INVOLUTION BY LOGARITHMS. RULE. Multiply the logarithm of the root by the index of the power; thus, to square any number, multiply its logarithm by 2; and to cube a number, multiply its logarithm by 3, and so on. Ex. 1. What is the square of 25; and the 5th power of 2? 25 = log. 1.8979400 25 2 625 log. 2.7958800 25..301030 X 5 = Ex. 2. What is the third power of? See p. 142. *By the table, I find that the number answering to this logarithm is more than 1490: by the rules already given, I put down .1731863 .176091329050 first diff., .1750041 18178 second diff., therefore As 29050 1: 18178: 625, which is to be annexed to 149 1499.25, because the index is 3. mits of other proofs: thus the log. 7.845098 2.535294 2.709270 and, subtracting the denominator from the numerator, we have -1.826024.67. EVOLUTION BY LOGARITHMS. To extract the root of any number. RULE. Divide the logarithm of the number by the proposed index, and the number answering to the quotient is the required root. Ex. 1. What is the square root of 225 ? Log. of 225 2.3521825, which by 2, gives 1.1760912, which is the log. of 15. Ex. 2. What is the square root of 6561? of course the square root of 6561 is found to be 81. Ex. 3. What is the 5th root of 1024? See p. 143. Ex. 4. What is the square root of .25? See p. 144. .69897.5 Answer. Ex. 5. What is the square root of 144? NOTES. *The learner may in this way work all the examples in P. 142. 1.942008 It may not occur at first sight to the reader, how × 3 should give-1.826024; but if he divide the expression into two sums, which he may, as 1 and .942008, and multiply each 3 and 2.826024. The plus 2 in the latter expression 2 of the former; the remainder will of course be by 3, he gets will destroy -1.826024. INTEREST. INTEREST, is the sum of money paid, or allowed for the loan or use of some other sum, lent for a certain time, according to a fixed rate. The sum lent, and on which the interest is reckoned, is called the PRINCIPAL. The sum per Cent, agreed on as interest, is called the RATE. The principal and interest added together, is called the AMOUNT. Interest is distinguished into SIMPLE and COMPOUND. SIMPLE INTEREST, is that which is reckoned on the principal only, at a certain rate for a year, and at a proportionately greater or less sum, for a greater or less term : thus, if 51. is the rate of interest of 1007. for one year, 107. is the interest for two years, 207. for four years, and so on. RULE (1). Multiply the principal by the rate, and divide the product by 100, and the quotient is the interest for one year: Thus the interest of 250l. at 5 per cent. is 250 X 5 100 12. 10s. (2). Multiply the interest for one year by the number of years, and the product is the interest for the same : Thus the interest of 2501. for 7 years is 127. 108. × 787l. 10s. (3). If parts of a year be given, they must he worked for by the aliquot parts of a year, as in Practice, or by the Rule of Three Direct. Ex. 1. What is the interest of 8537. 10s. for 4 years and 8 months, at 5 per cent. per annum ?* NOTE. *By law, more than 5 per cent. cannot be received as interest of money in this country; though at various periods of our history different rates of interest have been allowed, as will be evident from the following table: To find the amount, I must add the principal to the interest. In this example, the amount is equal to 8531. 10s. + 1991. 38. 1052/. 13s. the amount of 1427. 10s. for four years per cent ?* £. s. d. 6 8 8 interest for one year. 4 25 13 0 interest for four years. To find the interest for the 52 days, I say, In 1255 1270 to 1307 1422 to 1470 1545 it was restricted to 1625 reduced to 1645 to 1660 1660 to 1690 1690 to 1697 1697 to 1706 1714 to the present time 5 0 0 In many parts of the world a much higher rate of interest is given, and also in the colonies belonging to this country. In India, for instance, 12 per cent. is the legal interest for money and in the English settlements in New South Wales, the rate of interest is fixed at 8 per cent. * In the courts of law, interest is always computed in years, quarters, and days; but in computing the interest on the public 18 3 interest for 52 days. Ex. 3. What is the interest of 4617. at 4 per cent. for 5 years? Ex. 4. What is the interest of 230l. 15s. for 6 years, at 5 per cent. per annum? Ex. 5. What is the amount of 2251. for 7 years, at 3 per cent. per annum. Ex. 6. How much shall I have to receive at the end of 5 years for 350l. supposing 4 per cent. be allowed as interest? In most computations relating to simple interest, the work is shortened, if the interest of 11. for a given term is known, as the interest of any other sum for the same term will then be found by only multiplying by the given sum, The interest of 11. for a year must be in the same proportion as the interest of 100l. to its principal; therefore, at 5 per cent., we say, as iool.: 5l. : : 1l. : .057. Hence the interest of 11. for one year £. At 3 per cent. is £. ,03 Ex. 7. What sum will one penny amount to in 1808 years, at 5 per cent. ?* NOTE. bonds of the South-Sea and East-India companies, the time generally taken is in calendar months and days; and on Exchequer-bills, in quarters of a year and days. * Here the sum is..004166; this multiplied by 1808, and the product multiplied by .05, gives something more than 7s. 6d. See COMPOUND INTEREST, where the difference between Simple and Compound Interest will be put in a most striking point of view by this same question. |