* Sight, because of the Uncertainty of their Arrival. Ufance from London to Lisbon, or Madrid, is two Months; to Leghorn, Venice, or any Part of the Levant, is three Months, and contra.

After Bills of Exchange become due, whether inland or foreign, payable at Sight or otherwise, there are, by Custom of Merchants, certain Days "of Grace allowed the Accepter over and above the "Time prefcribed by the Bill, which are more or

lefs, according to the Ufage of the Country where"in they are to be paid; as, in Rotterdam, they al"low three Days; Rouen, five; Paris, ten; Hamburgh, twelve; Antwerp and Madrid, fourteen;

and London always three: And, on the third Day, "before Sun-fet, Payment must be demanded on "the Part of the Prefenter; and, if not complied "with, the Bill muft that very Day (being the ut"most Time allowed by the Law for that Purpose) "be noted, in Order to be protefted for Non-pay.

"ment.

If a Bill fall due on a Sunday, or other great "Holiday, it is to be demanded and paid, or pro"tefted, the Day before."

353 Question 2. Suppofe a Bill of Exchange for 600l. dated at Antwerp the 19th of September 1752, at double Ufance, is accepted at London, and Payment offered the Second of November, 1752: What Money must be then received, Rebate being made at the Rate of 61. per Cent. per Annum?

Solution. In September there remain 11 Days, October 31, November 19, Days of Grace 3, the Sum of those Numbers is 64 Days the Time the Bill is due; but Payment is offered in 11+31 + 2 = 44 Days, 64 4420 Days the Time the Bill is paid before due, for which Time the Discount is to be computed; and therefore the firft Stating is, If 365 Days: 5760 Farthings (61): 20 Days 315 Farthings nearly, and the fecond, as 96315 Farthings(Tool.+315 Farthings: 96000 Farthings (100) 5760co Farthings(600 : 5891.

: 5891. os. 9d. nearly, the present Worth, or Money to be received. 2. E. I.

354. We have here only treated of fimple Interest, because, as has been already hinted, the Law does not allow of compound Intereft herein. We have only one Thing farther to hint before we put an End to this Chapter, and that is, that, in paying a Bill before it falls due, the Payer ought to be well fatisfied (in his Mind) that the Receiver is not likely to fail fhortly, becaufe, if the Receiver "fhould fail before "it falls due, he will be liable to pay it to the Re"mitter's Order a fecond Time."

355.

ES

QUATION of Payments is a Rule by which when feveral Debts are payable at different Times (and are not fuppofed to bear Intereft till after the Time when they become due) we may be able to determine fuch a Time for Payment of all the Debts, that neither the Debtor nor Creditor may be wronged thereby; and the finding fuch a Time is called equating the Times of Payment, or reducing them to one.

356. The common Method of working this Rule, is, to multiply the feveral Sums by their refpective. Times, and to divide the Sum of all thefe Products by the whole Debt, and the Quotient, thence arifing, is called the equated Time, for Payment of the whole Debt.

357. Example. Suppofe A owes B 2051. to be paid in 2 Years, and 2007. to be paid in 1 Year, what is the proper Time for paying the whole Debt (to prevent the Trouble of two Meetings) at the Rate of 51. per Cent. per Annum, fimple Intereft?

Solution. In working this by the above common Method, we have nothing to do with the Rate of In

terest,

1

tereft, but work thus, 205 × 24 (the Months in 2 Years) 4920, and 200 x 12 (the Months in 1 Year) =2400; then 4920 + 2400 7320, and 205 +

30 200405. Laftly, 7320405 = 18 Months 405

=1 Year 6 Months and 30 of a Month, for the An

fwer.

405

358. Scholium. Though the above Method is that which is commonly used, and taught, in moft arithmetical Books and Schools, it is not true; however, we shall not here tire the Reader's Patience, by ftaying to demonstrate the Fallacy of this, and fome other Methods, given by arithmetical Writers, for folving this Rule; for, when we give the true Solution, the Demonftrating of that to be true will be a fufficient Demonstration, that the above, and all other Methods which do not agree with that, are falfe. Farther, amongst all the Treatifes of Arithmetic which have come to our Hand, (and thefe not a few) we, do not remember to have met with any true Solution, save one, by the laborious and learned Mr. Malcolm ; but as neither this Gentleman's, nor our own Solution, could be understood by the Learner in this Place, and as an accurate Solution is but of little Moment in Bufinefs, we shall defer giving a true Solution, till we treat of Decimal Arithmetic.

359,

CHAP. XXV.

BARTER, the first SORT.

