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are found to be worth no more than 1702 148 ; how must it be divided aniong his creditors ? Ans. O must have 371 158 5d 2,

110791.

70 15 2 2-7499 Q

14 8 4 0.4720

47 14 11 2 1358 Ex. 8. A ship worth 9001, being entirely lost, of which belonged to s, i to T, and ihe rest to v; what loss will each sustain, supposing 5401 of her were insured ?

Ans. s will lose 451, T 901, and v 2251. 9. Four persons, w. X Y, and 2, spent among them 258, and agree that w shall pay of it, x }, y , and a ž; that is, their shares are to be in proportion as $, s, #, and }: What are their shares?

Ans. w must pay 98 8d 379.

6. 5 33. 4 O 1464

310 379 10. A detachment, consisting of 5 companies, being sent into a garrison, in which the duty required 76 men a day; what number of men must be furnished by each company.

in proportion to their strength ; the first consisting of 54 men, the 2d of 51 men, the 3d of 48 men, the 4th of 39, and the 5th of 36 men ? Ans. The 1st must furnish 18, the 2d 17, the 3d 16, the

4th 13, and the 5th 12 men.

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DOUBLE FELLOWSHIP.

DOUBLÉ FELLOWSHIP, as has been said, is concerned in Cases in which the stocks of partners are employed or continued for different times.

Questions of this nature frequently occurring in military service, General Haviland, an officer of great merit, contrived an ingenious in. strument, for more expeditiously resolving them; which is distinguish. et by the name of the inventor, being called a Haviland.

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RULE*-Multiply each person's stock by the time of its continuance; then divide the quantity, as in Single Fe:low. ship, into shares, in proportion to these products, by saying,

As the total sumn of all the said products,
Is to the whole gain or loss, or quantity to be parted,
So is each particular product,
To the correspondent share of the gain or loss.

EXAMPLES

1. A had in company 501 for 4 months, and a had 601 for 5 months ; at the end of which time they find 24i gained : how must it be divided between them?

Here 50 60

5

200 + 300 - 500

Then, as 500 : 24 : : 200 : = 91 128 = A's share. and as 500 : 24 :: 300 : 143

B's share. 2. c and o hold a piece of ground in common, for which they are to pay 541. c put in 23 horses for 27 days, and d 21 horses for 39 days ; how much ought each man to pay of the rent ?

Ans. c must pay 231 58 9d,

D must pay 30 14 S 4. Three persons, E, F, G, hold a pasture in common, for which they are to pay 397 per annum; into which e put 7 oxen for 3 months, F put 9 oxen for 5 months, and G put in 4 oxen for 12 months; how much must each person pay of the rent?

Ans. E must pay 51 10s 6d 19.

16 10 0.8

12 12 7 2.6

15° 4. A ship's company take a prize of 10001 which they agree to divide among them according to their pay and the time they have been on board : now the officers and midshipmen have been on board 6 months, and the sailors 3 months ;

• The proof of this rule is as follows : When the times are equal the shares of the gain or loss are evidently as the stocks, as in Single Fe lowship; and when the stocks are equal, the shares as the times ; Therefore, when neither are equal the shares must be as their products,

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When interest is at 3 per cent, the rate is 3;

4 per cent.
5 per cent.

6 per cent. But, by law in England, interest.ought not to be taken highcr than at the rate of 5 per cent.

Interest is of two sorts; Simple and Compound.

Simple Interest is that which is allowed for the principal lent or forborn only, for the whole time of forbearance. As the interest of any sum, for any time, is directly proportional to the principal sum, and also to the time of continue ance ; hence arises the following general rule of calculation.

As 1001 is to the rate of interest, so is any given principal to its interest for one year. And again,

As 1 year is to any given time, so is the interest for a year, just found, to the interest of the given sum for that time.

OTHERWISE. Take the interest of 1 pound for a year, which multiply by the given principal, and this product again by the time of loan or forbearance, in years and parts, for the interest of the proposed sum for that time.

Note, When there are certain parts of years in the time, as quarters or months, or days : they may be worked for, either by taking the aliquot or like parts of the interest of a year, or by the Rule of Three, in the usual way. Also to divide by 100, is done by only pointing off two figures for decimals,

EXAMPLES.

1. To find the interest of 2302 108, for 1 year, at the rate of 4 per cent. per annum.

Here, As 100 : 4 :: 2302 108 : 91 48 4zd.

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Ex. 2. To find the interest of 5471 158, for 3 years, at 5 per cent. per annum.

As 100: 5 :: 547.75:
Or 20: 1 :: 547.75 : 27 3875 interest for 1 year.

3

1 82 1625 ditto for 3 years.

20

S 3 2500

12

.d 300 Ans. 321 33 3d.

or

3. To find the interest of 200 guincas, for 4 years 7 months and 25 days, al 4) per cent. per annum.

ds 1 ds
210L

As 365 :: 9 45 : 25 : 1
73::9:45 : 5 : 6472

5
840
105

73) 47 25 ( 6472

345
9.45 interest for 1 yr.

530
19

37.80

ditto 4 years. 6 mo = 4 725 ditto 6 months. I mo=7875 ditto 1 month.

-6472 ditto 25 days.

243.9597

20

8 19 1940

12

d 2.3280

Ans. 431 198 2 d.

9 13120

4. To find the interest of 4501, for a year at 5 per cent, per annum.

Ans 2211 08. 5. To find the interest of 7152 128 6d, for a year, at 4 per cent. per annum

Ans. 321 4.O d. 6. To find the interest of 720l, for3 years, at 5 per cent, per annum.

Ans. 1081.

Ex.

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