4. How often will a wheel, of 16 feet and 6 inches circumference, turn round in the distance from Newburyport to Cambridge, it being 42 miles ? Anf. 13440 times. 5. In 190080 inches, how many yards and leagues ? Anf. 528oyds. and i league. year 631152000 seconds in ditto. 2. Suppose your age to be 159. 19d. 11h. 37m. 455. how many seconds are there in it, allowing 365 days and 6 hours to the Anf. 475047465. 3. How many minutes from the first day of January to the 14th day of August, inclusively ? Ans: 325440. 4. How many days since the commencement of the Chriftian Æra ? 5. minutes since the commencement of the American war, which happened on the 19th day of April, 1775? 6. How many feconds between the commencement of the war, April 19th, 1775, and the Independence of the United States of America, which took place zac 4th day of July, 1776? Anf. 38102400. 8. L AND or SQUARE ME A S U R E. 1. In 29 acres, 3 roods, 19 poles, how many roods and perches ? Proof 29 3 19 4!0)47719 4 4)119-19P. Acr. r. p. 119 roods. Anf. 4779 perches. 2. In 1997 poles, how many acres ? Anf. 124. 17. 3714 9. SOLID ME A SU RE, 50 feet. 1. In 15 tons of hewn timber, how many folid inches? 15 tons. Proof 50 50 1728) 1296000(7510 12096 1728 15 tons. 8640 8640 .418.1296000 inches. 2. In 9 tons of round timber, how many inches? Anj. 622080. IO. WINE ME AS U R E. 1. In ghhds. 15gal. 39ts. of wine, how many quarts bhds.gal. qts. Proof. 9 15 3 4)2331 63)582-39ts. 9hhds--158 582 gallons. 4 Anf.2331 quarts. Anf. 12096. 3. In 9758 pints of brandy, how many pipes ? Ans: 9p. Ihhd. 22gal. 3qts. 4. In 1008 quarts of cider, how many tons ? Ans, 1 ton. II. ALE or BEER MEASURE. 1. In 29hhds. of beer, how many pints ? bhds. Proof. 29 2)12528 4)6264 54) 1566 1566 gallone. 4 29hhds. 6264 quarts. 2 Anf. 12528 pints. F2 2. In 2. In 47 ar. 18ysl. of ale, how many pints? Anf. 12928. 3. In 36 puncheons of beer, how many butts ? Anf. 24 12. DR Y ME A S U R E. 1. In 42 chaldrons of coals, how many pecks ? Chaldrons. Proof. 42 4)5376 32 32):344(42 128 84 Any 5376 pecks. 2. In 75 bushels of corn, how many pints ? Anf. 4800. 3. In 9376 quarts, how many bushels ? Ans. 293. VULGAR FRACTIONS. Fracions, or broken numbers, are expreffions for any affignable parts of an uit, or whole number ; aici are represented by two numbers, placed one above another, vitale dravn begieen them, thus, , , &c. fignify ve eightlu, four thirds, that is one and one third, &c. The tisare, above the line, is called the pumerator, and 'that bdew it, the dinondor, T. donorjantur (which is the divilor in division) fies how many parts th: integer is divided into ; and the warcrator (ivisich is the remainder after divifion) fas WS 07 shews how many of those parts are meant by the fraction. I 2 Fractions are either proper, improper, fingle, compound, or mixed. Any whole number may be made an improper fraction, by drawing a line under it, and putting unity, or i for a denominator, as 9 may be expressed fractionwise, thus, , and 12 thus, ??, &c. 1. A single, fimple, or proper fraction is, when the numerator is less than the denominator,as }, }, }, }},&c. and is a simple expresiion for any number of parts of the integer. 2. An improper fraction is, when thę numerator exceeds the denominator, as jo go , &c. 3. A compound fracion is the fraction of a fraction, coupled by the word of, thus, į of }, { of } of }, &c. which are read thus, two thirds of three fourths ; one half of three fifths of seven eigliths. 4. A mixed number is composed of a whole number and a fraction, as 7}, 35 145, &c. that is, feven and three fifths, &c. 15. A fraction is said to be in its leaft, or lowest terms, when it is expressed by the least numbers possible. 6. The common measure of two or more numbers, is that number which will divide each of them, without a remainder : Thus, 5 is the common measure of 10, 20 and 30.; and the greatejl number, which will do this, is called the greatest commo: measure. 7. A number, which can be measured by two, or more numbers, is called their common multiple ; and, if ith the least number, which can be fo meafured, it is caili le leal common multiple ; thus, 40, 60, 80, ico are not of 4 and 5 ; but their leat common inultiple is a |