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Qu. 16. For 9431. 145. 8d. paid in London, how many rubles must be received at Petersburgh, exchange by way of Holland at 345. 9d. Flemish per pound sterling, and exchange from Holland to Petersburgh at 50 ftivers per ruble?-Anf 7870 rubles 36 copecs.

In Poland and Pruffia

Accompts are kept in florins, gros, and penins. The exchange is by the way of Holland, and from 240 to 295 gros per pound Flemish.

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Qu. 17. In 4377. 175. 4d. sterling, how many rix-dollars Polish, exchange 290 gros per pound Flemish, and 34s. 4. Flemish per pound sterling ?-Anf. 2422 rix-dollars 4 gros 13 penins.

In Sweden

Accompts are kept in copper dollars, and oorts or filver dollars. The exchange is by the copper dollar, and moftly from 46 to 50 copper dollars per pound sterling.

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2. 18. In 5838 filver dollars 9 runftychens 3 penins,

how many pounds fterling, exchange at 49 copper dollars per pound sterling? Anf. 3571. Ss. Std.

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In Ireland, America, and the Weft Indies,

Accompts are kept in pounds, fhillings, and pence, as in England, but the course of exchange between England and Ireland is from 5 to 12 per cent. in favour of England, and the course of exchange of the paper of America and the West Indies is never at any certain standard.

Qu. 19. If 21727. be remitted to Ireland, how much money sterling may be drawn for it,, exchange at 8 per cent. ? -Ans. 2345l. 155. 24d.

Qu. 20. A merchant fells goods in London, and remits to his correspondent in Bofton, the value amounting to 11517. 195. how much must the merchant at Bolton receive in paper currency, exchange at 333 per cent. in favour of England-Anf. 1535. 18s. 8d.

Questions of the nature of these two are refolved by the rule of three: thus, in the 19th question, I fay, if 100l. require 1081. what will 21724. require? and the anfwer is 2345l. 155. 2‡d.

The arbitration of exchange is the method of finding the courfe of exchange between any two places, by having the courfe of exchange between each of these two places and a third place.

By comparing the par of exchange thus found with the courfe of exchange, a person can tell which way to draw or remit his money to the most advantage.

All questions in arbitration of exchange are refolved by the rule of three direct, comparing the course of exchange between any two places, with that of a third place to a fourth.

Example 2. If the exchange between London and Paris be 33d. per ecu, and the exchange between London and Amsterdam be 345. 6d. per pound sterling, what is the par of arbitration between Paris and Amfterdam?

As

As 240d. London is to 34s. 6d. Amsterdam, so is 33d. Paris to

12

414

33

1242

1242

24,0)1366,2(56d.

120

166

144

222

4

24,0)58,8(3.
72

168

Anfwer 564d. Flemish per ecu for Paris.

Here I fay, as 240d. the pence in a pound sterling of London, is to 345 64. the Flemish exchange, so is 33d. the exchange for an ecu, or crown, tournois of Paris, tó gáð. 3- farthings the Flemish exchange for an ecu, and is the courfe of exchange between Paris and Amfterdam.

This example will be fufficient, as the rule never varies, though the course of exchange between several countries be given to find a proportional course between any two; in which cafe they may be refolved into as many questions as is neceffary in the rule of three, and all the first numbers multiplied together for a divifor, and the fecond and third num bers in each question multiplied together for a dividend, then the quotient will be the answer.

Qu. 22. A merchant in London is drawn upon by his correfpondent in Ruffia for money to the amount of 12 500 rubles; the exchange between England and Ruffia being at 50d. per ruble; between Ruffia and Holland 90d. per ruble; and between England and Holland 36s. 4d. per pound sterling; which is the most advantageous method for the London merchant to pay by; directly to Ruffia or by way of Holland, and what is the advantage?—Answer, the London merchant will gain 231. 175. 10 d. by making payment by way of Holland.

SECT.

SECT. XX.

OF THE RELATION OF NUMBERS.

ANY fet of numbers that conftantly increase or decrease by a common difference are faid to bear a relation to each other, which relation is called progreffion, and is divided into two kinds: arithmetical progreffion and geometrical progreffion.

Arithmetical progreffion is, when any fet or series of numbers conftantly increase or decrease by a given number, called from thence their common difference ; fuch are the natural orders of numbers, 1, 2, 3, 4, 5, 6, 7, 8, &c, each of which increases by ; and the fame in inverted order 8, 7, 6, 5, 4, &c. decrease by 1; 1 is therefore their common difference.

Again, the numbers 2, 5, 8, 11, 14, 17, &c. increase by 3; and 27, 23, 19, 15, 11, 7, &c. decrease by 4: therefore 3 is the common difference of the former, and 4 that of the latter.

i

.. The numbers themselves that form the series are called the terms of the progreffion.

Of every series of arithmetical progreffion having any three of the five following terms the other two may be found readily;

1, the first term or number
2, the last term or number

3, the number of terms.
4, the common difference.
5, the fum of all the terms..

3

called the extremes.

PROBLEM

PROBLEM Ì.

The first and laft terms, and number of terms, being given, to find the sum of all the terms, and the common difference. Rule. To find the fum of all the terms, multiply the fum of the extremes by the number of terms, and half the product will be the answer; and to find the common difference of the terms, divide the difference of the extremes by the number of terms, made lefs by 1, and the quotient will be the answer. Example 1. What is the fum of the feries, and the com mon difference of that progreffion, whose first term is 3, laft term 67, and number of terms 33 ?

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In the first operation, 70, the fum of the extremes, is multiplied by 33 the number of terms, and half the product 1155 is the fum of the feries, or fum of all the numbers, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65,. 67, added together.

In the fecond operation the difference of the two extremes 67 and 3, or 64, is divided by 32, which is one less than the number of terms, and the quotient 2 is the common differ

ence.

PROBLEM II.

Having the two extremes and the common difference, to find the number of terms.

Rule. Divide the difference of the extremes by the com->

VOL, I.

I i

mon

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