22. The solid content of a square stone is found to be 136 feet; its length is 9 feet: what is the area of one end? and if the breadth be 3 feet 11 inches, what is the depth?

136.5×1728

9.5×12

inches, Ans.

area 2069 C526 inches, and

2069-0526
47

= 44-022

23. I would have a cubick box made capable of receiving just 50 bushels, the bushel containing 2150 425 solid inches: what will be the length of the side?.

3

2150 4X50=47·55 inches.. 24. A statute bushel is to be made 8 inches high, and 181 inches diameter, to contain 2176 cubick inches; (though the content of the dimensions is but 2150 425 inches) I demand what the diameter of the bushel must be, the height being 8 inches; and what the height, the diameter being 18 inches, to contain 2176 cubick inches?

Solidity.

Height 8)2176 and

Area 272

272×1·273=18 6 diameter. 18.5×18.5 × 7854268 80315=area, and the solidity. 2176-268-8-8-0956 inches, height.

25, There is a garden rolling stone 66 inches in circumference, and 3 cubick feet are to be cut off from one end, perpendicular to the axis: where must the section be made?

1728X3-5

Area 412.5

14.65 inches from one end, Ans.

26. I would have a syringe of 14 inch diameter in the bore, to hold a quart, wine measure: what must be the length of the piston, sufficient to make an injection with?

1·5×1·5×·7854=1·76715, and 231÷4=57-75 the cubick inches

in a quart, then

57.75

1.76715

32 679 inches, Ans.

27. If a round pillar, 9 inches diameter, contain 5 feet: of what diameter is that column, of equal length, which measures 10 times as much?

As 5: 9x9 :: 5×10 : 810, and 810-28-46 inches, Ans. 28. There is a square pyramid, each side of whose base is 30 inches, and whose perpendicular height is 120 inches, to be divided by sections parallel to its base into 3 equal parts: required the perpendicular height of each part?

30×30×40=36000 the solidity in inches, now thereof is 24000, and is 12000. Therefore,

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. 29. Suppose the diameter of the base of a conical ingot of gold to be 3 inches, and its height 9 inches; what length of wire may

be expected from it, without loss of metal, the diameter of the wire being one hundredth part of an inch?

3×3ו7854×3=212058 the solidity of the cone.

21.2058

01X 01X-7854

=270000 inch.4 miles, and 460 yards, Ans.

:

30. Suppose a pole to stand on a horizontal plane 75 feet in height above the surface at what height from the ground must it be cut off, so as that the top of it may fall on a point 55 feet from the bottom of the pole, the end, where it was cut off, resting on the stump, or upright part?

As the whole length of the pole is equal to the sum of the hypotenuse and perpendicular of a triangle, (the 55 feet on the ground being the base) this, as well as the following question, may be solved by this

RULE. From the square of the length of the pole (that is, of the sum of the hypotenuse and perpendicular) take the square of the base; divide the remainder by twice the length of the pole, and the quotient will be the perpendicular, or height at which it must be cut off.

31. Suppose a ship sails from latitude 43°, north, between north and east, till her departure from the meridian be 45 leagues, and the sum of her distance and difference of latitude to be 135 leagues : I demand her distance sailed, and latitude come to?

135X135-45X45

135×2

60 leagues, and 60×3=180 miles=3 de

grees the difference of latitude, 135-60-75 leagues the distance. Now as the vessel is sailing from the equator, and consequently the latitude is increasing: Therefore,

To the latitude sailed from

Add the difference of latitude

43°,00' N.

3,00

And the sum is the latitude come to=46,00 N.

J

BOOK KEEPING.

BOOK KEEPING is a systematic record of mercantile transactions.

Every mercantile transaction consists in giving one thing for another. This change of property requires a distinct record in the books prepared for the purpose, so as to enable the man of business to know the true state of his affairs, and of his accounts with an individual.

The importance of a correct knowledge of Book keeping, to the man of business is obvious. His books, should exhibit the result of each transaction, and the general result of the whole.

