PROOF.

As in Single Fellowship.

EXAMPLES.

(1) Three Merchants, A B and C enter into Partnership, thus: A puts into the Stock 240/ for 4 Months, B 120/ for 6 Months, and C 200/ for 8 Months; with this joint Stock they traffic, and gain 2607. It is required to find each Person's Share of the Gain, proportionable to his Stock and Time of employing it? (2) A Ship's Company take a Prize, Value 4000l. which they agree to divide amongst them, according to their Pay and Time they have been on board; now the Officers and Midshipmen have been on board 4 Months, and the Sailors 3; the Officers have 50s a Month; the Midshipmen 40s, and the Sailors 28s. Moreover, there are 4 Officers, 8 Midshipmen, and 120 Sailors. I demand to know what each Person's Share is of the said Prize?

(3) A B and C rent a Piece of Land, for which they pay 407 per Annum ; A puts in 60 Oxen for 4 Months, B 40 Öxen for 5 Months, and C 30 Oxen for the Remainder of the Year; what must each Person pay of the said Rent?

(4) Three Merchants, A B and C, in Partnership together for a Year, put into one common Stock as follows, viz. A puts in 400, and at 6 Months' End withdraws 2001. B puts in 3601, and at 7 Montlis' End 100/ more; but at the End of 9 Months he takes out 120/. C puts in 190/, and at 8 Months' End 110/ more; but at the End of 10 Months he takes out 100%. They gain 460%. What is each Man's Share?

QUESTIONS for Exercise at Leisure Hours.

(5) A and B in Partnership equally divide the Gain: A's Money, which was 847 12s 6d, lay for 19 Months, and B's for no more than 7: the Adventure of the latter is sought?

(6) A for 9 Months' Adventure received 201. B for one of 7 Months received 25 Guineas, and C for lying out

of his Contributions 5 Months had a Title to 321. The Total of their Adventures, multiplied into their respective Times, was 640. What then were the Particulars?

(7) A clears 131 in 6 Months, B 181 in 5 Months, and C 231 in 9 Months, with a Stock of 72/ 10s. What then did the general Stock amount to?

(8) X Y and Z in Company, make one common Stock of 42621. X's Money was in 4 Months, Y's 6 Months, and Z's 9 Months; they gained 4201, which was to be divided in the following Manner, viz. of X's Gain to be equal to of Y's, and of Y's Gain to be equal to 4 of Z's. Quere, what each Person gained and put in ?

(9) A B and C in Company: A put in his Share of the Stock for 5 Months, and laid Claim to of the Profits ; B put in his for 8 Months; C advanced 4001 for 7 Months, and required on the Balance of the Gain: the Stock of the other two Adventurers is sought? (10) A and B paid equally for a Horse, Feb. 7, 1793; A on the 10th took him a Journey to the West, and returned on the 10th of June following: B on the 2d of August took him into Scotland, and staid till Nov. 13, and thus concluded his Service for this Year. From Jan. 17th following, A used him ten Days; and, in six Weeks after his Return, employed him till April 30th. B then rode him from May-day to Midsummer: A had him from the 14th of July to 14 Days after St. James's Tide; B, on Sept. 30th, took him into Norfolk, and came back Oct. 19th: he then was sold for 77 10, and they would have the Money parted equally between them, viz. in Proportion to the Use each made of their Steed.

XXIV. BARTER

IS the changing of one Commodity for another, and informs us how to proportion the Value of any Goods, so that neither Party may sustain Loss. And if the Commodities exchanged are not of equal Value, the Defect is supplied with Money.

RULE.

1. Find the Value of that Commodity, whose Quantity is given: then find what Quantity of the other, at the given Rate, you can have for the aforesaid Value; which Quantity will be the Answer

2. When one has Goods at a certain Price ready Money, but in Barterage advances it to something more, say, As the ready money Price of the one is to its Bartering Price :: so is the ready Money Price of the other to its Bartering Price: then the Quantity of the latter Commodity may be found, either from the ready Money or Bartering Price.

EXAMPLES.

(1) How much Sugar at 1/ 10s per cwt. must be given in Barter for 4 cwt. of Tea, at 12s per Pound?

(2) How n

many Yards of Cloth, at 18 per Yard, must I give for 45 Yards of Shalloon, at 16s per Yard? (3) A and B barter: A hath 30 cwt. of Prunes, at 6d per lb. ready Money, but in Barter will have 7 d per lb. B hath Hops worth 36s per cwt. ready Money. What ought B to rate his Hops in Barter, and what Quantity must be given for the 30 cwt. of Prunes?

