GEOGRAPHICAL OR NAUTICAL MEASURE. 1 Geographical mile. 3 60 " 360 miles 1 degree. marked deg. or [°]. "degs. or about 24,855 imp. miles = Circumference of the earth. The degree is divided into 60 minutes (marked '), and the minute into 60 seconds (marked "). This measure is used for geographical purposes, and in reckoning distances at sea. At the equator, a degree of longitude is 69 imperial miles. In Scotland, a quire consists of 24 sheets of folio paper, but of 48 sheets of quarto and octavo size. QUARTERLY TERMS FOR LEASES, ETC. ENGLAND AND IRELAND. SCOTLAND. Midsummer Michaelmas Christmas September 29 Lammas December 25 Martinmas When a Scottish Term falls on Sunday, the Monday following is considered Term-day. REDUCTION is that process by which numbers that are expressed in one or more denominations, are reduced or converted into numbers of other denominations having the same value. The calculations are made by means of the rules of Multiplication and Division, in connection with the preceding Arithmetical Tables. I. TO CONVERT A GIVEN QUANTITY FROM A HIGHER TO A lower DENOMINATION. [Multiply the quantity.] RULE.-1. Consider how many of the next lower denomination make one of the highest, and by that number multiply the highest denomination, adding to the product any of the lower denomination in the given sum. * For instance, if the highest denomination were pounds, find how many shillings make one pound. 2. If the reduction is to be carried further, convert this product into the next lower denomination, in a similar way; and so on with each denomination, till the whole has been reduced to the lowest given term. Example 1.—Reduce £31, 17s. 2ąd. to farthings. In this example the highest denomination is pounds, therefore, to change these to shillings, we multiply by 20, and add 17 to the product; the given sum now consists of 6378. 2 d. We then change the shillings to pence by multiplying by 12, and adding the 2d.; the sum is now changed to 7646d. and 3d.: changing the pence to farthings by multiplying by 4, and adding 3 farthings, we have the given sum, £31, 17s. 2ąd., changed to 30587 farthings, the name required. The example may be abridged, and the pupil required to go over it in the following manner : £ S. d. 31 17 23 20 637 Shillings. 12 7646 Pence. Pupil. Here I am required to reduce £31, 178. 2 d. to farthings. First, to change pounds to shillings. Since 20s. make £1, I must have 20 times as many shillings as pounds; therefore, I multiply by 20, and take in the 17s., because it is only numbers of the same name that can be added together: this gives 637s. Next, to change shillings to pence. Since 12 pence make 1 shilling, I must have 12 times as many pence as shillings; therefore, I multiply by 12, and take in 2d., because it is only numbers of the same name that can be added together: this gives 7646d. Lastly, to change pence to farthings. Since farthings make 1 penny, I must have 4 times as many farthings as pence; hence, I multiply by 4, and take in the 3 farthings, because, &c. : this gives 30587 farthings, the denomination required. 4 30587 Farthings. II. TO CONVERT A GIVEN QUANTITY FROM A LOWER TO A higher DENOMINATION. [Divide the quantity.] RULE.-1. Consider how many of the given denomination make one of the next higher,* and by that number divide the given sum, which is thus converted to the denomination immediately above it. *For instance, if the given denomination were farthings, find how many farthings make one penny. 2. If the conversion is to be carried further, divide the new denomination in a similar way; and so on, dividing each denomination in succession, till the sum has been converted to its highest required denomination. The remainders at each stage of the division are of the same denomination as the number from which they arise, and must be marked as such in the answer. All questions of Reduction of money, weights, measures, &c., whether from a higher to a lower, or from a lower to a higher denomination, are wrought by these two rules of Reduction. Example 2.-Convert 17127 farthings to pounds. Farthings. 4)17127 In this example-Pupil. I divide by 4, because 4 farthings make a penny, the quotient, 4281, is pence, and 3 farthings over; I divide 4281d. by 12, to change them to shillings, the quotient is 356s., and 9d. over. Lastly, I divide 356s. by 20, to change them to pounds, the quotient is £17, and £17, 16s. 9 d. 16s. over; therefore, 17127 farthings is equal in value to £17, 16s. 9 d. 12)42812 2,0)35,6" 9 Exercises. 1. Reduce the following compound numbers to farthings: £17, 13s. 43d.; £63, 13s. 114d.; £302, 5s. 94d.; 16s. 82d.; £2763, 14s. 8d.; £4587, 19s. 113d.; £209, 14s. 9d.; £5129, 4s. 54d.; 19s. 11ąd.; £670, 11s. 7ąd.; £27, 13s. 41⁄2d. 2. Reduce the following compound numbers to halfpence: £34, 14s. 7d.; £207, 4s. 3 d.; £7624, 13s. 8d.; £391, 12s. 8d.; 17s. 5d.; £706, 15s. 11d.; £310, 10s. 0дd.; £206, 15s.; £3726, 15s. 4 d. 3. Convert the following simple numbers to pounds: 7314 farthings; 59633 farthings; 71058 farthings; 3827 halfpence; 76419 halfpence; 710 halfpence; 38295 pence; 9163 pence; 12345 pence; 7987 farthings; 39276 halfpence; 49168 Example 3.-Reduce 3 lb. 4 oz. 17 dwt. 21 gr. to grains. Example 4.-Convert 39257 Troy grains to pounds. 11. Convert 23 lb. 7 oz. 3 dwt. 12 gr. to grains Troy, 9 oz. 17 dwt, to grains, Ans. 135924 gr. Ans. 4728 gr. Ans. 4 oz. 19 dwt. 9 gr. Ans. 30 lb. 2 dwt. 11 gr. 17 tons 13 cwt. of sugar to pounds, Ans. 39536 lb. 54726 lb. to tons, Ans. 4439 lb. Ans. 3023 lb. Ans. 42 cwt. 1 qr. 25 lb. 11 oz. Ans. 24 tons 8 cwt. 2 qr. 14 lb. Ans. 216 nails. Ans. 4 tons 1 cwt. 3 qr. 6 lb. 12 oz. 14 dr. 13 yd. 2 qr. to nails, 23 miles 2 fur. 219 yd. to feet, 78235 square poles to acres, Ans. 123417 feet. Ans. 488 ac. 3 ro. 35 po. Ans. 135 yd. 3 qr. 2 nl. 234 ac. 3 ro. 27 po. to poles, fur. 73 yd. 1 ft. 6 in. Ans. 5700 Eng. ells. Ans. 29345 yd. 1 qr. Ans. 2800 po. Ans. 244 ac. 2 ro. 7 po. Ans. 1 m. 1 41. How many seconds in 365 days 5 hours 48 min. 51 sec.? 42. How many solid yards in 391256 Ans. 31556931 sec. solid inches? Ans. 8 yd. 10 ft. 728 in. |