Book keeping may be performed either by Single or Double Entry.

The method of book keeping by single entry is the most simple, and is sufficient for the generality of Mechanics, Farmers, Retail Merchants, &c. The method by Double Entry is more systematic in its principles. and more certain in its conclusions, and is much to be preferred for wholesale or any extensive business.

In Single Entry only, persons are entered as debtor and creditor.

BOOK KEEPING BY SINGLE ENTRY.

In the practice of single entry, two principal books, the Day Book or Waste Book, and the Leger, and one auxiliary book, the Cash Book, are necessary.

1. THE DAY BOOK OR WASTE BOOK.

The Day Book should begin with an account of all the property; debts, &c. of the person, and be followed by a distinct record of all the transactions of the trade in the order of time in which they occur.

Some accountants use also a Blotter, in which the changes of property are recorded, and the Day Book is only a copy of the Blotter, written in a more fair and plain manner.

Each page of the Day Book should be ruled with three columns on the right side for pounds, shillings, and pence, or with two columns for dollars and cents, as the accounts are to be kept in one or the other of these denominations of money.

The following is the order observed in making an account in the Day Book: First, the date; next, the name of the person with the abbreviation Dr. or Cr. at the right hand, as he is debtor or creditor by the transaction; and then, the article or articles with the price annexed, unless the article be money, and the value carried

out in the ruled columns, with the sum of the whole placed directly under, when there is more than one charged. Thus, for example,

The following rule shows whether a person is to be entered as Dr. or Cr. on the Day Book. The person who receives any thing from 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, 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.

The following general direction is to be observed in keeping the Day Book, viz.

Enter on the Day Book every case of debt or credit relating to the business in the order of time in which it takes place, and in language so explicit as not to be mistaken.

This rule is most important, because the Day Book is the decisive book of reference in case of any supposed mistake or error in the accounts in the Leger.

2. THE LEGER.

The various accounts of each person are collected from the Day Book, and placed or posted under his name, and on two opposite pages of the Leger, as they are Dr. or Cr. The name of the person is to be written in large and fair characters as a title, and the accounts in which he is Dr. are to be written on the test hand page, and those in which he is Cr. on the right hand page of the same folio. If the name be written only on the Dr. page, the title of the other page is to be, Contra or Ca. Cr. The Leger is ruled with a margin for the date of each transaction, or with a column for the page of the Day Book which contains the account, or with both. It must also be ruled with two or three columns on the right of each page for the denominations of money, as they may be Dolls. and Cents, or £ s. and d. If the Leger be a wide Folio, the accounts of Dr. and Cr. may be placed on the same page, as in the following example.

In the preceding example, the two columns on the left both of the Dr. and Cr. accounts contain the date of the transaction and the page of the Day Book on which the original account is to be found. Next follows the article and its quantity, which should be written in few words, and then its amount in the money columns. Either the date or the page of the Day Book which contains the account, is amply sufficient in the Leger, and the latter is to be preferred.

The Leger exhibits at one view the accounts with an individual, as it contains on the Dr. side whatever he has received, and on the Cr. side whatever he has paid. The difference between the sums of Dr. and Cr. called the Balance, shows the state of the trade in this instance.

An Index must accompany the Legcr, in which the names are arranged alphabetically, with the page of the Leger on which each account is to be found. See the Index to the Leger for Ex. 2.

The following general directions are to be observed in forming the Leger. Let each account be posted from the Day Book in its proper place in the Leger. If a mistake be made, let it be corrected by an account in the Day Book, clearly stating the correction, and then let this account be posted in its proper place in the Leger, that no blot or erasure may disfigure its pages.

THE CASH BOOK.

In this book are recorded the daily receipt and payment of money. For this purpose there are two 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. By some accountants other auxiliary books are used, which are found to be useful or important in some particular business. These the accountant will readily form for himself, as circumstances may render

necessary.

Note 1. As several of the preceding books may be necessary in the progress of business, they should be distinguished by lettering them in the following manner. 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 the one or the other. See Example 2.