We first multiplied the decimal of a £ by 20, because 20 shillings make 1 pound; pointing off by the rule for decimals, we found 15s. and 0.5625 of a shilling. Then we multiplied this decimal of a shilling by 12, because 12 pence make 1 shilling; pointing off, we found 6d. and 0.75 of a penny, which being multiplied by 4, because 4 farthings make 1 penny, gave just 3 farthings. By carefully considering the above operation, we deduce this RULE. Multiply the decimal by the number expressing how many of the next lower denomination make a unit of the denomination of the decimal; point off by the usual rule for decimals; multiply the decimal part, thus pointed off, as before; and so continue to the lowest denomination ; the several denominate values sought will appear at the left of the decimal point of the successive products. Repeat this Rule. EXAMPLES 1. What is the value of 0.9075 of an acre? 4. What is the value of 0.375 of a hogshead of wine? Ans. 23gal. 2qt. 1pt. 5. What is the value of 0.121212 of a year of 365 days? Ans. 44da. 5hr. 49m. 1.632sec. 6. What is the value of 0.3355 of a pound avoirdupois ? Ans. 5oz. 5.888dr. 7. What is the value of 0.3322 of a ton? Ans. 6cwt. 2qr. 16lb. 2·048oz. 8. What is the value of 0.2525 of a mile? Ans. 2fur. Ord. 4yd. 1ft. 2.4in. 9. What is the value of 0.345 of a £ ? Ans. 6s. 10d. 3·2far. 10. What is the value of 0.121212 of a day? Ans. 2hr. 54m. 32.7168sec. 11. What is the value of 0.3456 of a £? Ans. 6s. 10d. 3·776far. 12. What is the value of 0.9875 of a £? Ans. 19s. 9d. 13. What is the value of 0-24224 of a solar day? Ans. 5hr. 48m. 49.536sec. DUODECIMALS. 100. IN decimals we have seen that the figures decrease in a tenfold ratio, from the left towards the right. In duodecimals, this decrement goes on in a twelvefold ratio. The different denominations are the foot (f.) the prime, or inch ('), the second ("), the third (""), the fourth (''''), the fifth (""""), and so on. Thus, 7f., 6', 3", 4"", 5""', is read 7 feet, 6 primes, 3 seconds, 4 thirds, 5 fourths. The accents used to distinguish the denominations below feet, are called indices. Taking the foot for the unit, we have the following relations : ADDITION AND SUBTRACTION OF DUODECIMALS. 101. ADDITION AND SUBTRACTION of duodecimals, are performed like addition and subtraction of other denominate numbers, remembering that 12 of any denomination make one of the next greater denomination. In decimals how do figures decrease from the left toward the right? In duodecimals how do they decrease? What are the different denominations of duodecimals? What are the accents called which are used to distinguish the different denominations below the foot? How is addition and subtraction of duodecimals performed? 3. What is the sum of 3f. 6′ 4′′, 8f. 3′ 4′′, 9f. 1′ 3′′, and 10f. 10' 10"? Ans. 31f. 9' 9". 4. What is the sum of 100f. 8' 8", 135f. 0′ 1′′, 65f. 9′ 2", 45f. 3′ 3′′, and 200f. 6′ 6′′ ? From 87f. Ans. 547f. 3' 8". 3' 4" 100f. 10' 10" Remainder 51f. 6′ 7. From 25f. 6′ 6′′ subtract 18f. 9′ 10′′. 8. From 100f. subtract 58f. 2′ 1′′. Ans. 6f. 8' 8". Ans. 41f. 9' 11". MULTIPLICATION OF DUODECIMALS. 102. SUPPOSE we wish to multiply 14f. 7' by 2f. 3' we should proceed as follows: 14f. 7' 2f. 3' 3f. 7' 9" 29f. 2′ Ans. 32f. 9′ 9′′=32f+1 of a foot of a foot. EXPLANATION. We begin on the right hand, and multiply the multiplicand through, first by the primes of the multiplier, then by the feet of the multiplier, thus: 3'x7'x=24 of a foot, which is 21"1'9"; we write down the 9", and reserve the l' for the next product; again, 14f. x3'=14x = t of a foot, which is 42'; now adding in the l′, which was reserved from the last product, we have 43′: 3f. 7', which we write down, thus finishing the first line of products. Again, we have 2f.×7=2× of a foot, which is 14'=1f. 2'; we write the 2' under the primes of the line above, and reserve the lf. for the next product; 2f.x 14f28f., to which, adding in the 1f. reserved from the last product, we have 29f., which we place underneath the feet of the line above. Taking the sum, we find 32f. 9' 9", for the answer. From the above we infer, that if we consider the index |