2-1 ment of the Christian Æra: What would it have amount. ed to in 1784 years ; and suppose the amount to be in standard gold, allowing a cubic inch to be worth £53 25. 8d. how large would the mass have been ? 2'50I Ans: x 1= £14867163465687482094357145 (51509860767065361 115. 3.d. =27980859722121230415979571232933594210766 cubic inches (of geld, As, 355 : 113:: 360 X69,5 : 7964 Earth's diameter. 360X69,5X7964X1327,33 = 26.4482820122 cubić miles in the globe=672733373088547 4136883 2000 cubic inches in the globe. Then, 2798085972212! 2304159795712329335942;0766 67273337308854741358832000 415,30899840288,8 which, however incredible may appear to fome, is more than four hun. dred and fifteen millions of millions, nine hundred and thirty thoufud, eight hundred and ninety nine millions, eight hundred and forty thousand, two hundred and eighty eight times larger than the globe we inhabit. 4 Problem 3. The first turn, the laufterm, for the extremes) and the ratio given, to find the sum of the series. RULE.-Divide the difference of the extremes by the ratio less by 1: Add the greater extreme to the quotient, and the result will be the sum of all the terms. Or, multiply the greatest term by the ratio, from the product subtract the least term; then divide the remain. der by the ratio, less by 1, and the quotient will be the fum of all the terms. Or, when all the terms are given, then, from the product of the second and last terms fubtract the square of the first term ; this remainder being divided by the secend term less the firit, will give the sum of the series. E x A M P L E s. 1. If the series be 2. 6. 18. 54. 162. 486. 1458.4374 ; What is its fuin total ? First Method. Subtract the least = 2 Divide by the ratio, less i=3--13:2)4372 diff. of ext. Quotient = 2186 6560 Or, 43742 3-1 Second Method. Greatest term = 4374 3 Product =13122 Divide by the ratio, less by 1x3-1=2)13120 Anf. 6360 Or, 4374 X 3-2 =6560 3 Third Method. Greatest term = 4374 Multiply by the iecond term = 437% Product = 26244 Subtract the square of the first term=2X2= 4 Diy. the rem. by the ad term less the ift=6–2=4)26240 Anf. 6560 Or, 4374 X 6–4 ": :6560 6--2 2. A man travelled 6 days ; the first day he went 4 miles, and each day doubling his day's travel, his last day's ride was 128 miles ; How far did he go in the whole ? 3. A gentleman dying, left 5 fans ; to whom he bequeathed his estate as follows, viz. to his youngest fon £ 1000; to the eldest £85062 10s. and ordered that each fon should exceed the next younger by the equal ratio of I; What did the several legacies amount to ? 5062,5-1000 +5062,5=£13187 10s. Ans. 1,5-I ProB. 4. Given the extremes and ratio, to find the numter of terms. Rule.--Divide the greatest term by the least ; find what power of the ratio is equal to the quotient; then, add í to the index of that power, and the sum will be the number of terms. Or, Subtract the logarithm* of the least term from that of the greatest ; divide the remainder by the logarithm of the ratio, and add i to the quotient, If the least term be 2, the greatest term 4374, and the ratio 3, What is the number of terms ? Divide by the least term=2)4374=greatest term.. 3X3X3X3X3X3X3=Quo. 2187=7th power, then 7+1=S, the Aul. Or, * Logarithms are artificial numbers, the addition of which answers to multiplication of whole numbers, and fubtraction to division.. Or, 3.64088 From the logarithm of the greatett term Subtract the logarithm of the least term 0.30103 Divide the re mainder by 3.33984 Prob. 5. Given the least term, the ratio, and the sum of the series, to find the last term. Rulé.—Multiply the sum of the series by the ratio, less 1 ; to that product add the first term, and the result, divided by the ratio, will give the last term. EXAMPLE. of the If the first term 2,. the ratio 3, and the series 6560 ; What is the last term ? 3-1X6560-4-2 =4374 Ang 3 SIMPLE IN T E R E S T. interest is a premium allowed by the borrower of any sum of money to the lender, according to a certain rate per cent. agreed on; which by law is stated at £6, that is, 5 for the ufe of £100 for one year. Principal is the money lent. Simple interest is that, which is allowed for the principal lent only. Note. The rules for simple interest serve also to calcu-late commission, brokerage, insurance, purchasing stocks, or any thing else rated at fo much per cent. GENERAL 2. GENERAL RUL E. 1. Multiply the principal by the rate, and divide the product by 100 (or, which is the same, cut off the two right hand figures in the pounds, which must be reduced to the lowest denomination, each time cutting off as at first) and the quotient will be the answer for one year: For more years than one, multiply the interest of one year by the given number of years, and the product will be the answer for that time. 3. If there be parts of a year, as months, or days, work for the months by the aliquot parts of a year, and for the days, by the Rule of Three Direct, or (which is fufficiently exact for common use, allowing 30 days to the month) take aliquot parts of the same. te the prin 2 Note, when 8 of the given mumber the rate per 6 multiply of months, cutting cent. per ane off, as before direct. 4 num, is cipal by ed, and you will have 3 the interest for the given time. EX AMP LE S. 1. What is the interest of £6573 13 9 for one year, at 6 per cent. per annum? £ d. 573 1393 34/42 29 20 8.42 I 2 5113 0!52 Anf. £34. 8.5 2. What |