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Thus, in the example above, we 402–1600 square each of the sides, take the 30%= 900 sum, which is 2500, the square root
2500 of which is 50. Hence, 50 is the
V2500=50 length of the required ladder.
57. If a house is 50 feet deep, and the upright which supports the ridge pole is 12 feet high, what will be the length of the rafters?
Ans. 27.7ft. t. 58. When it is 12 o'clock at New York, what is the hour at London, New York being 75° of longitude west of London ?
Since the circumference of the earth is supposed to be divided into 360 degrees (ART. 94), and since the sun apparently passes through these 360° every twenty-four hours, it follows that in a single hour it will pass through one twenty-fourth of 360° or 150. Hence there are
15° of motion in 1 hour of time,
l' of motion in 4 seconds. If two places, therefore, have different longitudes, they will have different times, and the difference of time will be one hour for every 15° of longitude, or 4 minutes for each degree, and 4 seconds for each minute. It must be observed that the place which is most easterly will have the time first, because the sun travels from east to west.
To return then to our question, the difference of longitude between London and New York being 75°, the difference of time will be found in
OPERATION. minutes by multiplying. 75° by 4,
750 giving 300 minutes, or 5 hours.
4 Now since New York is west of London, the time will be later -in- 60)300 London : that is, when it is twelve Ans. 5 hours. o'clock at New York, it will be five P. M. in London; or when it is twelve at London, it will be seven A. M at New York. 59. Boston is 6° 40' east longitude from the city of
Washington: when it is 6 o'clock P. M. at Washington what is the hour at Boston ?
The 6 degrees being multiplied by 4 gives
6X4=24m. 24 minutes of time, 40 X4=160sec.= 2m. 40sec. and the 40 minutes
26m. 40sec. being multiplied by 4
Ans. 26m. 40sec. past 6. gives 160 seconds, or 2 minutes 40 seconds. The sum is 26 minutes 40 sec. onds, and since Boston is east of Washington the time is later at Boston.
60. The difference of longitude of two places is 850 20: what is the difference of time?
Ans. 5hr. 41m. 20 sec. 61. A traveller leaves New Haven at 8 o'clock on Monday morning, and walks towards Albany at the rate of 3 miles an hour. Another traveller sets out from Albany at 4 o'clock on the same evening and walks towards New Haven, at the rate of 4 miles an hour. Now supposing the distance to be 130 miles, whereabout on the road will they meet ?
Ans. 694 miles from New Haven. 62. A thief is escaping from an officer. He has 40 miles the start, and travels at the rate of 5 miles an hour, the officer in pursuit travels at the rate of 7 miles an hour: how far must he travel before he overtakes the thief? Ans. He travels 20 hours, and 140 miles.
63. 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. 64. The accounts of a certain school are as follows: viz., lo of the boys learn geometry, š learn grammar, io learn arithmetic, o learn to write, and 9 learn to read : what is the number in each branch ?
$ 5 learn geometry, 30 grammar, 24 arith65. If $120 be divided among three persons, A, B, and C, so that when A has $3, B shall have 5 and 7: how much will each receive ?
Ans. A $24, B $40, and C $56.
A PRACTICAL SYSTEM OF BOOK-KEEPING.
PERSONs transacting business find it necessary to write down the articles bought or sold, together with their prices and the names of the persons with whom the bargains are made.
BOOK-KEEPING is the method of recording such transactions in a regular manner. It is divided into two kinds, called Single Entry and Double Entry. The method by Single Entry is the most simple, and answers for all common busi
This method we will here explain. Book-keeping by Single Entry requires two books, a Daybook' and a Ledger; and when cash sales are extensive, an additional book is necessary, which is called a Cash-book.
This book should contain a full history of the business transactions, in the precise order in which they may occur.
The transfer of an account from the Day-book to the Ledger, is called posting the account.
Each page of the Day-book should be ruled with two columns on the right hand of the page, one for dollars, and one for cents, and one column on the left hand for entering the page of the Ledger on which the account may be posted.
