degree on the circumference of a circle, whose radius or semidiameter is 58 miles, is one mile; if the radius is 58 rods, the length of the degree is one rod. In this measure are reckoned latitude, longitude, and the planetary motions.” OBS.-Points and lines are applied to measuring pendulums of clocks; hands, to measuring horses; fathoms, to measuring depths of the sea. Books. is called Folio. When a sheet is folded into two leaves, When folded into 24, it is called 24mo. A gallon of train oil weighs... A stone of butcher's meat weighs.. A stone of iron A firkin of butter 7 pounds. 8 66 11 .............. Art. 117.-REDUCTION is the changing of numbers from one denomination to another, without altering their value. 1. In £6 7s. 8d. 2qrs., how many farthings? QUESTIONS.-1. What is Reduction? 2. By what numbers do you multiply in Example 1st? and why? Operation. £6 7s. 8d. 2qrs. 20 127 12 1532 4 It is plain, that if in one pound there are 20s., in 6 pounds there are 6 times as many, or 120s. ; and in £6 7s. there are 127s. Again, if in one shilling there are 12d., in 127s. there are 127 times 12, which, with the 8d. added, equals 1532d. Lastly, it is evident that, if in 1 penny there are 4 farthings, in 1532d. there are 4 times the number of farthings, or 6130, the 2qrs. in the given question being added. Hence it appears, that in any given number of pounds there are 20 times as many shillings as pounds, 12 times as many pence as shillings, and 4 times as many farthings as pence. This process is called Reduction Descending, because higher denominations are brought into lower. 6130qrs. Ans. 2. In 6130 farthings, how many pounds? Operation. 4)6130 12)1532 2qrs. 2/0)12/7 8d. It will be seen that this question is the reverse of the former; and as 4 farthings are equal to 1 penny, so the number of pence in 6130grs. will equal the number of times it £6 7s. 8d. 2qrs. Ans. contains 4, or 1532d. and 2qrs. over. Again, as 12d. are equal to 1 shilling, so in 1532d. the number of shillings will equal the number of times it contains 12, or 127s. and 8d. over. Lastly, since 20s. is equal to 1 pound, 127s. must equal 6 pounds and 7s., because 20 is contained in 127s. 6 times, and 7s. over. It is always to be remembered, that the remainder is of the same denomination as the dividend, whatever may be the divisor. This latter process is called Reduction Ascending, because lower denominations are brought into higher. By these examples, it appears that Reduction Ascending and Descending mutually prove each other. From the preceding operations we derive the following Rules: Art. 118. RULE. Multiply the highest denomination given by that number which expresses how many it takes of the Art. 119. RULE. Divide the denomination given by that number which expresses how many of that denomination it next lower to make one of the | takes to make one of the next highhigher, observing to add the next er. Divide farthings by as many lower denomination to the product. farthings as it takes to make a Multiply pounds by what makes a penny; pence by as many pence pound; shillings by what makes as it takes to make a shilling, and a shilling, and so on, until you so on, until you have reduced it to have reduced it to the denomina- the denomination required. tion sought in the question. QUESTIONS.-3. What is the process called? 4. By what numbers do you divide in question 2? and why? 5. What is this process called? 6. What is the rule for Reduction Ascending? 7. For Reduction Descending? Long Measure. 25. Reduce 640 degrees to 26. In 234854400 feet, how many degrees? feet. 29. A teamster, after travelling 30. If a teamster receive for 20 miles, met a man who offered his load $264.00, being paid 5 him as many 5 cent pieces for his cents for each revolution of the load, as his larger wheel had turn- larger wagon-wheel, the circumed round times since he com- ference being 20 feet, how far menced his journey, the wheel had he travelled? being 20 feet in circumference. How much did he get for his load? 31. How many barleycorns 32. In 4755801600 barley will reach round the globe, it corns, how many degrees? being 360 degrees? Land, or Square Measure. 33. If in a county there are 34. How many square miles 1200 square miles, how many in 122880000 square rods ? square rods are there in this county? 35. How many square inches in 430 square acres? 36. In 2697235200 square inches, how many square acres? Solid, or Cubic Measure. 37. How many solid inches in 10 cords of wood? 39. In 40 cords, how many cord feet? 41. How many solid inches in a pile of timber containing 54 tons? 38. Reduce 2211840 solid inches to cords. 40. In 320 cord feet, how many cords? 42. In 3732480 solid inches of round timber, how many tons? 61. How many minutes in 10 yrs. 30 da. 18 hrs. 45 m.? 63. How many seconds from May 1, 1830, to April 12, 1837, inclusive? 65. Alexander the Great as 62. In 5303925 minutes, how many years? 64. In 219326400 seconds, how many years? 66. In 1140807240 minutes, cended the throne 332 years be- how many years? fore the Christian era. How many minutes from that period to 1837 ? |