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utilize the services of each in the department in which he can best serve the interests of the firm ; etc.

NOTE. — In the absence of an agreement to the contrary, each partner is entitled to an equal share of the profits, and is liable for an equal portion of the losses ; in the examples given, however, the gains and the losses are distributed according to the amount invested by each and the length of time each one's capital remains in the business. See also Art. 977.

6. A, ut of $13; B, 24; C, 2009; D, 34; etc.

7. The analysis of a mathematical problem or operation should be occasionally used as an exercise in composition, the same attention being given to penmanship, spelling, language, and arrangement as in other such exercises.

1122. 1. Make men the last term ; Art. 974, 8.
If 1 be eaten in 35 da. at 24 oz. daily by 3600 men,
2 will be eaten in 45 da. at 14 oz. daily by ? men.
3600 men x 35 x 24 x 2 = 9600 men. Ans.

45 x 14 4. $3700 = (1 -.075).

8. See Arithmetic Art. 1005, 2. £500 = £ of $4866.50. Take £250, £25, £5, 10s., 58., 28. 6d., 1s. 3d., 2d. Or,

20) $ 4.8665 x 780 =
12) $ .2433 x 18=

$ .0203 x il= 9. See Art. 1250, 8. Calling the part remaining x, the part broken off will be 100 — X. The latter is the hypotenuse of a right-angled triangle; x is the perpendicular ; 40 is the base.

40+ x2 = (100 — x)?,
1600+x2 = 10000 – 200 x + x*,
200 x = 10000 - 1600 = 8400,

x= 42.

100 — x = 58.
The length of the part broken off = 58 ft. Ans.

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The above represents the account as it stands upon the books of Samuel Adams. The debit column contains the amounts due from the Treasury Department, and the credit column contains the sums received, etc. The account is balanced by placing the footing of the debit column under each, and by writing in the credit side the words “By Balance” in red ink, followed by the sum necessary to make the total of the credit column equal to the total of the debit column. Red ink is used to show that the money has not been paid. The account is reopened by writing "To Balance" on the debit side, followed by the sum remaining due.

The statement rendered by Samuel Adams to the Treasury Department would be made out as follows:

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The quantities and prices are omitted, as they have been given in the bills rendered at the time the articles were supplied.

For the form of this account as it would appear on the books of the Treasury Department, see Art. 1146, 24.

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The owner of a cyclometer should calculate the number of revolutions of a wheel necessary to move the index of the cyclometer over one of its smallest divisions. The circumference of a wheel, 26 in. in diameter, measures nearly 21 yd. Nine revolutions of the wheel should indicate a trifle over 20 yd. on the cyclometer ; 8 revolutions should indicate a trifle over ido mile, 17.6 yd.

3. The premium = of of $6000 = $33.75. The loss will be the value of the uninsured one-quarter, $1500, and the above premium.

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1124. 2. į circumference = 3.1416x; } diameter = x; area = 3.1416x”.

NOTE. — The pupil should memorize the ratio between the circumference and the diameter, 3.1416. After learning from Art. 1274, 6-14, that the area of a circle is equal to the product of the semi-circumference by the semi-diameter, and ascertaining from 2 that this is equal to the square of the radius multiplied by 3.1416, the latter rule can occasionally be employed. See 6. 4. When the circumference is a, the diameter=

3.1416

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