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EXAMPLE 1.

If 14 horses eat 56 busnels of oats in 16 days, how many bushels will be sufficient for 20 horses for 24 days?

B.

20 horses

Dir. If 14 horses require 56 what will {24 days?

Dir. in 16 days

224

480

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To be read thus-If 14 horses in 16 days require 56 bushels, what will 20 horses in 24 days require? Both questions are direct, because the more horses the more bushels, and the more days the more bushels?

EXAMPLE 2.

If 8 men in 14 days can mow 112 acres of grass, how many men must there be to mow 2000 acres in 10 days?

Dir. If 112 acres

MEN

{

2000 acres

Inv. in 14 days require 8 what will in 10 days?

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The first proportion is direct, because a greater number of acres requires a greater number of men to mow them; but the second is inverse, because the less number of days requires a greater number of men.

It may also be worked thus ;

Divide 14 and 112 by 14, the quotients are 1 and 8, and dividing 8 and 8 by 8, the quotients are 1 and 1, and using these quotients instead of the original numbers, we have only to divide 2000 by 10.

EXERCISES.

Ex. 1. If £ 100 in 12 months gain £ 6 Interest, how much will £75 gain in 9 months?

Statement.
£

Dir. If £ 100

Dir. mo. 12

} gain

£75

6 what will

9 mo. ?

Ex. 2. If a regiment of Soldiers consisting of 600 men, consume 162 quarters of wheat in 108 days, how many quarters of wheat will 11232 men consume in 56 days.

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Ex. 3. If 40 acres of Grass be mowed by 8 men in 7 days, how many acres could be mowed by 24 men in 28 days?

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Ex. 4. If £ 100 in 12 months gain £ 6 Interest, what Principal will gain 67 s. 6 d. in 9 months?

Dir. If £ 6

Statement.
£

Inv. 12 months require 100 what will

}

67 s. 6 d.
9 months?

Ex. 5. If £ 100 in 365 days gain £ 5 Interest, what will

£ 847 gain in 87 days?

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Ex. 6. If by working 16 hours per day, a piece of work requires 100 men for 15 days, how many men will be required to perform the same in 25 days, working 12 hours per day.

Statement.

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CONTINUED PROPORTION.

Continued Proportion is a combination of two or more Proportions, when the product or fourth term of each simple proportion forms the third term of the following proportion.

Instead of working these proportions separately, they may be performed together like Compound Proportion, by the following Rule, called the Chain Rule.

CHAIN RULE.

Arrange the given quantities in the following order; make the quantity whose value, weight, or other result is required, the term of demand; and in order to distinguish it, place against it a note of interrogation; then place the first and second terms of the given proportions, so that the first term of the first proportion may be similar to the term of demand, and that the first term of each following proportion may be similar to the last second term.

Reduce, if necessary, the similar terms into their lowest denomination, multiply the last term by the numbers in succession of all the second terms, and also the term of demand, and divide the product by the product of the numbers of the first terms.

Observe 1. The first terms are usually called the antecedents, and the others consequents; and the statement of them is called an equation, because each consequent is the value or equivalent of its antecedent, each pair of terms being called a rate of the equation.

2. Any antecedent and any consequent may be divided by a number, that will exactly divide them, and their quotients may be used in their places; and this may be repeated as often as practicable, taking only two terms, one on each side, at a time.

3. When the equation is complete, the last quantity will be of the same species as the quantity which is required to be equivalent to the term of demand.

4. The rule may be thus expressed: "Having made the necessary reductions, multiply the numbers of the consequents together for a dividend, and the numbers of the antecedents together for a divisor, and the quotient will be the number of the product required."

EXAMPLE 1.

If 22 oz. of fine gold make 24 oz. of standard gold, and 12 oz. make 1 pound, and for the journey of 15 lb. of standard gold the Royal Mint delivered 701 sovereigns, what number of sovereigns were delivered in return for 367 oz. of fine gold?

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The term of demand is here 367 oz. of fine gold, and the value of this quantity is required in sovereigns, which therefore forms the last consequent.

Or, dividing 12 and 22 by 12 and by 2 for 24, and dividing 24 by 24, we have on one side 11, 1, and 15, and on the other 367, 1, 1, and 701, and the statement of the calculation is expressed

thus,

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EXERCISES.

Ex. 1. The Cologne mark weighs 3608 grains Troy. What is then the value of this weight of fine silver, when 37 oz. of fine silver make 40 oz. of British standard silver, and 1 oz. of standard silver is worth 60 d. sterling?

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Ex. 2. 10 ells of Vienna are equal to 3454 old French lines, 44329 French lines are equal to 100 metres, 1000 metres are equal to 39371 English inches, and 36 English inches are equal to 1 English yard. How many English yards are equal to 1000

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Ex. 3. The Berlin quart contains 64 Prussian cubic inches, 1728 cubic inches make 1 cubic foot, 10 P. cubic feet equal 15585 old French cubic inches, 50412 French cubic inches equal 1000 litres, and 10,000 litres equal 2201 Imperial gallons. How many Imperial gallons are therefore equal to 1000 Berlin quarts?

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