (cm.); 10 centimeters=1 decimeter (dm.); 10 decimeters=1 meter, (M.); 10 meters=1 decameter (DM.); 10 decameters=1 hectometer (HM.); 10 hectometers=1 kilometer (KM.); 10 kilometers= 1 myriameter (MM.). NOTES.-1. The meter is very nearly 3 feet, 3 inches, and 3-eighths of an inch in length, which may be easily remembered as the rule of three threes. 2. Cloth, etc., are measured by the meter; very small distances, by the millimeter; great distances, by the kilometer. 3. The 5-cent piece of 1866 is very nearly 5 of a meter in diameter; hence its diameter is about of a decimeter, or 2 centimeters. It was ordered to be o of a meter in diameter, but owing to the composition of the alloy it was necessary to make its diameter a little greater ; 48.6 nickel 5-cent pieces laid side by side measure one meter. 4. A decimeter is about 4 inches ; a kilometer, about 200 rods, or of a mile ; a millimeter, about of an inch. The inch is about 21 centimeters ; the foot 3 decimeters; the rod, 5 meters; the mile, 1600 meters, or 16 hectometers. MEASURES OF SURFACE. 418. The Are is the unit of surface used to measure land. The are is a square decameter. It equals 119.6 sq. yd., or 0.0247 acre. TABLE.—10 centiares (ca.)=1 deciare (da.); 10 deciares= 1 are (A.); 10 ares=1 decare (DA.; 10 decares=1 hectare (HA.). NOTES.-1. The are, centiare, and hectare are the denominations princi. pally used, as these are exact squares. The centiare is a square whose side is 1 meter ; the hectare is a square whose side is 100 meters. The are = 100 square meters. The centiare = 1 square meter. The hectare = 10,000 square meters. 2. The deciare is not a square, it is merely the tenth of an are; the decare is not a square, it is merely 10 ares. 3. A hectare equals very nearly 24 acres; a centiare equals nearly 13 sq. yd. An acre is very nearly 40 ares. MEASURES OF OTHER SURFACES. 419. All surfaces besides land are measured by the square meter, square decimeter, etc. The measures are shown by the following table : TABLE.—100 sq. millimeters (mm2.)=l sq. centimeter (cm.2); 100 sq. centimeters=1 sq. decimeter (dm.2); 100 sq. decimeters=1 sq. meter (M2.). NOTE.-- The measures higher than these are not generally used. The usual method of notation is to write sq. before the denomination ; but I suggest as an abbreviation that we indicate the square by an exponent. MEASURES OF VOLUME. 420. The Stere is the unit of volume. It is a cubic meter, and equals 35.3166 cubic feet, or 1.308 cu. yd. TABLE.—10 decisteres (ds.)=1 stere (S.); 10 steres—1 decastere (DS.). NOTE.-Wood is measured by this measure. The stere, decastere, and decistere are principally used. 3.6 steres, or 36 decisteres very nearly equal the common cord. MEASURES OF OTHER VOLUMES. 421. Other solid bodies are usually measured by the cubic meter and its divisions. The measures are shown by the following table: TABLE.—1000 cubic millimeters (mm.3)=1 cubic centi. |