6. In 285290205 seconds, how many years of 365da. 6hr. each? 7. How many hours in any year from the 31st day of March to the 1st day of January following, neither day named being counted? CIRCULAR MEASURE. 118. Circular measure is used in estimating latitude and longitude, and also in measuring the motions of the heavenly bodies. The circumference of every circle is supposed to be divided into 360 equal parts, called degrees. Each degree is divided into 60 minutes, and each minute into 60 seconds. 1. How many seconds in 3 minutes? In 4? In 5? 2. How many minutes in 6 degrees? In 4? In 5? 3. How many degrees in 4 signs? In 6? In 7? In 8? 4. How many degrees in 240 minutes? In 720? How many signs in 90°? In 150°? In 180° ? EXAMPLES. 1. In 5s. 29° 25', how many minutes? 3. In 27894 seconds, how many degrees, &c.? : 118. For what is circular measure used? How is every circle supposed to be divided? Repeat the table. The terms, folio, quarto, octavo, duodecimo, &c., indicate the number of leaves into which a sheet of paper is folded. A sheet folded in 2 leaves is called a folio. MISCELLANEOUS EXAMPLES. 1. How many hours in 344wk. 6da. 17hr.? 2. In 6 signs, how many minutes? 3. In 15 tons of hewn timber, how many cubic inches ?4. In 171360 pence, how many pounds? 5. In 1720320 drams, how many tons? 6. In 55799 grains of laudanum, how many pounds? 7. In 9739 grains, how many pounds Troy? 8. In 59lb. 13pwt. 5gr., how many grains? 9. In £85 8s., how many guineas? 10. In 346 E. F., how many Ells English? 11. In 3hhd. 18gal. 2qt., how many half-pints? 12. In 12T. 15cwt. 1gr. 19lb. 12dr., how many drams? 13. In 40144896 square inches, how many acres? 14. In 5760 grains Troy, how many pounds? 15. In 6 years (of 52 weeks each), 32wk. 6da. 17hr., how many hours? 16. In 811480", how many signs? 17. In 2654208 cubic inches, how many cords? 18. In 18 tons of round timber, how many cubic inches? 19. In 84 chaldrons of coal, how many pecks? 20. In 302 ells English, how many yards? 21. In 24hhd. 18gal. 2qt. of molasses, how many gills? 25. In 37444325 square inches, how many acres? 26. If the entire surface of the earth is found to contain 791300159907840000 square inches, how many square miles are there? 27. How many times will a wheel 16 feet and 6 inches in circumference, turn round in a distance of 84 miles ? 28. What will 28 rods, 129 square feet of land cost at $12 a square foot? 29. What will be the cost of a pile of wood 36 feet long 6 feet high and 4 feet wide, at 50 cents a cord foot? 30. A man has a journey to perform of 288 miles. He travels the distance in 12 days, travelling 6 hours each day: at what rate does he travel per hour? 31. How many yards of carpeting 1 yard wide, will carpet a room 18 feet by 20? 32. If the number of inhabitants in the United States is 24 millions, how long will it take a person to count them, counting at the rate of 100 a minute? 33. A merchant wishes to bottle a cask of wine containing 126 gallons, in bottles containing 1 pint each: how many bottles are necessary? 34. There is a cube, or square piece of wood, 4 feet each way: how many small cubes of 1 inch each way, can be sawed from it, allowing no waste in sawing? 35. A merchant wishes to ship 285 bushels of flax-seed in casks containing 7 bushels 2 pecks each: what number of casks are required? 36. How many times will the wheel of a car, 10 feet and 6 inches in circumference, turn round in going from Hartford to New Haven, a distance of 34 miles? 37. How many seconds old is a man who has lived 32 years and 40 days? 38. There are 15713280 inches in the distance from New York to Boston, how many miles? 39. What will be the cost of 3 loads of hay, each weighing 18cwt. 3qr. 24lb., at 7 mills a pound? ADDITION OF DENOMINATE NUMBERS. 119. Addition of denominate numbers is the operation of finding a single number equivalent in value to two or more given numbers. Such single number is called the sum. How many pounds, shillings, and pence in £4 8s. 9d., £27 14s. 11d., and £156 17s. 10d.? ANALYSIS.-We write the units of the same name in the same column. Add the column of pence; then 30 pence are equal to 2 shillings and 6 pence: writing down the 6, carrying the two to the shillings. Find the sum of the shillings, which is 41; that is, 2 pounds and 1 shilling over. Write down 18.; then, carrying the 2 to the column of pounds, we find the sum to be £189 18. 6d. OPERATION. £. S. d. 4 8 9 27 14 11 156 17 10 £189 1s. 6d. NOTE.-In simple numbers, the number of units of the scale, at any place, is always 10. Hence, we carry 1 for every 10. In denominate numbers, the scale varies. The number of units, in passing from pence to shillings, is 12; hence, we carry one for every 12. In passing from shillings to pounds, it is 20; hence, we carry one for every 20. In passing from one denomination to another, we carry 1 for so many units as are contained in the scale at that place. Hence, for the addition of denominate numbers, we have the following RULE.-I. Set down the numbers so that units of the same name shall stand in the same column; II. Add as in simple numbers, and carry from one denomination to another according to the scale. PROOF. The same as in simple numbers. 119. What is addition of denominate numbers? How do you set down the numbers for addition? How do you add? How do you prove addition ? |