68. A can do a piece of work alone in 10 days, and B in 13 days in what time can they do it if they work together? Ans.

1 16

3

69. The accounts of a certain school are as follows: viz, of the boys learn geometry, learn grammar, 10 learn arithmetic, 20 learn to write, and 9 learn to read: what is the number in each branch?

Ans.

3

5 learn geometry, 30 grammar, 24 arith{metic, 15 writing, and 9 reading.

70. If $120 be divided among three persons, A, B, and C, so that when A has $3, B shall have 5 and C 7: how much will each receive? Ans. A $24, B $40, and C $56.

71. The head diameter of a cask is 20 inches and the bung diameter 26 inches: how many wine gallons does it contain, and how many beer gallons?/

The mean diameter of a cask is found by adding to the head diameter, two-thirds of the difference between the bung and head diameters, or if the staves are not much curved, by adding six-tenths. This reduces the cask to a cylinder. Then, to find the solidity, we multiply the square of the mean diameter by the decimal ,7854 and the product by the length;-this will give the solid content in cubic inches. Then if we divide by 231 we have the content in wine gallons (see § 66 NOTE), or if divide by 282 we have the content in beer gallons (see § 67 NOTE:)

For wine measure we multiply the length by the square of the mean diameter, then by the decimal ,7854, and divide by 231.

OPERATION.

lxd2x,7854.
lxd2,0034

231

If then, we divide the decimal ,7854 by 231, the quotient carried to four places of decimals is ,0034, and this decimal multiplied by the square of the mean diameter and by the length of the cask, will give the content in wine gallons.

For similar reasons, the content is found in beer gallons by multiplying together the length, the square of the mean diameter, and the decimal ,0028.

OPERATION.

lxd2 x 7854

282

=lxd2,0028

Hence for guaging or measuring casks, we have the following

RULE.

Multiply the length by the square of the mean diameter, then multiply by 34 for wine, and by 28 for beer measure, and point off in the product four decimal places. The product will then express gallons, and the decimals of a gallon.

72. How many wine gallons in a cask, whose bung diameter is 36 inches, head diameter 30 inches, and length 50 inches.

We first find the difference of the diameters, of which we take two thirds and add to the head diameter. We then multiply the square of the mean diameter, the length and 34 together, and point off four decimal places in the product.

OPERATION. 36-30-6 of 6=4 30+4=34 342=1156 1156×50x34= =196,52 gal.

73. What is the number of beer gallons in the last example?

Ans.

74. How many wine, and how many beer gallons in a cask whose length is 36 inches, bung diameter 35 inches, and head diameter 30 inches?

Ans.

136 wine gal. 112 beer gal.

75. A stationer sold quills at 11s a thousand, by which he cleared of the money; but they growing scarce he raised the price to 13s 6d a thousand: what did he clear at the last price, on each £100 laid out?

Ans.

76. A water tub holds 147 gallons; the pipe usually brings in 14 gallons in 9 minutes: the tap discharges, at a medium, 40 gallons in 31 minutes. Now, supposing these to be left open, and the water to be turned on at 2 o'clock in the morning; a servant at 5 shuts the tap, and is solicitous to know in what time the tub will be filled in case the water continues to flow.

Ans. the tub will be full at 3 min. 48114sec. after 6.

FORMS RELATING TO BUSINESS.

FORMS OF ORDERS.

MESSRS. M. JAMES & Co.

Please pay John Thompson, or order,

five hundred dollars, and place the same to my account.

New York, June 1, 1833.

PETER WORTHY.

MR. JOSEPH RICH,

Please pay the bearer sixty-one dollars and twenty cents, in goods from your store, and charge the same to the account of your

New York, July 1, 1837.

Obedient Servant,

JOHN PARSONS.

FORMS OF RECEIPTS.

Receipt for Money on Account.

Received, New York, June 2nd, 1837, of John Ward, sixty dollars on account.

$60,00

JOHN P. FAY.

Receipt for Money on a Note.

Received, New York, June 5, 1837, of Leonard Walsh, six hundred and forty dollars, on his note for one thousand dollars, dated New York, January 1, 1837.

$640,00

J. N. WEEKS.

No. 1.

$25,50.

FORMS OF NOTES.

Negotiable Note.

New York, May 1, 1837.

For value received I promise to pay on demand, to Abel Bond, or order, twenty-five dollars and fifty cents. REUBEN HOLMES.

Note Payable to Bearer.

No. 2.

$875,39.

New York, May 2, 1837.

For value received I promise to pay, six months after date, to John Johns, or bearer, eight hundred and seventy-five dollars and thirty-nine cents.

PIERCE PENNY.

No. 3. $659,27.

Note by two Persons.

New York, June 2, 1837.

For value received, we, jointly and severally, promise to pay to Richard Ricks, or order, on demand, six hundred and fifty-nine dollars and twenty-seven cents.

ENOS ALLAN.

JOHN ALLAN.

Note Payable at a Bank.

No. 4. $20,25.

New York, May 7, 1837.

Sixty days after date, I promise to pay John Anderson, or order, at the Bank of the United States, twenty dollars and twenty-five cents, for value received. JESSE STOKES.

Remarks relating to Notes.

1. The person who signs a note, is called the drawer or maker of the note: thus, Reuben Holmes is the drawer of note No. 1.

2. The person who has the rightful possession of a note, is called the holder of the note.

3. A note is said to be negotiable when it is made payable to A B, or order, (See No. I.) Now if Abel Bond to whom this note is made payable, writes his name on the back of it, he is said to endorse the note, and he is called the endorser; and when the note becomes due, the holder must first demand payment of the maker, Reuben Holmes, and if he declines paying it, the holder may then require payment of Abel Bond, the endorser.

4. If the note is made payable to A B, or bearer, then the drawer alone is responsible, and he must pay to any person who holds the note.

5. The time at which a note is to be paid should always be named, but if no time is specified, the drawer must pay when required to do so, and the note will draw interest after the payment is demanded.

6. When a note, payable at a future day, becomes due, it will draw interest, though no mention is made of interest. 7. In each of the States there is a rate of interest established by law, which is called the legal interest, and when no rate is specified, the note will always draw legal interest. If a rate higher than legal interest be taken, the drawer, in most of the States, is not bound to pay the

note.

8. If two persons jointly and severally give their note, (See No. 3) it may be collected of either of them.

9. The words "For value received," should be expressed in every note.

10. When a note is given, payable on a fixed day, and in a specific article, as in wheat or rye, payment must be offered at the specified time, and if it is not, the holder can demand the value in money.