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Then if the Blank or Term fought, fall under the third Place, s in this Question,

It will be { Ge=g. Which gives this Rule.

r Multiply the three laft Terms together for a Dividend; Rule 1. } and the two first together for à Divisor; the Quotient

Carising from them will be the fixth Term.

That is, in our proposed Example 1.
Thus 6 x 300 x9=16200 the Dividend.

And 100 x 12 = 1200 the Divisor.
Then 1200) 16200 (13 i the Answer, as before.

But if the Blank or Term sought fall under the fift Place, then

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Or if the Blank fall under the second Place;

It will b -=t. Either of these gives this Rule.

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Queft. 3. What Principal or Stock will gain 20 l. in 8 Months át 6 per Cent. per Annum?

Prin. Time. Gain.
100 · 12 · 6 Terms in the Suppofition.

. 8 . 20 In this Queftion the Blank falls under the first Place, therefore it must be found by the second Rule.

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CHA P. VIII. Of Trading in Company, usually called the Rule of Fellow

fhip; alfo Bartering, and Erchanging of Coins, &c. THE 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 juft Part of the Loss; according to the Proportion or Share of Money he hath in the Joint-Stock: Now this falls under two Condiderations, called the Single and Double Rules of Fellowship. Sect. 1. The Single Rule of Fellowship; viz. That

without Time. B Y the Single Rule of Fellowship is adjusted the Accompts of D those Partners that put all their several and perhaps different Sums of Money, into a common Stock at one and the same 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 Loss: fo is every Man's particular Part of that Stock; to his particular Share of that Gain, or Loss.

Queft. 1. Three Partners, suppose A, B, and C, make a JointStock of 961. in this manner.

A, puts in 24 1. B, puts in 32 l. and C, puts in 401. with this 961. 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 2 961. :121. :: 3321.:41. = B's Part of the Gain.

(401 : 5l. =C's) Proof 31. + 41. +5.1.=121, 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 thọ common Consequent in all the three Proportions. . 02

There

Then 242

Therefore 96 : 12 :: 1 : 0,125 a common Multiplicator.

(3 l.)
32x0,125 341. for 3B, as before.
40),

51.

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

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That is, A, ought to have 6. Tun and 63 Gallons. B, ought to have 53 Tun and 189 Gallons. And C, ought to have 40 Tun of what was left.

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puts in

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00

254 · 10 = 254,50

365 . 05 = 365,25

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

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82,71250

for

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With this Stock of 25581. they trade eighteen Months, and gain 831 1. 7s. It is required to find every Man's Part or Share of that Gain.

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

Firft, 25581. : 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 .
480,00

J156,00000 for J C.
254,50
365,25

118,70625
260,00

( 84, 50000 J CE

I. parts. l. s. d. That is, as 212,71250 = 212 . 14. 03

176,71875 = 176 . 14 . 041 J 156,00000=156 . 00.00

82,71250 = 82 . 14 03 118,70625 = 18. 14 . ork

( 84,50000 = 84 . 10, 00 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 i, leaving that for the Learner's Practice.

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

Time,

THIS 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 3 Months : Then B, is to lay down his rool, and with the whole Stock of 200 l. 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.

Herc

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