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Queft. 3. What Principal or Stock will gain 20 l. in 8 Months at 6 per cent. per Annum ? Prin. Time. Gain.

6 Terms in the Supposition.

8 In this Question the Blank falls under the first Place, therefore it muft be found by the second Rule.

100

I 2

20

Thus 100 x 12 x 20 = 24000 the Dividend.
And

8 x6 = 48 the Divisor.

Then 48) 24000 (500l. the Answer required. The Proof of all Questions in this Double Rule of five Numbers, is best performed by varying the Question ; viz. by stating it in another Order, as in the last Example: Thus,

If rool. gain 61. in 12 Months, what will 500 l. gain in 8 Months?

The Answer to this Question must be 201. if the Work of the last Example be true.

i

I 2

Prin. Time. Gain.
100

6

8
500 x 8 x 6 = 24000. And 100 x 12 = 1200.

Then 1200) 24000 (20 1. the Answer, &c.

6}then, per Rule 1,

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Queft. 4. If two Men can do 12 Rods of Ditching in 6 Days, How many Rods may

be done by 8 Men in 24 Days, at the fame Rate of working ?

Answ. 192 Rods. Queft. 5. If the Carriage of 5 C. 3 grs. Weight, 150 Miles, cost 37. 7s. 4 d. What must be paid for the Carriage of 7 C. 2 grs. 25 lb Weight, 64 Miles, at the same Rate?

Answ. il. 18 s. 7 į d. Queft. 6. If 8 Men deserve 2 1. Wages for 5 Days Work, How much will 32 Men deserve for 24 Days, at the same Rate?

Answ. 38 l. 8 s. Quest.7. Suppose a Hundred Pounds would defray the Expences of five Men for Twenty-two Weeks and fix Days, How long would twelve Men be in spending of one Hundred and Fifty Pounds, at the same Rate?

Answ. 14 Weeks and 2 Days.,

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CHAP

CHA P. VIII.

THE

Of Trading in Company, usually called the Rule of Fellowfhip ; also Bartering, and Erchanging of Coins, &c. 'HE Rule of Fellowship is that by which the Accompts of several

Partners trading in a Company, are so adjusted or made up, that every Partner may have his just Part of the Gain, or sustain his just Part of the Loss; according to the Proportion or Share of Money he hath in the Joint-Stock: Now this falls under two Considerations, called the Single and Double Rules of Fellow/bip. Sect. 1. The Single Rule of Fellowship ; viz. That

without Time.

BY Y the Single Rule of Fellowship is adjusted the Accompts of

those Partners that put all their several and perhaps different Sums of Money, into a common Stock at one and the fame Time; and therefore it is usually called the Rule of Fellowship without Time: Now all Questions of this Nature are answered by so many several Operations in the Rule of Three Direct, as there are Partners in the Stock.

For, as the Total Sum of Money in the Stock is in Proportion to the whole Gain, or Lofs: so is every Man's particular Part of that Stock; to his particular Share of that Gain, or Lofs.

Queft. 1. Three Partners, fuppose 4, B, and C, make a JointScock of 96 1. in this manner.

4, puts in 24h. B, puts in 32 l. and C, puts in 401. with this 96 1. they trade and gain 12l. It is required to find each Man's true Part of that Gain. The Operation will stand, thus

241. : 31. = A's
961.:12 1. :: 32 1. : 41.=B's Part of the Gain.

401. : Sl. =C's
Proof 36. + 41. +5l. = 12 1. the whole Gain.

That is, if the Sum of each Man's particular Gain, amount to the whole Gain, the work is true ; if not, fome Error is committed which must be found out,

Note, These Operations will be very much abbreviated, if you work them by Theorem 2. page 87. For here 96 is a common Antecedent, and 12 is the common Consequent in all the three Proportions

02

There

Therefore 96 : 12 :: : 0,125 a common Multiplicator.
Then 24

A,
32 x 0,125=341. for B, as before.
40

C,

31.

20,13

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51,

Now this Method is more readily performed than the other, especially when the Partners are many; because one Single Division serves for all the Work.

Queft. 2. Three Merchants, 1, B, and C, freight a Ship with 248 Tun of Wine : Thus, A, loaded 98 Tun, B, 86 Tun, and C, 64. Tun. By Extremity of Weather the Seamen were forced to cast or throw 93 Tun of it over-board. How much of this Lors must each Merchant sustain?

First 248 : 93: 1: 0,375 the common Multiplier,
Then 98

36,75 for AS a
86

x 0,375 = 32,25 for B’s Loss. 64

Proof 93,00 = the whole Lols.