(4) A hath Tea at 8s 6d per lb. ready Money, but in Barter will have 10s per lb. B hath Tobacco worth 18d per lb. ready Money. How must B rate his Tobacco per lb. that his Profit may be equivalent with A's?

QUESTIONS for Exercise at Leisure Hours.

(5) A has Currants worth 4d per lb. but in Truck charges 6d, and also requires one Half of that in ready Money; B. has Candles worth 6s 8d the Dozen, and he in Barter, honest Man, charges but 7s. Should these Persons deal together for the Value of 201, how much will A have got of B. ?

(6) A lets B have a Hogshead of Sugar, Weight 18 cwt. worth 31s for 425 per cwt. one-third of which he is to pay in Cash; B hath Paper worth 14s the Ream, which it is agreed shall bear no more than 15s 6d. At that Rate, and Truck for the rest, how stood the Account?

(7) A has Kerseys at 4/ 5s a Piece, ready Money; in Barter they are charged by him at 5/ 6s each, and of that required down: B has Flax at 3d per lb. How ought he to rate it in Truck, not to be hurt by the Extortion of A?

(8) A has 50 Broad Cloths, at 117 10s a Piece, but in Change required 137, taking Wool at 2s 6d per Stone, of B in return, that was really worth but 4s 2d a Tod. The Question is, how many Sacks of Wool will pay, for the Cloth, and which of the Dealers has the better in the Bargain?

(9) A with an Intention to clear 30 Guineas on a Bargain with B, rates Hops at 16d per lb. that stood him in 10d. B apprised of that, set down Malt which cost 20s a Quarter at an adequate Price. How much Malt did they contract for?

(10) A in order to put off to B 720 Eils of damaged Holland, worth 5s an Ell, at 6s 8d, proposes, in case he has half the Value in Money, to give B thereon a Discount of 10 per Cent. The rest A is to take out in Saffron, which B apprised of the whole Management, rates in Justice at 30s the Pound. Pray what was it really worth in ready Money, and what Quantity of Saffron was he to deliver on the Change? (11) A has 100 Reams of Paper, at 8s ready Money, which in Barter he sets down at 10s. B sensible of this, has Pamphlets at 6d a Piece ready Money, which he adequately charges, and insists, besides, on of the Price of those he parts with in Specie: what Number of the Books is he to deliver in lieu of A's Paper? What Cash will make good the Difference? and how much is B the Gainer by this Affair?

(12) A and B barter; A has 140 lb. 11 oz. of Plate, at 6s 4d the Ounce, which in Truck he rates at 7s 2d an Ounce, and allows a Discount on his Part, to have

1

T

of that in ready Specie, B has Tea worth 9s 6d the lb. which he rates at 11s 2d. When they come to strike the Balance, A received but 7 cwt. 2 qrs. 18 lb. of Tea. Pray what Discount did A allow B, which of them had the Advantage, and how much, in an Article of Trade thus circumstanced?

(13) A and B truck; A has 14 cwt. 2 qrs. 25 lb. of Farnham Hops, at 2/ 19s per cwt but in Barter insists on 3 Guineas; B has Wine worth 6s per Gallon, which

he raises in Proportion to A's Demand: on the Ba lance, A received but a Hogshead and a Half of Wine. Pray what had he in ready Money?

XXV. LOSS and GAIN

IS a Rule by which we discover the Gain or Loss by any Parcel of Goods, and so instructs us how to raise or fall the Price of any Commodity in such Proportions, that neither our Gain may be so exorbitant as to injure our Customers, nor our Loss so great as to impoverish ourselves; which is generally at so much per Cent.

In this Rule there are a great Variety of Examples, all of which may be easily solved (with a little Consideration) by the following Proportion :

Case 1. When the Quantity lost and gained of the Whole is given to find the Value of any Part thereof.

RULE.

:

Say, As the whole Quantity of Goods is to the Sum of the whole Cost and proposed Gain :: so is any Part of said Goods to the Price they must be sold for.

Case 2. When the proposed Gain or Loss is at so much per Cent. make 100/ with the Gain or Loss added to it, your second Term.

EXAMPLES.

(1) Bought 240 Yards of Cloth, at

sold it again at 18s per Yard.

the Whole?

14s 6d per Yard, and What did I gain by

(2) Suppose I give 46/ for 9 cwt. 2 qrs. 18 lb. of Sugar, at what Rate must I sell it per lb. to gain 12 Guineas by the Whole?

(3) If I buy Tea at 8s 6d per lb. and sell it again for 10s 6d. what is the Gain per Cent?

The five following Examples, in the Authors mentioned, are wrong answered, which is the Reason of my inserting them here:-the Error consists i. stating the Question, by making the Gain or Loss of 1007 the second Term, instead of its Amount.