BAR

ARTER is the Rule by which Merchants proportion the Prices, or Quantities of their Goods, in fuch a Manner, that in exchanging them heither may fuftain a Lofs by fuch Traffic.

360. Barter is divided into two Parts, called by Authors the first and fecond Sort. Sort the first is

when

when the Rate and Quantity of any Kind of Goods, and the Rate of any other Kind of Goods, is given to find the Quantity of thefe Goods that must be exchanged. Note, Both thefe Rules are folved by the Rule of direct Proportion.

361. Example 1. Two Men William and Thomas barter; William hath 45 Yards of Cloth at 4s. 6d. per Yard; and Thomas has Sugar at 7 d. per tb; how much Sugar ought Themas to give William in Exchange for his Cloth?

Solution. Firft by the Rule of Three direct or Practice, find what is the Value of 45 Yards (of Cloth) at 4s. 6d. per Yard, which is 2430d; then, we are to find what Quantity of Sugar is equal in Value to 2430d, and we fay by the Golden Rule, If 7d: 1 ib:: 2430d.: 3+7fb by Reduction 3C. oqr. 11th and of a tb, for the Answer.

362. Quelion 2. John and James barter thus: John fells James ico Dozen of Rabbit Skins, at is. per Dozen; and is to have in Return, of fames, Hats of two Sorts, viz. of 5 Shillings and 9s. each, and of each Sort an equal Number. It is required to find the Number of each Sort ?

I

Solution. Firft fay, if 1 Dozen: 15.:: 100 Dozen 100s. the Value of the Rabbit Skins. Now, 55.95. 145. the Value of 2 Hats, viż. 1 of each Sort. Whence, we have this Stating, if 145.: 1 Hat of each Sort:: 100s.: 7 or 7 the Number of Hats of each Sort; but, fince there is no fuch Thing as felling a Part of a Hat, John ought to have of fames 7 Hats of 5 Shillings each, and 7 Hats of 9s. each, and G of 55. and of 9s, or of 7 5+gor of 145.=) 2 Shillings in Money.-But if the Number of each Kind was not to have been equal, but in a given Proportion to each other, then we work as in the following Question.

9

363. Question 3. Suppofe two Men A and B barter; A has 210 Yards of Cloth at 4 Shillings per Yard, which he exchanges with B for Spoons at 5s. and Tea Spoons at 25. each; and being willing, that the Num

ber

1

ber of large Spoons fhall be, to the Number of TeaSpoons, as 2 to 5, that is, for every 2 large Spoons he is willing to have 5 Tea-Spoons: It is required to find how many Spoons of each Sort A must have for his Cloth?

Solution. First 21o Yards, at 45. per Yard, are equal in Value to 210 x 4840 Shillings; and 2 Spoons at 55.2 x 510 Shillings; and 5 Spoons, at 2 s. each, 5 x 2 = 10 Shillings, whence ios. x 10s. 20s. the Value of 7 Spoons, viz. 2 Spoons of the large Sort, and 5 Tea-Spoons; whence, as often as the Value of the 7 Spoons, viz. 20s, is contained in 840 Shillings, fo many 2 Spoons of the larger, and alfo 5 Spoons of the finaller Sort, must be taken; * 840

20=42= the Times that 7 Spoons, viz. 5 of the leffer, and 2 of the greater, is contained in the whole Number of Spoons; 42 x 2 = 84 Spoons of the large Sort, and 42 x 5 210 Spoons of the leffer Sort, and, for Proof, 84 Spoons at 5s. each 4205. and 210 Spoons at 2s. each 210 x 2 = 420s, and and 420s. +420s. 840s. the Value of the Spoons the Price of the Cloth as above.

The Operation for the Number of Spoons, pèrhaps, if found by the following Method, may appears fomething clearer to the Learner. By the above, 840 Shillings are the Value of the Cloth, and 20s. the Value of 7 Spoons;, by the Golden Rule, if 20s. 7 Spoons: 840s.: 294 Spoons. But these Spoons are to be divided into two Numbers, in the Proportion of 2 to 5; whence, by Fellowship, as 2+5=7:2942: 84 the Spoons of the larger Kind; and as 7: 294: 5: 210 the Number of Spoons of the leffer Sort. And 84 + 210 Spoons as above, for Proof.

294

Corollary. Hence follows the Reafon of the first Method of Solution. For here in one Stating we are to multiply by 7, and divide by 20; and, in the other two Statings, we are to multiply the Number that comes out by the above Stating by 2 and 5 refpectively, and divide by 7; whence, as we are both to N

mul