ment of the Chriftian Æra: What would it have amounted to in 1784 years; and fuppofe the amount to be in ftandard gold, allowing a cubic inch to be worth £53 25. 8d. how large would the mafs have been ?

150 2

Anf.

2-I

X1=14867163465687482094357145 (51509890767065361 11s. 33d. =27980859722121230415979571232933594210766 cubic inches

(of gold, As, 355 113:: 360X69,5: 7964 Earth's diameter. 360X69,5X7964X1327,33 264482820122 cubic miles in the globe 67273337308854741368832000 cubic inches in the globe. Then, 2798085972212123041597957 1 2 3 29 33 594210766÷ 67273337308854741368832000

41530899840288,8

which, however incredible it may appear to fome, is more than four hundred and fifteen millions of millions, nine hundred and thirty thoufand, eight hundred and ninety nine millions, eight hundred and forty thousand, two hundred and eighty eight times larger than the globe we inhabit.

PROBLEM 3. The first term, the last term, (or the extremes) and the ratio given, to find the fum of the feries.

RULE. Divide the difference of the extremes by the ratio lefs by 1: Add the greater extreme to the quotient, and the refult will be the fum of all the terms.

Or, multiply the greatest term by the ratio, from the product fubtract the leaft term; then divide the remainder by the ratio, lefs 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 fecond and last terms fubtract the fquare of the first term; this remainder being divided by the second term lefs the first, will give the fum of the feries.

1. If the feries be 2. 6. 18. 54. 162. 486. 1458. 4374;

What is its fum total ?

First Method.

From the greatest term = 4374
Subtract the leaft - 2

Divide by the ratio, less 1=3-12)4372 diff. of ext.

Divide by the ratio, lefs by 1X3-1=2)13120

Diy. the rem. by the 2d term lefs the 1ft 6-24)26240

Product

26244

4

2. A man travelled 6 days; the first day he went 4 miles, and each day doubling his day's travel, his lat 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 eftate as follows, viz. to his youngest fon 1000; to the eldest £5062 10s. and ordered that each fon fhould exceed the next younger by the equal ratio of 1; What did the feveral legacies amount to ?

5062,5-1000

1,5-1

·+5062,5= £13187 10s. Anf.

PROB. 4. Given the extremes and ratio, to find the number of terms.

RULE. Divide the greatest term by the leaft; find what power of the ratio is equal to the quotient; then, add to the index of that power, and the fum will be the number of terms.

Or, Subtract the logarithm* of the leaft term from that of the greatest; divide the remainder by the logarithm of the ratio, and add 1 to the quotient,

EXAMPLE.

If the leaft term be 2, the greateft term 4374, and the ratio 3, What is the number of terms?

Divide by the leaft term 2)4374-greatest term.

3×3×3×3×3 × 3 × 3=Quo. 21877th power, then 7+1=8, the Anf.

Or,

*Logarithms are artificial numbers, the addition of which answers; to multiplication of whole numbers, and fubtraction to divifion.,

mainder

by

the logarithm=47712)3.33985(7+1=8 Anf

of the ratio

3.33984

I

PROB. 5. Given the leaft term, the ratio, and the fum of the feries, to find the last term.

RULE.-Multiply the fum of the feries by the ratio, lefs; to that product add the first term, and the result, divided by the ratio, will give the last term.

EXAMPLE.

If the first term be 2, the ratio 3, and the sum of the feries 6560; What is the last term?

3-1×6560+2

3

=4374 Anf

SIMPLE INTEREST.

Intereft is a premium allowed by the borrower of any fum of money to the lender, according to a certain rate per cent. agreed on, which by law is ftated at £6, that is, 6 for the ufe of £100 for one year.

Principal is the money lent.

Rate is the fum per cent. agreed on.

Amount is the principal and intereft added together. Intereft is of two forts, fimple and compound.

Simple interest is that, which is allowed for the principal lent only.

Note. The rules for fimple interest serve alfo to calcu late commiffion, brokerage, infurance, purchafing flocks, or any thing elfe rated at fo much per cent.

GENERAL

GENERAL RULE.

1. Multiply the principal by the rate, and divide the product by 100 (or, which is the fame, cut off the two right hand figures in the pounds, which must be reduced to the lowest denomination, each time cutting off as at firft) and the quotient will be the answer for one year.

2.

For more years than one, multiply the intereft of one year by the given number of years, and the product will be the anfwer 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 ufe, allowing 30 days to the month) take aliquot parts of the fame.

1. What is the intereft of £573 13 9 for one year, at 6 per cent. per annum?

S. d.