dollars, at 58d sterling per rix dollar, value received,

and place it to the account of

To Mr. Abraham Schulhausen,

Merchant, Geneva.

Your humble, servant,

Jocobus Schomberg.

What is the value of this bill in rix dollars? Answer 1558 Rix Dollars.

CASE 10.

Q. What particular piece of money does London exchange with Denmark for?

A. For Rix-Dollars; one being valued at about 4s 6d Sterling.

Q. How do they keep their accounts in Denmark ?
A. In Marks and Shillings

Note 1.

16 Shillings make 1 Mark.

2. The Rix-dollar in exchange, goes 45d to 58d sterl.

EXAMPLES.

1. London draws on Copenhagen in Denmark, for 1847 16s 7d sterling; what sum must be answered for that in rix dollars, at 50d each? Answer 887 dollars.

2. My correspondent in London, stands indebted to me, according to my books, in the sum of 1000 Rix-Dollars, what sum must he answer for that at London aforesaid, when the Rix Dollar, by way of exchange, is valued at 58d? Answer 243/ 15s.

3. A merchant in London draws upon his correspondent in Copenhagen, for 400l. sterling, but will give no more for a rix dollar than 55d sterling, that being the price of exchange; how many rix dollars must be receive, and what is his whole loss and the loss per cent. they being above par? Answer 17453 Rix-Dollars-the whole loss was 71 5s 3d and the loss per cent was 1 16s Su.

d. Dol. 1. Dol.

55: 1 :: 400: 174525

25

55

1745 at 4s 6d=392/ 14s 9d. at par.

40

-3927. 14s. 9d.=7l. 5s. 3d. loss.

7531. 16s. 3d. loss per cent.

4

CASE 11.

Q. What places does London exchange with for the Copper Dilar ?

A With Stockholm in Sweden.

Q. How do they keep their accounts in Stockholm? A. In Rix-Dollars, Copper Dollars, and Bunstics.

1. Bills Payable, i. e. such as you

have accepted.

Ducat Sterl.

The Schoolmaster's Assistant.

for.

of abode.

jance.

Note.

32 Runstics make 1 Copper Dollar.

6 Copper Dollars 1 Rix Dollar.

2. The Par of the Rix-Dollar is equal to about 6s. sterling, conse quently the par of the copper-dollar is equal to 1s sterling, or 20 copperdollars make 11. sterling, though the course of exchange is sometimes to 28 or 20 copper dollars per pound sterling.

3. In England sums of money are paid in the best specie, viz. Guineas, by which means 10007. or more may be put into a small bag and conveyed away in the pocket-but in Sweden they often pay sums of money in copper, and the Merchant is obliged to send wheel barrows instead of bags, to receive it.

EXAMPLES.

1. A merchant in Stockholm draws upon his correspondent in London for 1184 Rix-Dollars; what sum must he answer for that in London aforesaid, when the course of exchange is at par? Ans. 355l 4s.

2. Stockholm draws upon London for 1276 Rix dollars; what sum must London answer for that, exchange at 25 copper dollars per sterling, and what is gained or lost. by the drawer at Stockholm aforesaid? Aus. 306l. 4s 9d 2qrs the bill; and the drawer loses 767 11s 2d qr 3. 25: 1: 1276×6: 306 4 9 2 the value of the bill. 25 5 7656 : : 76 11 2 13 loss.

CASE 12.

Of the Comparison of Weights and Measures.

EXAMPLES.

1. If 112lb. at London make 991b. at Lisbon, how many Id. at London are equal to 1049 lb. at Lisbon? Ans. 1186lb. 1333/31/180

74

2. If 112lb. at London make 98lb. at Roan, how many Ib. at Roan are equal to 1000lb. at London? Ans. 875lb. 3. In 10 ells English make 108 braces at Venice, how many ells English are equal to 1000 braces at Venice? Ans. 925 ells, 4qrs. 2na. 108

56

4. If 100 ells at London make 145 ells at Vienna, how many ells at Vienna are equal to 10 ells at London? Ans. 14 ells.

Nore. Hence appears the reason of those rules, laid down in conjoined proportion for placing the last number in the Q either on the right hand, or the left, as the nature of the question requires.

lb.Lis.lb.Lon. lb. Lis.

