What is the solid content (in cubic inches) of a triangular prism, whose height is 24 inches, and the length of each side 12 inches ? Ans. 1496 inches. 2. MULTIPLICATION ON THE SLIDING RULE. Find the multiplier on the B line, and place it under 1 on the A line; then find the multiplicand on the A line, and under it will be found the product or answer on the line B. EXAMPLES FOR PRACTICE. 1. To multiply by 3: bring 3 on the line B under 1 on the line A, then under 2 on A you will find 6 on the line B, which is the product of 3 times 2; and under 3 you will find the product of 3 times 3, or 9; and under 4 you will find 12, and under 5, 15; under 6, 18; under 10, 30; under 12, 36; under 20, 60; under 25, 75; under 30, 90; under 35, 105; under 40, 120; under 50, 150; under 60, 180; under 75, 225; under 80, 240. 2. To multiply by 5: move the slider till you bring 5 on the line B under 1 on the line A, then under 12 on the A line you will find the product, 60, on the line B; and under 20 you will find 100; under 25, 125; or calling the multiplier 5 fifty, then under the 12 you will find 600; under 20, 1,000; under 25, 1,250; under 30, 1,500; under 45, 2,250; and under 75, 3,750. 3. To multiply by 2.5: bring 2.5 under 1, and under 2 you will find the product of 2 times 2.5, viz. 5; under 4 you will find 10; under 5, 12.5; under 6, 15; under 12, 30; under 20, 50; and under 40, 100. Or, call the 2.5 twenty-five, and under 2 you will have 50; under 3, 75; under 4, 100; under 5, 125; under 10, 250; under 20, 500; under 25, 625; under 35, 875; under 40, 1,000; under 45, 1,125; under 50, 1,250; under 55, 1,375; under 60, 1,500; under 80, 2,000; under 85, 2,125; under 90, 2,250; under 100, 2,500 under 120, 3,000; and under 125, 3,125. 4. Multiply 7.3 by 20.2, and the product will be 147.5; or multiply 5.7 by 13.5, and the product will be 76.95; or multiply 9.4 by 7.6, and the product will be 71.4; and multiply 6.8 by 13.1, and the product will be 89.1; and multiply 18.6 by 6.2, and the product will be 115.3; and multiply 2.7 by 6.8, and the product will be 18.4. Or, calling the 2.7 two hundred and seventy, under 2 you will find 540; under 6, 1,620; under 6.8, 1,896; under 7.5, 2,025; under 8, 2,160; and under 8.6, 2,322. With a good rule, multiplication may be performed with perfect accuracy, when the product does not exceed 5,000, by determining the unit figure in the mind. 8. TO DIVIDE BY THE SLIDING RULE. Find the DIVISOR on the line B, and place it under 1 on the line A; then find the DIVIDEND on the line B, and over it you will find the QUOTIENT on the line A. EXAMPLES. 1. To divide 48 by 12, find the divisor, 12, on the line B, and place it under 1 on the line A; then find the dividend on B, and over it you will find the quotient, 4, on A; and over 60 you will find the quotient of 60 divided by 12, viz. 5; and over 84 you will find 7, the quotient of 84, divided by 12; and over 90, 7.5; or, calling the 9 nine, the quotient will be .75; or, calling the 9 nine hundred, the quotient will be 75; or, calling the 9 nine thousand, the quotient will be 750. 2. Divide 48, and 60, and 72, by 24. Bring the divisor, 24, on B, under 1 on A, then over 48 on B you will find 2, the quotient, on A; and over 60 you will find 2.5; over 72, 3; over 70, 2.91; over 95, 3.95; over 100, 4.15, &c. 3. Divide the following numbers, 66, 77, 88, 110, 150, 220, 300, 440, 600, 700, 1,000, 1,500, 2,200, and 3,000, by 44. Answers, or quotients, 1.5; 1.75; 2; 2.5; 3.3; 5; 6.8; 10; 13.6; 15.9; 22.72; 34; 50; 68. 