31. I have a square stick of timber 18 inches by 14, but one with a third part of the timber in it, provided it be 8 inches deep, will serve; how wide will it be? Ans. 10 inches.

32. There are 4 spheres, each 4 inches in diameter, lying so as to touch each other, in the form of a square, and on the middle of this square is put a fifth ball of the same diameter; what is the distance between the two horizontal planes passing through the centres of the balls?

√42+42÷÷÷2=2.828+ inches, Ans.

33. There are 2 balls, each 4 inches in diameter, which touch each other, and another ball of the same diameter is so placed between them that their centres are in the same verlical plane; what is the distance between the horizontal planes which pass through their centres? 142—22-3.46+in. Ans.

34. A military officer drew up his soldiers in rank and file, having the number in rank and file equal; on being reinforced with three times his first number of men, he placed them all in the same form, and then the number in rank and file was just double what it was at first; he was again reinforced with three times his number of men, and after placing the whole in the same form as at first, his number in rank and file was 40 men each; how many men had he at first? Ans. 100. 35. If a weight of 1440 lb. be placed 1 foot from the prop, at what distance from the prop must a power of 160 lb. be applied to balance it? Ans. 9 feet.

36. Three men wishing to carry a stick of timber, which is of uniform size and density, and 30 feet long; if one man takes hold at one end of the stick, how far from the other end must the other two take hold together, that each may bear an equal portion? Ans. 7 feet.

The centre of gravity being in the middle of the stick, we may regard its weight as all accumulated in that point, and the stick itself as a lever supporting it; and then the parts boine will be inversely as the distances from the middle, and the reverse, i. e. the man at the end being 15 feet from the middle, the 2 must be of 15, or 7.5 feet from the middle, and 15-7.5 7.5 the distance from the end.

Where ought the 2 men to

the stick?

take hold in order to carry of

The one being 15 feet from the middle, the two. in order to carry 3 times as much, must be 1-3d of 15-5 feet from the middle, and 15-5== 10ft. the distance from the end.

37. Suppose a pole 100 feet high, to be 24 inches in diameter at the ground, and 4in. do. at the top, and a vine 11⁄2 inch in diameter at the ground to run up this pole, winding round every 3 feet, and gradually diminishing so as to come to a point at the top of the pole, what is the length of the vine?

Ans. 126 feet, 11.94 inches.

1. Book=Keeping.

342. BOOK-KEEPING is the method of recording a systematic account of mercantile transactions.

Every mercantile transaction consists in giving one thing for another. This change of property should be distinctly recorded in a book or books, prepared for the purpose, so that the man of business may at all times know the true state of his affairs.

FARMER'S BOOK-KEEPING.

FIRST METHOD.

343. By this method but one book is necessary, which should be ruled with four columns on the right hand side of each page, two for debtor columns, and two for credit, and one column on the left hand side for the date, as in the following example.

On account of its simplicity, the above method is probably the best which can be recommended to farmers and country mechanics. In keep ing books in this way, it will be necessary to leave a considerable blank after each man's account, that it may be continued without transferring it to another part of the book; and also to have a list of the names with the pages standing against them for the more convenient reference to the sev eral accounts.

244. The person who receives any thing of me is Dr. to me, and the person from whom I receive is Cr. Or, the person, who becomes indebted to me, whether by receiving goods or money, or by my paying his debts, &c. must be entered Dr.: and the person to whom I become indebted, whether by receiving from him goods or money, or by the payment of my debts, must be entered Cr.

SECOND METHOD.

10345. By this method the debt and credit are entered on separate pages facing each other, with the debt on the left hand, and the credit on the right hand, as in the following example.

1825. PETER PINDLE, Dr. $cts.|| 1825. PETER PINDLE, Cr.cts. Jan. 1. To 3 cords of wood,

Jan. 1.

By 121b. shingle-nails]

4 50

6

at 10 cts.
By 25lb. of sugar, at

1 20

2 75

11 cts.

275

19 To 7 bush. of oats, at 25 cts.

tea at $1 10
13 By 10lb. of loaf sugar,

2 20

at 30 cts.

3 00

24 To cash to balance

1231 55

123155

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 per fect system, and far best for wholesale dealers, but as it is more complicated and seldom used, we shall confine our attention to the former, which is generally adopted 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.

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, debts, &c. of the person, and is followed by a distinct record of all the 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 observed: 1, the date; 2, the name of the person, with the abbreviation Dr. or Cr. at the right hand as he is debtor or creditor, by the transaction; 3, the article or articles with the price annexed, and the value carried out into the ruled columns, with the 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 perspicuity 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 book. When several things 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 commencement 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: daybook 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 money received, and 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 not absolutely necessary. Other auxiliary books are sometimes used, and are important in some kinds of business, but the accountand will readily form these for himself, as circumstances render them necessary.

*By single entry, goods bought are entered, either in an invoice book, kept for the purpose, or posted immediately into the leger from the invoices, or bills of parcels. This method is not however adopted here but the goods are credited the sellet, and afterwards transferred to his account in the leger.