131 or $13,20 Ans. by which I answer re Here the second term 6 being the lesser of the second and third terms, I divide it by 5 the first term, the quotient is 1 multiply the third term 11, and the product (134) is the quired. Here follows an easy method of ascertaining the contents, &c. of land, very useful to farmers. EXAMPLES. 1. If a lot of land be 100 rods long, and 96 rods wide, how many acres does it contain ? RULE. Multiply the length by the breadth, divide the product by 160, and you have the contents in acres. Thus : Rods. Rods. 2. If a lot of land be 100 rods long, how many rods wide shall it be to contain 60 acres? Rods. A. Square kods. As 1.0.0: 60:: 16.0 Ans. 96, the breadth required. N. B A lot of land, 160 rods long and 1 rod broad, contains 1 acre; therefore the two ones cancel each other, and leave 160 for a multiplier, or divisor, according to the nature of the question, that is when acres are required, 160 will be a divisor: and when either the length or the breadth is required, and the contents given, 160 will be a multiplier universally. 3. The earth being 350 degrees in circumference, revolves on its own axis once in 24 hours, how far does it turn in one minute, in the latitude of 43 degrees; the degree of longitude in this latitude being supposed to be 51 statute miles? Deg. H. 24 60 51 M. METHOD OF ASSESSING TOWN OR PARISH TAXES. 1. An inventory of the value of all the estates, both real and personal, and the number of polls for which each person is rateable, must be taken in separate columns. Then to know what must be paid on the pound, or on the dollar, make the total value of the inventory, the first term; the tax to be assessed the second; and 1 pound or 1 dollar the third, and the fourth number will show the value on the pound, or on the dollar. 2. Make a table by multiplying the value on the dollar or on the pound by 1, 2, 3, 4, 5, &c. 3. From the inventory take the real and personal estates of each man, and find them separately, in the table, which will show you each man's proportional share of the tax for real and personal estates. If any part of the tax be averaged on the polls, before stating to find the value on the pound, or on the dollar, deduct the sum of the average tax from the whole sum to be assessed; for which average make a separate column, as well as for the real and personal estates. EXAMPLE. Suppose the general court should grant a tax of 150000 dollars, of which a certain town is to pay $3250.72, and of which the polls being 624 are to pay 75 cents each; the town's inventory is 69568 dollars; what will it be on the dollar; and what is A's tar as by the inventory, whose estate is as follows, viz. real, $856; personal $103; and he has 4 polls? Pol. Cts. Pol. 1. As 1 : 75 : : 624 468 dollars, the average part of the tax to deducted from $3250,72, and there will remain $2782,72. NOTE. This method of assesssing taxes, is taken from Mr. Pike's Arithmetick, and is so plain, that it needs no further comment. RULE OF THREE DIRECT IN VULGAR FRACTIONS. In the Rule of Three in Vulgar Fractions, if any of your terms be integers, mixed numbers, &c. reduce them to improper fractions, as directed in multiplication of decimals; state your question as in whole numbers, and then proceed as in the following rule. Multiply the second and third terms, and divide the product by the first term; that is, multiply the numerator of the first term by the denominators of the second and third for a divisor (or denominator) of the answer; and the denominator of the first term by the numerators of the second and third, for a dividend (or the numerator) of the an swer. EXAMPLES. 1. If a yard of cloth cost £, what will yard cost? NOTE-The Rule of Three in Vulgar Fractions, admits of contraction (or cancelling) the same as the Rule of Three in whole numbers; therefore observe the numerators of the second and third terms, and denominator of the first term oppose the numerator of the first, and denominators of the second and third terms. Thus, as before : EXPLANATION. Here 4, the denominator of the first term cancele 8, the denominator of the second, equal 2; 5, the numerator of the second, cancels 10, the denominator of the third, equal 2; and 3, the RULE OF THREE DIRECT IN DECIMALS. 209 numerator of the first cancels 9, the numerator of the third equal 3; therefore, the proportion is reduced to of a £, equal to 15 shillings; and so on universally. 2. If yard cost £3 what will yard cost? As Yd. £. Yd. THE RULE OF THREE DIRECT IN DECIMALS We shall not, in this place, give a definition of the rule of three, that being sufficiently done in the rule of three in whole numbers. For seeing the rule of three in decimals, is the same, both in the stating and working the question, as in whole numbers, respect being had to the rules in decimals before taught, which, if well understood, any question of the rule of three, though consisting of never so cross fractional parts, will receive its solution as easily as if the question were composed of integers only, which shall be made plain in the following examples. 1. If of a yard cost of a pound, what will 9 yards come to ? $,625,58 3 and 1,5. Then Yds. £. Yds. As ,625,58.3 : : 9,5 Having reduced the fractional parts to decimals, and stated your question as in whole numbers, multiply the second and third together; divide by the first and the quotient is the answer as above. 2. If 72 yards cloth cost £2 12s. 9d. what will 140 yards of the same cloth cost at that rate? 7,75)370,56875(47,815-£47 16s. 33d. Ans. INVERSE PROPORTION OR RULE OF THREE INVERSE, Teaches, by having three numbers given, to find a fourth, which shall have the proportion to the second, as the first has to the third. Therefore the less the third term is in proportion to the first, the greater the fourth must be in proportion to the second; or the greater the third term is, in respect to the first, the less will the ourth term be, in respect to the second; and this is called reciprocal, inverted or indirect proportion. To distinguish, when a given proportion is direct,and when indirect, has been taught in the rule of three direct. RULE. State the terms as directed in the rule of three direct, then multiply the first and second terms together, and divide the product by the third; the quotient will be the answer in the same denomination of the middle term. N. B. Contraction and cancelling have the same force here as in the rule of three direct. EXAMPLE. If 8 men can do a piece of work in 12 days, in how many days wil 16 men do the same ? EXPLANATION. In this question the supposition is, if 8 men do a piece of work in 12 days, and the two terms contained in it, are 8 men and 12 days: The demand lies in these words: In how many days will 16 men do the same? And the only term contained in it is 16 men. The number sought here, is the days in which 16 men will do the work, and the term in the supposition of the same kind, is 12 days ; wherefore I place 12 days as the middle term, the two remaining terms are extremes, and of the same kind, viz. both of them men, It is obvious that the answer must be less than the middle term; for 16 men will do the work in fewer days than 8 men; and therefore the greater extreme, viz. 16, is the divisor; which I place on the right hand, and the other extreme on the left. Then multiplying the first and second, and dividing the product by the third, the quotient comes out in days; that is, of the same name with the middle term. And because the extreme found in the demand, happens to be the divisor, the proportion is inverse. The same by contraction. M. Days. M. As 8 12 1·6 Ans. 6 days as before. 2 Here 16 being the divisor, and 8 and 12 the opposite numbers, or terms which form the dividend, 8 destroys 16, equal 2, and this 2 wwer required. destroys 12, equal 6, the |