TABLE SHOWING THE NUMBER OF DAYS FROM ANY DAY OF ONE MONTH TO THE SAME DAY OF ANY OTHER MONTH IN THE SAME YEAR. FROM ANY TO THE SAME DAY OF NEXT DAY OF Jan. Feb. Mar. Apr. May. June July. Aug. Sept. Oct. Nov. Dec. 243 273 304 334 365 181 212 242 273 303 334 365 30 61 91 243 273 61 AUGUST 153 184 212 335 365 31 For example, suppose we wish to find the number of days from April 4th to November 4th, we look for April in the left-hand vertical column, and for November at the top, and where the lines intersect is 214, the number sought. Again, if we wish the number of days from June 10th to September 16th, we find the difference between June 10th and September 10th to be 92 days, and add 6 days for the excess of the 16th over the 10th of September, and so we have 98 days as the exact difference. If the end of February be included between the points of time, a day must be added in leap year. When the time includes more than one year, there must be added 365 days for each year. EXAMPLES. 1. How many seconds in a solar year ? 2. In 31556929 seconds how many days? 3. How many seconds from the deluge, which took place 2348 years before Christ, to the year 1856, a year being 365 days? Ans. 132636592800. 4. In 74726807872 seconds how many solar years? Ans. 2368 years. 5. How long did the last war with England continue; it having commenced June 18th, 1812, and ended February Ans. 974 days 2 = 17th, 1815? years CIRCULAR ANGULAR MEASURE. 244 days. 143. Circular Angular Measure is applied to the measurement of circles and angles, and is used in reckoning latitude and longitude, and the revolutions of the planets round the sun. A 330 360 30 300 09 270 06 Я 240 210 a 180 150 The Circumference of a circle is the line which bounds it, as shown by the diagram. An Arc of a circle is any part of its circumference; as AB. A Radius of a circle is a straight line drawn from its center to its circumference; as CA, CB, or CD. Every circle, large or small, is supposed to be divided into 360 equal parts, called degrees. A Quadrant is one fourth of a circle, or an arc of 900; as AB. An Angle, as ACB, is the inclination or opening of two lines which meet at a point, as C. The point is the vertex of the angle. If a circle be drawn around the vertex of an angle as a center, the two sides of the angle, as radii of the circle, will include an arc, which is the measure of the angle; as the arc AD = 1200 is the measure of the angle ACD, and AB 90°, the measure of the angle ACB; hence the one is called an angle of 1200, and the other an angle of 900. = NOTE 2. As the earth turns on its axis from west to east every 24 hours, the sun appears to pass from east to west of 360° of longitude every hour, or 150 of longitude in 1 hour's time, or 10 in 4 minutes of time, and 1' in 4 seconds of time; so that, for instance, when it is noon at any place, it is 1 hour earlier for every 15° of longitude westward, and 1 hour later for every 150 of longitude eastward. Thus, Boston being 71° 4' west of Greenwich, and San Francisco 51° 17' west of Boston, when it is noon at Boston, it is 4h. 44m. 16sec. past noon at Greenwich, and wanting 3h. 25m. 8sec. of noon at San Francisco. EXAMPLES. 1. How many minutes in 27S. 27° 43'? 5. How many seconds in 360° ? 6. How many degrees in 1296000"? MISCELLANEOUS TABLE. 144. The following denominations, frequently used, are not 100 pounds of Grain 220 pounds of Fish, in Md. 256 pounds of Soap 30 gallons of Fish, in Mass. 66 1 quintal. 66 1 barrel. 66 1 barrel. 66 1 cental. 200 pounds of Shad or Salmon, in N. Y. & Ct. " 300 pounds of Hydraulic Cement 5 bushels of Shelled Corn, in Southern States " 8 bushels of Salt NOTE 1. A sheet of paper folded into 2 leaves forms a folio; a sheet folded into 4 leaves, a quarto; a sheet folded into 8 leaves, an octavo; a sheet folded into 12 leaves, a 12mo; a sheet folded into 18 leaves, an 18mo; a sheet folded into 24 leaves, a 24mo. NOTE 2. Of shoemaker's measure, No. 1 of small size is 4 inches in length; and No. 1, large size, is 84 inches in length; and each succeeding number of either size is of an inch additional length. 