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341. 25. Four men bought a grindstone 60 inches in diame. ter; how much of its diameter must each griod off to have an equal share of the stone, if one grind bis share first, and then another, till the stone is ground away, making no allow. ance for the eye?
RULE. - Divide the square of the diameter by the number of men, sutie tract the quotient from the square, aud extract the squar mainder, which is the length of the diameter after the first share is taken off; and by repeating the latter part of the process, all the several shares. may be found, 60x60;-4=900, the subtrahend.
3600-900=51.96+ and 60-51.96=8.04, 1st share. ✓2700-900=42.42+ and 51.96-42.42–9.54, 2d share. ~1800-900—30. and 42.42-30=12.42, 3d share.
aod 30, 4th's share, 26. Suppose one of those meteors called fireballs to move parallel to the earth's surface, and 50 miles above it, at the rate of 20 miles per second ; in what time will it move round the earth?
The earth's diameter being 7964 miles, the diameter of the orbit will be 7964+50 x2=8064, and 8064x3.1416=25333.8624 its circumference. Then 25333.8624;-20=1266.69312s.=21 6" 41" 35" 13" 55""" Ans.
27. When first the marriage knot was tied betwixt my wise and me, My age with hers did so agree as nineteen toes with eight and three ; But after ten and half ten years we man and wife had been, Her age came up as near to mine as two tiines three to nine. What were our ages at marriage ?
Ans. 57 and 33. 28. A body weighing 3016. is impelled by such a force as to send it 20 rods in a second; with what velocity would a body weighing 121b. move, if it were impelled by the same force ?
Ans. 50 rods. 29. la a thunder storm I observed by my clock that it was 6 seconds between the lightning and thunder; at what distance was the explosion ?
Ans. 6852ft.=1131 miles. 30. There is a square pyramid, each side of whose hase is 30 inches, and whose perpendicular height is 120 inches, to be divided into three equal parts by sections parallel to its base ; what will be the perpendicular height of each part ?
30x30x40=36000, the solidity in inches. Now of this is 24000, and i is 12000. Therefore, as 36000 : 120x120x120
524000 : 1152000) :: (12000 : 576000 $ Then, ✓ 1152000=104.8. Also, ♡ 576000=83.2. Then 120–104.8=15.2, length of the thickest part, and 104.8–83.2=21.6, length of the middle part, consequently, 83.2 is the length of the top part.
346. Either of the foregoing methods may answer for farmers, and for mechanics generally, but to the retail merchant, and others whose business is extensive, an acquaintance with book-keeping by the day-book and leger, called SINGLE ENTRY, or by the day-book, journal and leger, called DOUBLE ENTRY, is indispensible. The latter is much the most perfect system, and far best for wholesale dealers, but as it is niore complicated and seldom used, we shall coubine our attention to the former, which is generally adopled by merchants and others in this country.
BOOK-KEEPING BY SINGLE ENTRY. Single Entry requires two principal books, the day book, or waste book, and the leger, and one auxiliary book, the cash book.
ke the cash book.
1. THE DAY BOOK. 347. This book is ruled with two columns on the right hand for dollars and cents, one coluinn on the left, for inserting the folio or page of the leger to which the account is transferred, and a top line over which is written the month, date and year. The articles are separated from each other by a line drawn across the page, and the transactions of one day from those of another by a double line, in the centre of which is the day of the month.
This book commences with an account of all the property, ciebts, &c. of the person, and is followed by a distinct record of all ihe transactions in trade in the order of time in which they occur, with every circumstance necessary to render the transaction plain and intelligible. *
In entering accounts in the day-book, the following order should be obe served: 1, the date; 2, the name of the person, with the abbreviation Dr. or Cr. at the right hand as he is debior or creditor, by the transaction; 3. the article or articles with the price annexed, and the value carried out into the ruled columns, with ike amount placed directly under, when there is more than one article charged ; and 4, the page to which the account is transferred in the leger. For the better understanding of the day-book, see the specimen annexed.
* As the day book is the decisive book of reference, in case of any sup, posed mistake, or error, in the accounts in the leger, it is of the greatest importance that every transaction be noted in it with particular perspicuis uy and accuracy,
2. THE LEGER. 348. Each page of the leger is ruled with a top line, on which is written the name of the person, and marked Dr. on the left hand for receiving the debited articles, and Cr. on the right for receiving the credited articles of the day.book. On the right hand of both Dr, and Cr. sides, are ruled two columns for dollars and cents, and on their left, three columns, one for the page of the day.book, one for the month, and one for the date. The leger has an index, in which the names of persons are arranged under their initial letters, with the page in the leger, where the account may be found.
349. Rule for Posting.Under the name of the person, enter the several transactions on the Dr, or Cr. side in the leger, as they stand debited or credited in the day buok. When several ihings are included in the same transaction, they are distinguished by the term "sundries.” Some accountants enter in the leger only the page of the dry-book and the amount of the transaction, without specifying the items, but the former is thought to be the most correct method.
350. Balancing Accounts.- When all the articles are correctly posted into the leger, each account is balanced by subtracting the less side from the greater, and entering the balance on the less side, by which both sides are made equal. The excess of all the balances on the Dr. over those on the Cr. sides, being added to the cash on hand and the value of the goods unsold, the sum is the net.of the estate, which, compared with the stock at the commencernent of business, exhibits the merchant's gain.
351. When the place assigned to any person's account is filled with items, the person's name must not be entered the second time, but may be transferred to another page in the following manner, viz. Add up the Dr. and Cr. columns and against the sums write, Amount transferred to page -, here inserting the page where the new account is opened. Begin the new account by entering on the Dr. side, To amount brought from page , inserting the page of the old account, and on the Cr. side, By amount brought from page , inserting the page of the old account, placing the sums in their proper columns.
As several day-books and legers may be necessary in the progress of business, they should be distinguished by lettering them, as follows: day, book A. day-book B. &c. -Leger A. leger B, &c. and in posting accounts into the leger, there must be a reference to day-book A or B, &c. as the account is found in one or another.
3. CASH-BOOK. 352. In the cash-book are recorded the daily receipt and payment of money. For this purpose it is ruled with separate columns, one for mon
d the other for money paid, in which should be recorded merely the date, to or by whom paid, and the sum. The cash-book is convenient, but rot absolutely necessary. Other auxiliary books are sometimes used, and are important in some kinds of business, but the account. and will readily form these for himself, as circumstances render them ner cessary.
* By single entry, goods bought are entered, either in an invoice book, kept for the purpose, or posted immediately juto the leger from the inuni. cer, or bills of parcels. This method is not however adoptert here : hur. the goods are credited the seller, and afterwards transferred to his account in the leger.