SUPPLEMENT TO THE CUBE ROOT.

1. What is a Cube?

QUESTIONS.

2. What is understood by the cube root?

3. What is it to extract the cube root?

4. In the operation, having found the first figure of the root, why is the cube of it subtracted from the period in which it was taken?

5. Why is the square of the quotient multiplied by 300 ?

6. Why is the quotient multiplied by 30?

7. Why do we add the triple square and triple quotient together, and the sum of them call the divisor?

8. To find the subtrahend, why do we multiply the triple square by the last quotient figure? the square of the last quotient figure by the triple quotient? Why do we cube the quotient figure? Why do these sums added, make the subtrahend?

9. How is the operation proved?

EXERCISES IN THE CUBE ROOT.

1. If a bullet 6 inches in diameter weigh 32lb. what will a bullet of the same metal weigh whose diameter is 3 inches?

Ans. 4lb. NOTE. "The solid contents of similar figures are in proportion

*** ponto each other, as the cubes of their similar sides, or diameters."

1

2. What is the side of a cubical mound, equal to one 288 feet long, 216 broad and 48 feet high?

Ans. 144 feet.

3. There is a cubical vessel whose side is two feet; I demand the side of a vessel which shall contain three times as much?

Ans. 2 feet ten inches and § nearly.

NOTE. Cube the given side, multiply it by the given proportion, and the cube root of the product will be the side sought.

5. FELLOWSHIP.

FELLOWSHIP is a rule by which merchants and others, trading in partnership, compute their particular shares of the gain or loss, in proportion to their stock and the time of its continuance in trade.

It is of two kinds, Single and Double.

SINGLE FELLOWSHIP,

Is when the stocks are employed equal times.

RULE.

As the whole sum of the stock is to the whole gain or loss, so is each man's particular stock to his particular share of the gain or loss.

PROOF. Add all the shares of the gain or loss together; and if the work be right, the sum will be equal to the whole gain or loss.

EXAMPLES.

1. Two merchants, A and B, make a joint stock of 200 dollars; A puts in 75 dollars, and B 125 dollars; they trade and gain 50 dollars; what is each man's share of the gain?

2 Divide the number 360 into 4 such parts, which shall be to each other

3. A man died leaving 3 sons, to whom he bequeathed his estate in the following manner, viz. to the eldest he gave 184 dollars, to the second 155 dollars, and to the third 96 dollars; but when his debts were paid, there were but 184 dollars left; What is each one's proportion of his estate? Ans. 77,829

4. A and B companied A put in £45, and took 3 of the gain; What did B put in ?

Ans. £39.

DOUBLE FELLOWSHIP.

DOUBLE FELLOWSHIP, or Fellowship with time, is when the stocks of partners are continued unequal times.

RULE.

Multiply each man's stock by the time it was continued in trade.

Then,

As the whole sum of the products is to the whole gain or loss, so is each inan's particular product to his particular share of the loss or gain.

EXAMPLES.

1. A, B, and C, entered into partnership; A put in 85 dollars for 8 inonths; B put in 60 dollars for 10 months; and C put in 120 dollars for 3 months; by misfortune they lost 41 dollars: What must each man sus tain of the loss?