Then if the Blank or Term fought, fall under the third Place, as in this Queftion,

It will be

{

Got

=8. Which gives this Rule.

TP

Rule I.

Multiply the three laft Terms together for a Dividends and the two first together for a Divifor; the Quotient arifing from them will be the fixth Term.

That is, in our propofed Example 1.

Thus 6 x 300 x 916200 the Dividend.
And 100 x 12 1200 the Divifor.

Then 1200) 16200 (13 the Anfwer, as before.

But if the Blank or Term fought fall under the firft Place,

Or if the Blank fall under the fecond Place,

Rule 2.

It will be

{{

T&P

t. Either of thefe gives this Rule.

Gp

Multiply the firft, fecond, and laft Terms together for a Dividend, and the other two together for a Divifor; the Quotient arifing from them will be the fixth Term.

And because our Example 2. falls under the Confideration both of Direct and Reciprocal Proportion, let it be here propofed again. Viz. If 6 Bufhels of Oats will ferve 4 Horfes 8 Days; how many Days will 21 Bufhels ferve 16 Horfes, &c.

If the Terms of this Queftion be placed down as before directed they will ftand

Here the Blank falls under the fecond Place, therefore it muft be found by the fecond Rule.

Thus 4 x 8 x 21672 the Dividend.

And

16 x 696 the Divifor.

Then 96) 672 (7 the Anfwer, as before.

Queft's

Quest. 3. What Principal or Stock will gain zo 7. in 8 Months at 6 per Cent. per Annum?

Prin. Time. Gain.

In this Question the Blank falls under the firft Place, therefore it must be found by the fecond Rule.

24000 the Dividend. 8 x 648 the Divifor.

Thus 100 x 12 x 20
And

Then 48) 24000 (500l. the Answer required.

The Proof of all Queftions in this Double Rule of five Numbers, is beft performed by varying the Question; viz. by stating it in another Order, as in the laft Example: Thus,

If 100l. gain 61. in 12 Months, what will 500l. gain in 8 Months?

The Anfwer to this Queftion must be 207. if the Work of the laft Example be true.

Prin.

100

Stated thus 500

500 x 8 X

6

Time. Gain.

12

8

24000.

6

} then, per Rule 1,

And 100 x 12 1200.

Then 1200) 24000 (201. the Answer, &c.

Quest. 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?

Anfw. 192 Rods.

Queft. 5. If the Carriage of 5 C. 3 qrs. Weight, 150 Miles, coft 3 1. 7 s. 4 d. What must be paid for the Carriage of 7 C. 2 qrs. 25 lb Weight, 64 Miles, at the fame Rate?

Anfw. II. 18 s. 7 d.

Quest. 6. If 8 Men deferve 2 1. Wages for 5 Days Work, How much will 32 Men deserve for 24 Days, at the fame Rate? Anfw. 381. 8 s.

Queft. 7. Suppofe a Hundred Pounds would defray the Expences of five Men for Twenty-two Weeks and fix Days, How long would twelve Men be in fpending of one Hundred and Fifty Pounds, at the fame Rate?

I

Anf. 14 Weeks and 2 Days.

CHAP.

CHAP. VIII.

Of Trading in Company, ufually called the Rule of Fellowhip; alfo Bartering, and Exchanging of Coins, &c.

THE Rule of Fellowship is that by which the Accompts of feveral Partners trading in a Company, are fo adjusted or made up, that every Partner may have his juft Part of the Gain, or fuftain his juft Part of the Lofs; according to the Proportion or Share of Money he hath in the Joint-Stock: Now this falls under two Confiderations, called the Single and Double Rules of Fellowship.

Sect. 1. The Single Rule of Fellowship; viz. That without Time.

BY the Single Rule of Fellowship is adjusted the Accompts of thofe Partners that put all their feveral and perhaps different Sums of Money, into a common Stock at one and the fame Time; and therefore it is ufually called the Rule of Fellowship without Time: Now all Queftions of this Nature are answered by fo many feveral 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: fo is every Man's particular Part of that Stock; to his particular Share of that Gain, or Lofs.

Queft. 1. Three Partners, fuppofe A, B, and C, make a JointStock of 96. in this manner.

A, puts in 241. B, puts in 327. and C, puts in 40%, with this 967. they trade and gain 12. It is required to find each Man's true Part of that Gain.

Proof 3.4.5.1.127. 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, Thefe 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 Confequent in all the three Proportions.

02

There

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

A,

Now this Method is more readily performed than the other, efpecially when the Partners are many; because one Single Divifion ferves for all the Work.

Quest. 2. Three Merchants, A, 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 caft or throw 93 Tun of it over-board. How much of this Lofs muft each Merchant fuftain?

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

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 Suppofe fix Men, viz. A, B, C, D, E, and F, make a Joint-Stock of 25581.

Co=2558,00 according to the Quest.

With this Stock of 25581, they trade eighteen Months, and gain 831 1.7 5. 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 obferve in the following Work.

Firft, 25581. 831,35l. :: 1 l.: 0,325 Decimal Parts. Confequently, 1l.: 0,325 :: 654,5 212,7125. That is,

I have omitted refolving this Queftion according to the ufual Method (as before directed) of finding every Man's particular Part of the Gain by the Golden Rule, as in the firft Work of Example 1. leaving that for the Learner's Practice.

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

THIS is ufually called the Double Rule of Fellowship, because every particular Man's Money is to be confidered with Relation to the Time of it's Continuance in the Joint-Stock.

Question 1. A, and B, join in Partnership upon thefe Terms, viz. A, agrees to lay down 100l. and to employ it in Trade 3 Months: Then B, is to lay down his 100l. 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 217. 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