In these examples, and all others of the like nature, where the different parts of the stock of each perfon are employed for a different time, the different parts of each person's stock are to be multiplied by their own feparate times, and these products added together to make up the product of each perfon; and then each perfon's product added together to make the total product.

Thus, in the last example, I first multiply the 7281.

put in by A, by 2, the number of months it is

employed alone, and the product is

1456

Then A put in 201. more, which, added to the 7281.
is 7481. and which multiplied by 10 months, the
product is
And which two added together gives A's product

7480 8940

1000

B put in 2001. for 5 months, which product is At the end of 5 months he took out 150l. and then there remained only 50l. which multiplied by 7 months, the product is The two products of B added together are his true one 1350

C put in at firft 40%. which continued alone 6 months, that product therefore is

At the end of 6 months he put in gol. more, which, added to the former 40%. is 90l. which multiplied by 4 months, gives

The last 2 months he had 100l. in the ftock, which,

multiplied by 2 months, gives

Therefore the product of C is

350

240

360

200

800

Then the work is wrought as before, faying, as 140867 (the fum of the products) is to 500l. (the total gain), fois 8936 (the product of A) to 4031. 03. 74d. 68265, the share of Aof the profits; and repeat the operation twice more; to find the fhares of B and C. v. 1. um eins to let ud a al ser .. 9:7 Bb 2 Answer.

THE rule of alligation teacheth how to mix different fubftances together, and to discover the value of any part of fuch mixture; or to make a mixture from known fubftances of any value.

Alligation is either medial or alternate.

Alligation medial is that which teacheth how to find the rate or price of any mixture or compound, from having the rates or prices, and the quantities of the feveral fubftances. given.

Rule. Multiply each quantity by its rate or price, and add the products together for a dividend; add the fums of the feveral quantities together for a divifor; and divide the fum of the products by the fum of the quantities, and the quotient will be the rate or price of the componnd.

Example 1. A mealman mixes 20 bushels of flour, worth 5 per bushel, with 12 bufhels worth 35. 4d. per bushel what is bufhel of this mixture worth?

In this example the price of the bushel is reduced into pence (as it mostly should). The anfwer is the price of the quantity, which is of the fame denomination with the divifor, which here is bufhels.

Proof. Find the value of the whole mixture from the value of any part, and if it be equal to the value of the original fimples, the work is right.

Thus, to prove the foregoing example, I multiply the price of one bufhel of the mixture by 4 and 8, or 32, the number of bushels in the whole, and the product, I find, is 7.; then I find the value of the feveral fimples, by multiplying the number of bushels in each by the number of pence in a bushel (which is already done in the example), and the product 1680 brought into pounds, gives 71. as follows:

Qua. A grocer mixed the following teas together, vizi 15lbs. at Ss. per lb. 20lbs at 75. 4d. per lb. olbs. at 6s. 8d. per lb. and 24lbs. at 4s. per lb. what is one pound of this mixture worth? Answer 6s. 24d. 46.

Qu. 3. A vintner mixes 5 gallons of wine at 75. per gallon, with 9 gallons at Ss. 6d. per gallon, and 14 gallons at 5s. 10d. per gallon; what is one gallon of this mixture worth?-Anfwer 6s. 10d. 14.

*

Qu. 4. A goldfmith melts 101 ounces of gold bullion, of 14 carats fine, with 152 ounces of 18 carats fine, how many carats fine is this mixture?-Answer 16284 carats fine. it pirexe chri

Alligation alternate is the method of finding what quantity of fimples, whofe rates or prices are given, will form a mixture of a certain given rate or price.

Rule 1. Write the rates or prices of the feveral fimples under each other. 2. Connect with a curve line the rate or price of each simple that is lets than the rate or price of the mixture, with one or more of thefe rates or prices that are greater than that of the mixture; and each greater rate with one or more that are lefs: and place the rate or price of the mixture on the left hand of the rates or prices. 3. Write the difference between the rate of the mixtures and the rate of each simple oppofite the rate with which such simple is connected or linked.

Then these differences which ftand opposite any rate is the quantity which that rate requires to form a mixture of the given rate; but if there is more than one difference oppofite any fimple, their fum is the true difference.

1

* Gold is generally mixed with copper or fome other bafe metal, which is called the allay; and the gold is faid to be so many carats fine as it contains pure gold: thus, if an article weighs 24 carats, and contains 22 carats of gold, and 2 of allay, it is faid to be 22 carats fine. What a carat is may be feen, page 135.

*

Example

Example 1. A grocer would mix teas at 45. per lb. 75. per lb. gs. per lb. and 10. per lb. in fuch proportion that the mixture may be worth 6s. per lb.; what quantity of each must be taken?...

In this example, I firft ftate the work as before directed, placing the prices of the teas in a column over each other, with 6, the given price of the mixture, on the left hand.

Secondly, I connect the prices with each other by curve lines; 4 the top figure, being less than the rate of the mixture, I connect with 7, 9, and 10, because they are all greaterthan 6, the rate of the mixture.

4

Thirdly, I find the difference between 6, the price of the mixture, and 4, that of the firft fimple, which is 2; I there-fore place 2 oppofite the 7, 9, and 10, as the 4 is linked to all of them. Then I find the difference between the 6 and the next figure 7, which is 1, I therefore place i oppofite sha 4, being the figure to which the 7 is linked. Then the difes ference between the 6 and 9 is 3, which I place alfo oppofites the 4 (the 9 being linked thereto), and the difference between 6 and 10, which is 4, I alfo place oppofite the 4 (as the on is alfo linked to it). Thefe differences, fo placed, contain the true proportion of each fort of tea at the price opposite: to each, that should be taken to form a mixture at the defired rate.

'But oppofite the 4 there are three differences, viza 1,33,4 and 4, which are to be added together, as feen in the laft column. Thus, there must be 8lb. of tea at 45. per la albas at 75. per lb. 2lb. at 9s. per lb. and 2lb. at 1on per bu; and: the whole quantity of the mixture is 14lb. at 6s. per lb.

Thefe