Now the weight of a cubic inch of distilled water is 252-458 grains Troy, the barometer being at 30 inches and the thermometer at 62°. This affords the means of recovering the Imperial Standard Pound should it be lost. In fact, the brass weight of 1758 was destroyed or lost at the above-mentioned fire. Thirdly; That the Standard Measure of Capacity for Liquids and Dry Goods shall be "the Imperial Standard Gallon," containing 10 Pounds Avoirdupois weight of distilled water, weighed in air at a temperature of 62° Fahrenheit's thermometer, and the barometer being at 30 inches. Now this weight fills 277-274 cubic inches, therefore the Imperial Standard Gallon contains 277.274 cubic inches. The Imperial Bushel, consisting of eight gallons, will consequently be 2218-192 cubic inches. REDUCTION. 116. REDUCTION is the method of expressing numbers of a superior denomination in units of a lower denomination, and conversely. Thus £1 is of the same value as 240d., and £21 as 5040d., and conversely; and the process, by which we ascertain this to be so, is termed Reduction. First. To express a number of a higher denomination in units of a lower denomination. RULE. 66 Multiply the number of the highest denomination in the proposed quantity by the number of units of the next lower denomination contained in one unit of the highest, and to the product add the number of that lower denomination, if there be any in the proposed quantity; repeat this process for each succeeding denomination till the required one is arrived at." Ex. 1. How many pence are there in £23. 15s.? Proceeding by the Rule given above, £23. 158. 20 460+15 or 475s. 12 5700d. or £23. 15s. = 5700d. Reason for the Process. There are 20 shillings in £1. Therefore there are (23 × 20) s. or 460s. in £23, and so there are 460s.+ 158., or 475s. in £23. 15s. Again, since there are 12 pence in 18.; therefore there are (475 × 12)d., or 5700d. in 475s. i.e. in £23. 15s. Ex. 2. Reduce 2 tons, 7 cwt., 3 qrs., 24 lbs. into lbs. tons cwt. qrs. 20 40+7 or 47 cwt. 4 lbs. 24 188 +3 or 191 qrs. 28 1528 382 5348 +24 or 5372 lbs. Ex. 3. Reduce 27 acres, 1 rood, 32 poles, into poles. Ex. 4. Reduce 73 days, 21 hours, 10 minutes, 9 seconds, to seconds. Ex. 5. How many inches are there in 106 miles, 6 furlongs, 25 perches, Secondly. To express a number of inferior denomination in units of a higher denomination. RULE. "Divide the given number by the number of units which connect that denomination with the next higher, and the remainder, if any, will be the number of surplus units of the lower denomination. Carry on this process, till you arrive at the denomination required." Ex. 1. How many pounds and shillings are there in 5700 pence? Proceeding by the Rule given above, In dividing 475 by 20 we cut off the 0 and 5 by Art. (43). Reason for the above process. Since 12 pence=1 shilling; therefore in any given number of pence, for every 12 pence there is 1 shilling, so that in 5700d. or (12 × 475)d. there are 4758. Again, since 20s. = £1; therefore in any given number of shillings, for every 20 shillings there is £1. Hence, in 475s., or (20 × 23+15)s. there are £23, and 15s. over. Note. Since each of the above Rules is the converse of the other, the accuracy of any result obtained by either of them may be tested by working the result back again by the other rule. Ex. 2. In 272668 inches how many miles &c. are there? Verify the result. In this Example it will be convenient to bring the inches to half-yards and the half-yards to poles. In a half-yard there are 18 or 3 × 6 inches, and in a pole there are 5 yards or 11 half-yards. therefore the answer is 4 miles, 2 fur., 17 po., 22 in. Ex. 3. Reduce 5813456 pounds to tons, and prove the correctness of the result. therefore the answer is 2595 tons, 5 cwt., 3 qrs., 12 lbs. 5813456 lbs. Ex. 4. How many grains of gold are contained in 9 lbs., 11 oz., 13 dwts., 20 grs.? Prove the result. lbs. oz. dwts. grs. 9. 11. 13. 20 12 108+11=119 oz. in 9 lbs., 11 oz. 20 2380+13 or 2393 dwts. in 9 lbs., 11 oz., 13 dwts. therefore in 57452 grs., there are 9 lbs., 11 oz., 13 dwts., 20 grs. |