Ex. 1. 99: 112 :: 1049

lb. Lon. b. R. ib. Lon. Ex. 2. 112. : 98: 1000

OF THE DOUBLE RULE OF THREE.

Q. By what is the Double Rule of Three known ? A. By five Terms which are always given in the question to find a sixth.

Q. In what proportion is the sixth term to be found?

A. If the proportion is direct, the sixth term must bear such proportion to the fourth and fifth, as the third bears to the first and second; but if the proportion is inverse, then the sixth term must bear such proportion to the fourth and fifth, as the first bears to the second and third, or as the second bears to the first and third.

Note. It is to be observed here, as in the Single Rule of Three, that Direct Proportion is, when more requires more, or less requires less, and Inverse Proportion is, when more requires less, or less requires

more.

Q. What do you observe concerning the five given terms? A. That the three first terms are a supposition; the two last are a demand.

Q. How must the numbers given in the questions he stated? A. By two Single Rules of Three; or otherwise thus, 1. Let the principal cause of loss or gain, interest or decrease, action or passion, be put in the first place.

2. Let that which betokeneth time, distance and place, and the like, be put in the second place; and the remaining one in the third place.

3. Place the other two terms under their like in the supposition.

4. If the blank falls under the third term, multiply the first and second term for a divisor, and the other three for a dividend.

5. If the blank falls under the first or second term, multiply the third and fourth terms, for a divisor, and the other three for a dividend, and the quotient will be the answer. Q. How are the following questions proved?

A. Let them be varied, or else work the same questions by two single rules of Three.

EXAMPLES.

1. If 7 men can reap 84 acres of wheat in 12 days, how many men can reap 100 acres in 5 days? Ans. 20 men. 2. If 7qrs of malt is sufficient for a family of 7 persons for 4 mouths; how many qrs are enough for 46 persons 10 months? Ans. 115 qrs.

3. If 8 reapers have 31 4s for 4 days work; how much will 48 men have for 16 days work? Ans. 76/ 16s.

4. If 10 bushels of oats be enough for 18 horses 20 days, how many bushels will serve 60 horses thirty-six days? Answer 60 bushels.

f

5. If a footman travels 240 miles in 12 days, when the days are 12 hours long; how many days may he travel 720 miles in, of 16 hours long. Ans. 27 days.

6. If 56 lb. of bread will be sufficient for 7 men 14 days; how much bread will serve 21 men 3 days? Ans. 36 lb. 7. If 700 in half a year raise 14/ interest; how much will 400 raise in 5 years? Answ. 801.

8. If 30s be the hire of 8 men for 3 days; how many days must 20 men work for 151? Answ. 12 days..

9. If 4 reapers have 24s for 3 days' work; how many men will earn 47 16s in 16 days? Answer 3 men.

10. An usurer put out 86 to receive interest for the same; and when it bad continued 8 months, he received for principal and interest 887 17s 4d; I demand at what rate per cent per annum he received interest? Answer, 51 per cent.

4

11. What is the interest of 2001 for 3 years, and 2, at 5 per cent per annum? Answer, 37/ 10s.

12. What is the interest of 400 for a week, at 5 per cent per annum? Answer, 7s 8d 1qr. 3.

2

13. What is the interest of 120 for 126 days, at 4 per cent per annum ? Answer, 17 13s 1d 2 qrs 358.

Note. The rule for working questions in Simple Interest for Days, p. 67, is taken from this rule, as appears from this last example.

OF CONJOINED PROPORTION.

Q. What is Conjoined Proportion?

A. Conjoined Proportion is when the coins, weights. or measures of several countries are compared in the same question; or it is a linking together of many proportions.

CASE 1.

Q. How are questions answered in this case?

A. When it is required to know how many of the first sort of coin, weight or measures, mentioned in the questions, are equal to a given number of the last: then 1. Place the numbers alternately, beginuing at the left hand, and let the last number stand on the left hand.

2. Multiply the first rank continually for a dividend, and the second for a divisor.

Note. See the Note in Comparison of Weights and Measures, p. 91, for the reason of this rule.