24,00 for C's S

Now if the Question were to find how much of the remaining Wine that was faved, belongs to A, to B, and to C.

Then 98 - 36,75 = 61,257

86 - 32,25 = 53,75 belongs to
64 24,00 40,00

B.

That is, A, ought to have 61 Tun and 63 Gallons. B, ought to have 53 Tun and 189 Gallons. And C, ought to have 40 Tun of what was left.

Quest. 3 Suppose fix Men, viz. A, B, C, D, E, and F, make a Joint-Stock of 2558).

1.

S,

Decimals. Thus A

654 . 10 = 654,50 B

543 15 543,75
с

480 . 00=480,00
254 · 10 = 254,50
365 .05 = 365,25

260.00 = 260,00 The whole Stock 2558 00=2558,00 according to the Queft,

puts in

With this Stock of 2558 1. they trade eighteen Months, and gain 831 1. 7 s. It is required to find every Man's Part or Share of that Gain.

Note, Although the Time of Trading, viz. eighteen Months, be mentioned in the Question, yet it is no Way concerned in answering of it; as you may observe in the following Work.

First, 2558 1. : 831,351. :: il. : 0,325 Decimal Parts, Consequently, il. : 0,325 :: 654,5 : 212,7125. That is, 654,50

212,71250

A.
543,75
176,71875

B.
480,00

156,00000

C. x 0,325 =

for 254,50

82,71250

D.
365,25
118,70625

E.
260,00

84,50000

F. 1.

d. That is, A 212,7 1250 = 2 1 2

14 . 03 B

176,71875 = 176. 14. 041 C

156,00000 = 156.00, 00 D

82,71250 = 82 . 14 . 03 E

118,70625 = 118. 14.01
F

84,50000 = 84
Proof,
Sum 831,35

= 831 . 07 . 00 I have omitted resolving this Question according to the usual Method (as before directed) of finding every Man's particular Part of the Gain by the Golden Rule, as in the first Work of Example 1. leaving that for the Learner's Practice.

1. parts.

gains

10

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Sect. 2. The Double Rule of Fellowship; or that with

Time.

HIS is usually called the Double Rule of Fellowship, because every particular

Man's Money is to be considered with Relation to the Time of it's Continuance in the Joint-Stock.

Question 1. A, and B, join in Partnership upon these Terms, viz. A, agrees to lay down 100 l, and to employ it in Trade a Months : Then B, is to lay down his 100 l, and with the whole Stock of 2001. they are to trade 3 Months more. Now at the End of that Time, they find their whole Gain to be 21 l. It is required to know what each Man's Part of the Gain ought to be, according to his Stock, and the Time of employing it.

Here

Here it is but reasonable to conclude, that A, ought to gain more than B, not withstanding their Stocks of Money are equal; because A employed his Money a longer Time than B.

Now for folving of this Question, let us suppose A's 100 l. employed the first three Months to gain Z= a Sum as yet unknown; then it must gain 2 Z in 6 Months; and to find what B, mut gain, it will be

.

TB's Gain} per Rule 1. Page 97.

1. Months.
100 6 22= A's Gain?
100 3

100 x 3 x 2 Z
Ergo

=B's Gain.

100 x 6 But A's Gain added to B's Gain muft = 211. the whole Gain by the Question. Therefore 2 Z+

100 x 3 x 2 Z

100x6 That is, 100 x 6 x 2 Z + 100 x 3 x 2 Z = 21* 100 * 6. Which contracted is, 900 x 2 2 = 21 x 600.

21 x 600 Confequently, 2 2=

which gives the following

900 Analogy,

Viz. 900 : 21 :: 600 : 2 Z=141. for A's Gain.
And 900:21 :: 100x3 = 300:7 1. for B's Gain.

211.

Now this way of arguing hath not only resolved the present Question, but it also affords (and demonstrates) a general Rule for resolving all Questions of this Nature, be the Partners never

so many

Multiply every particular Man's Stock, with the Time it

is employed, then it will be, As the Sum of all those Rule. Products Is to the whole Gain (or Loss), So is every

one of those Products to it's proportional Part of that

whole Gain (or Loss). Question 2. Three Merchants A, B, and C, enter into Partnerfhip, thus ; A puts into the Stock 65 1. for 8 Months ; B puts in 787. for 12 Months; and C puts in 84 1. for 6 Months. With these they traffick, and gain 1661. 12 s. It is required to find each Man's Share of the Gain, proportionable to the Stock and Time of employing it,

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