the middle of each stating, which is of the same name, nature, or quality, with the term required to be known.

2. Place the statings regularly one under another, so that each conditional term, or term of supposition, may stand on the left-hand of the middle term, and have a proper reference to it. The terms of demand will then stand under each other on the right-hand of the middle term, and each will refer separately to the answer correspondent to each stating.

3. From the nature of proportion the first and third terms of every stating will be of the same kind, and must be reduced to the same denomination. Examine every. stating separately (using the middle term in common for each stating) by saying, if the first term give the second, does the third require more or less? if more, mark the less extreme; if less, mark the greater extreme for a divisor.

4. Multiply all the numbers together which are marked, for a divisor; and those which are not marked for a dividend, and the quotient will be the answer.

5. The work may be contracted by throwing out such numbers as occur both in the divisor and the dividend; or by dividing any two numbers in the divisor and dividend by their common measure, and using the quotients instead of the original numbers.

RULE II.

1. Set down the terms expressing the conditions of the question in one line, taking care to separate the cause from the effect.

2. Under each conditional term set its corresponding one in another line, marking the term sought, or wanting, with an asterisk (*).

3. Draw cross lines from the cause term, or terms, in the first part of the first line, to the effect term, or terms, in the second part of the second line; and, from the effect term, or terms, in the second part of the first line, to the cause term, or terms, in the first part of the second line.

4. Multiply the term, or terms, at the end of the cross

line, where the star-term is found, into the term, or terms, at the other end of that line for a divisor. Then multiply all the terms together, standing at contrary ends of the other cross-line for a dividend. The quotient will be the answer, and of the same name with that term under which the asterisk is placed.

NOTE. When a term is only understood, and not expressed, the place of that term must always be supplied by an unit.

The marks (†) point out the divisors in the single statings.

(3.) If 7 men in 12 days can reap 126 many days will 16 men reap 72 acres?

: 16m.

acres, in how Ans. 3 days. (4.) A carrier receives 157. 12s. for the carriage of 4 tons 18 miles, how much will he carry 72 miles for 20 guineas?

(5.) If 100l. principal gain 47. in 12 months, what principal will gain 207. in 19 months?

(6.) The carriage of 11cwt. 2qr. for 150 miles costs 6l. 14s. 8d., how much must be paid for the carriage of 15cwt. 1qr. 22lb. for 64 miles at the same rate?

(7.) If a regiment of 1878 soldiers consume 702 quarters of wheat in 336 days, how many quarters will an army of 22536 soldiers consume in 112 days?

G

(8.) If 1007. at interest for 1 year, or 365 days, gain 57., how much will 144/. 14s. 9d. gain in 495 days?

(9.) If 12 taylors in 7 days can finish 13 suits of clothes, how many taylors, in 19 days of the same length, can finish the clothes of a regiment of soldiers consisting of 494 men?

(10.) An ordinary of 100 men drank 207. worth of wire at 2s. 6d. per bottle; how many men, at the same rate of drinking, will 77. worth suffice, when wine is rated at 1s. 9d. per bottle?

(11.) If the carriage of 126lb. for 100 miles cost 6s., how many pounds may I have carried 750 miles for a guinea?

(12.) If 60 bushels of oats will serve 24 horses for 40 days, how long will 30 bushels serve 48 horses at the same rate?

.

CLASS II.

Examples wherein the number of terms exceeds five.

(13.) If 4 compositers, in 16 days of 12 hours long, can compose 14 sheets, of 24 pages in each sheet, 44 lines in a page, and 40 letters in a line,-in how many days, of 10 hours long, may 9 compositors compose a volume, to be printed on the same letter, consisting of 30 sheets, 16 pages in a sheet, 48 lines in a page, and 45 letters in a line?-Heath.

=

4x16x12x30x16x48x45 796262400 dividend.
9x10×14×24×44×40: = 53222400 divisor.

Then 796262400, divided by 53222400, gives 14511188 days, — 147; days, Answer.

(14.) If 24 measures of wine, at 3s. 4d. each, serve 16. men for 6 days, how many measures, at 2s. 8d. each, will serve 48 men for 4 days?

(15.) If a garrison of 3600 men, in 35 days, at 24oz. per day each man, eat a certain quantity of bread, how many men, in 45 days, at the rate of 140z. per day each man, will eat double the quantity?

(16.) A garrison of 3600 men has just bread enough to allow 24oz. a day to each man for 35 days; but, a siege coming on, the garrison was reinforced to the number of 4800 men: how many ounces of bread a day must each man be allowed, to hold out 45 days against the siege of the enemy

?

(17.) If the carriage of 150 feet of wood, that weighs 3 stone a foot, comes to 31. for 40 miles, how much will the carriage of 54 feet of free-stone, that weighs 8 stone a foot, cost for 25 miles?

(18.) If, when wine is 307. per tun, 201, worth will serve a ship's company of 336 men for 4 days, at a pint a day for each man-how long will 500l. worth serve a crew of 250 men, at 1 pint a day to each man, when the tun is worth but 247.?

(19.) If 336 men, in 5 days of 10 hours each, dig a trench of 5 degrees of hardness, 70 yards long, 3 wide, and 2 deep, what length of trench, of 6 degrees of hardness, 5 yards wide, and 3 deep, may be dug by 240 men in 9 days of 12 hours each?

(20.) If 12 pieces of cannon, eighteen pounders, scan batter down a castle in an hour, in what time would nine twenty-four pounders batter down the same castle, both pieces of cannon being fired the same number of times, and their balls flying with the same degree of velocity?

(21) If 12 oxen will eat 3 acres of grass in 4 weeks, and 21 oxen will eat 10 acres in 9 weeks, how many oxen will eat 24 acres in 18 weeks, the grass being allowed to grow uniformly?-Newton.

(22.) If 6 oxen or 10 colts can eat up 21 acres of pasture in 14 weeks, and 10 oxen and 6 colts can eat up 45 acres of a similar pasture in 20 weeks, the grass growing uniformly; how many sheep will eat up 240 acres in 40 weeks, admitting that 1134 sheep can eat the same quantity as 12 oxen and 22 colts?

VULGAR FRACTIONS.

DEFINITIONS.

1. A Fraction is a part, or a collection of several parts, of an unit, or of any whole quantity expressed by an

unit.

A fraction is represented by two numbers placed one above the other, with a line drawn between them, as 4, three-fourths of an unit, or one-fourth of three units; five-eighth of an unit, or one-eighth of five units, &c.-The lower number is called the denominator, and shews how many parts the unit is divided into; the upper is called the numerator, and shews how many of these parts are to be taken. Thus, , one-fourth, shews that an unit is to be divided into four equal parts, and one of these parts are to be taken; 2, three-fourths, shews that an unit is to be divided into four equal parts, and three of these parts are to be taken, or, which is the same thing, that the number 3 is to be divided into four equal parts, and one of these parts are to be taken.-Hence it appears that every fraction denotes a division of its numerator by its denominator, and that its value is equal to the quotient obtained by such a division.

2. A proper fraction is that wherein the numerator is less than the denominator, as 1, 3, 4, &c. Hence the value of such a fraction is less than an unit.

3. An improper fraction is that wherein the numerator is greater than the denominator, or equal to the denomi