The Day-book should begin with the name of the owner, and his place of residence; and then should follow a full account of the transactions in business in the exact order in which they may have taken place.
The name of the person, or customer, is first written with the term Dr. or Cr. opposite, according as he becomes à debtor or creditor by the transaction.
Generally, the person who receives is Debtor, and the person who parts with his property is the Creditor.
Thus, if I sell goods to A B, on credit, he becomes my debtor to the amount of the goods, and the goods should be specified particularly in making the charge.
If I buy goods on credit of C D, I enter C D Cr. by the amount of the goods, taking care to specify the goods in the charge.
If I pay money for, or on account of another person, he becomes Þr. to me for the amount paid.
The Day-book and Ledger are generally designated, Daybook A, Day-book B, Ledger A, Ledger B, &c. : for when one book, in the course of business, is filled with charges a new one is taken.
New York, June 18t, 1846. Ledger.
George Wilson, ✓ 1. To 11 cwt. of sugar at $9 per cwt.
To 66 lb. of coffee at 20 cents per lb.
$ cts. Dr. $99,00
13,20 || 112 20.
Dr. ✓ 1. To balance of former account
$159,10 To 5 gals. of molasses at 32 cts. per gal. 1,60 | 160 70.
2d. Charles Patch,
Dr. ✓ 2. To Cash,
$327,09 To 1 hogshead of molasses
124,02 || 451 11. 3d. Henry Jones,
Cr. ✓ 1. By Cash,
160 70. 5th. George Wilson,
Cr. ✓ 1. By Cash
$100,00 By his note of date for
12,20 || 112 20. 6th. Charles Patch,
Dr. ✓ 2. To Cash
$275,10 To 1 horse
125,00 To 85 lb. of butter at 20 cents per
Ib. 17,00 | 417| 10.
Cr. ✓ 2. By Cash
$400,00 By his note of this date, due Aug. 1, 1846 251,11 | 651 11.
8th. Jared Newton,
Dr. ✓ 2. To 1 piece of linen 36 yards
$42,50 To 3 yds. of broadcloth at $4,50 per yd.
13,50 To 46 lb. of nails at 6cts.
2,76 58 76. 10th. Jared Newton,
Cr. ✓ 2. By Cash
$37,50 By do.
21,26 | 58 76
The LEDGER is a book into which are collected, in a condensed form, all the scattered accounts from the Day-book.
Two pages of the Ledger, facing each other, are generally used in stating an account, in which case each is regarded as half a page ; but sometimes a page is divided into two equal parts. The name of the person with whom the account is stated should be written in large letters at the top of the page.
Two columns should be ruled on the right of each half page of the Ledger, one for dollars and one for cents; there should also be two columns on the left to insert the date of the transaction, and a column for inserting the page of the Day-book from which the account is transferred.
The Debits are entered on the left-hand side of the page, and the Credits on the other side directly opposite. The difference between the debits and credits is always entered under the least sum when the account is closed, and is called the balance, as in the account of Charles Patch.
At the top of the left-hand column we enter the year, under which we enter the day of the month on which the transaction took place; and in the column adjoining the column for dollars and cents, we enter the page of the Day-book from which the account is transferred.
When there are several articles charged in the Day-book, we need not specify them all, but may enter them in the Ledger under the general name of "Sundries.” Having posted the account, we enter the page of the Ledger to which it has been transferred, in the left-hand column of the Daybook and opposite the account, and make a mark v to show that the account is correctly posted. This we make also against the dollar column of the Ledger.
We begin posting with the account of George Wilson, who stands charged on the Day-book with $112,20. We then open an account with Henry Jones, who stands next in the Day-book, and so with each
person named, in his order. On passing through the Day-book we find George Wilson credited on page 1 by 100 dollars cash, and a note for $12,20. These items we enter in the Ledger, on the credit side of his account, and as the debits and credits are equal, his account is balanced. No erasure should ever be made in the account books. When an error is discovered, if it be in favor