1 barrel. 1 barrel. 1. In 4 bales 4 bundles 1 ream 10 quires of paper how many sheets? Ans. 23760. 2. In 23760 sheets of paper how many bales? 3. In 10 fothers 6 pigs 8 stones of iron how many pounds? 4. In 25998 pounds of iron how many fothers? ó. At 23 cents a pound, what will 12 firkins of butter cost? 6. If $22 is paid for a barrel of pork, how much is that by the pound? Ans. 11 cents. 7. How much must be paid for 302 hogsheads of salt at $0.30 a bushel? Ans. $724.80. 8. At $4 per quintal, how many pounds of fish may be bought for $50.24? Ans. 1256 pounds. 9. If the wholesale price of one writing-book be 4 cents, what will be the cost of a great-gross of writing-books? 10. A dairyman sells 2 firkins of butter at 20 cents a pound, and takes in pay half a barrel of flour at 5 cents a pound, and the balance in cash. How much cash does he receive? Ans. $17.50. MISCELLANEOUS EXAMPLES IN REDUCTION. 1. In 57£. 15s. how many half-pence? Ans. 27720. Ans. 608 E. E. 4qr. 5. How many yards in 61 ells Flemish? Ans. 45yd. 3qr. 6. How many bottles, that contain 3 pints each, will it take to hold a hogshead of wine? 7. How many steps, of 2ft. 8in. each, will walking from Bradford to Newburyport, the fifteen miles? Ans. 168. a man take in distance being Ans. 29700. 8. How many spoons, each weighing 2oz. 12pwt., can be made from 5lb. 2oz. 8pwt. of silver? Ans. 24. 9. How many times will the wheel of a coach revolve, whose circumference is 14ft. 9in., in passing from Boston to Washington, the distance being 436 miles? Ans. 15607332. 10. I have a field of corn, consisting of 123 rows, and each row contains 78 hills, and each hill has 4 ears of corn; now if it takes 8 ears of corn to make a quart, how many bushels does the field contain? Ans. 149bu. 3pk. 5qt. Opt. 11. If it take 5yd. 2qr. 3na. to make a suit of clothes, how many suits can be made from 182 yards? 12. A goldsmith wishes to make a number of rings, each weighing 5pwt. 10gr., from 3lb. 1oz. 2pwt. 2gr. of gold; how many will there be? Ans. 137. 13. How many shingles will it take to cover the roof of a building, which is 60 feet long and 56 feet wide, allowing each shingle to be 4 inches wide and 18 inches long, and to lie one third to the weather? Ans. 20160. 14. There is a house 56 feet long, and each of the two sides of the roof is 25 feet wide; how many shingles will it take to cover it, if it require 6 shingles to cover a square foot? Ans. 16800. 15. If a man can travel 22m. 3fur. 17rd. a day, how long would it take him to walk round the globe, the distance being about 25000 miles? Ans. 1114482 days. 16. If a family consume 7lb. 10oz. of sugar in a week, how long would 10cwt. 3qr. 16lb. last them? Ans. 143 weeks. 17. What will 7 hogsheads of wine cost, at 9 cents a quart? 18. What will 15 hogsheads of beer cost, at 3 cents a pint? Ans. $194.40. 19. What will 73 bushels of meal cost, at 2 cents a quart? Ans. $46.72. 20. A merchant has 29 bales of cotton cloth; each bale contains 57 yards; what is the value of the whole at 15 cents a yard? Ans. $247.95. 21. There is a certain pile of wood 120 feet long, 41 feet high, and 4 feet wide; what is its value at $4.00 per cord? Ans. $67.50. 22. How much must be paid, at twenty cents a square yard, for plastering overhead in a room which is 33 feet long and 18 feet wide? 23. An apothecary, in compounding 20 boxes of pills, each box containing 25 pills, used 6 grains of aloes, 5 grains of rhubarb, and 4 grains of calomel in each pill. What was the entire quantity used? Ans. 7500 grains. 24. Purchased a cargo of molasses, consisting of 87 hogsheads; what is the value of it at 33 cents a gallon? Ans. $1808.73. 25. If a cubic foot of white-oak wood weighs 880 ounces, and a cubic foot of white-pine wood weighs 480 ounces, how much will a load weigh, which is composed of half a cord of white-oak, and of a cord of white-pine? Ans. 7360lbs. |