4. Divide 120, 150, 180, 240, 300, 450, 600, 700, 800, 1,200, 3,000, 4,400, 5,000, and 6,000, by 60. are respectively, 2; 2.5; 3; 4; 5; 7.5; 10; 20; 50; 73.33; 83.33; 100. The quotients 11.66; 13.33; 5. Divide 6.4, 4, 2, 1.2, 1, and .8, by 1.6. Quotients in order, 4; 2.5; 1.25; .75; .625; and .5. ¶ 4. THE RULE OF THREE ON THE SLIDING RULE. Find the FIRST term on the A line, and the SECOND term on the line B: then place the SECOND term under the FIRST, and find the THIRD term on the line A, and under it you will find the FOURTH term, or answer, on the line B. EXAMPLES. 1. If 3 pounds of beef cost 21 cents, what will 2 pounds cost? what 6 lbs.? 8 lbs. ? 11 lbs.? 15 lbs. ? 22 lbs.? 27 lbs. ? 45 lbs.? 60 lbs. ? and 100 lbs. ? Find 21, the second term, on the line B, and place it under 3, the first term, on A; then find 2 on A, and under 2 you will find the price, or cost of 2 pounds, on B, viz. 14 cents; and under 6 you will find the cost of 6 lbs., viz. 42 cents; under 8 you will find the cost of 8 lbs., viz. 56 cents; under 11, 77; under 15, 1.05, or $1.05; under 22, 1.54; under 27, 1.89; and under 45, 3.15, or $3.15. 2. A school district wishes to raise a tax of $30, to be made up on the scholars, each patron of the school being required to pay such proportion of the $30, as the number of days he has sent to the school bears to the number of days all the pupils in the school have attended. If, then, the whole number of days be 3,600, how much must A pay for 240 days' tuition? how much must B pay for 200? C for 150? D for 120? E for 100? F for 90? G for 70? H for 60? I for 36? J for 30? K for 20? L for 15? M for 8? N for 4? and O for 1? In cases like the present, it will be found most convenient to place the first term of the proportion on the line A, to the right of the middle of the rule. Hence, in this case, draw the slider a little to the right, placing 3, or 30, on B, under 3.6, or 3,600, on A; then, since under the whole number of days on the A line, you have the whole amount of money to be raised, so under any number of days found on the A line, will be found the tax, or tuition to be paid for that number of days, on the line B. Thus, under 240 on the A line, we find 2, or 2 dollars, on the line B, which is the amount of A's tax; under 200 days we find $1.66 for B's tax; under 150, $1.25 ; under 120, 1 dollar; under 100, 83 cents; under 90, 75 cents; under 70, 58 cents; under 60, 50 cents; under 36, 30 cents; under 30, 25 cents; under 20, 163 cents; under 15, 12 cents; under 8, 6 cents and 7 mills, or .067; under 4, .0335; under 1,.0084, or 8 mills and 4 tenths nearly. 3. A school tax of $45 is to be raised; the whole number of days is 4,000; what must C pay for 400 days' tuition? D for 200? G for 80? H for 35? and K for 30 days? Answers. C must pay $4.50; D, $2.25; G, 90 cents; H, 39 cents; and K, 34 cents. 4. What is the interest on 100 dollars at 9 per cent. for 150 days, for 100 days, for 80 days, for 70 days, for 50 days, for 30 days, for 12 days, and for 3 days? In calculating interest for days, it is customary to call 30 days one month, and 360 days one year; consequently make 360 days the first term, and 9 dollars the second, and proceed as in the last example. Then, under 150 days you will find $3.75; under 100, $2.50; under 80, 2 dollars; under 70, $1.75; under 50, $1.25; under 30, 75 cents; under 12, 30 cents; and under 3 days, 7 cents. 5. If the grand list of a certain town be $250,000, and the tax to be raised on the property of that town is $2,100, what will be the tax on an estate valued at $2,500? and what on one valued at $1,000, on one valued at $650, on one valued at $500, on one valued at $400, on one valued at $250, on one valued at $200, on one valued at $100, on one valued at $75, on one valued at $25, and on one valued at 8 dollars? And what will be the tax on one dollar? In this example $250,000 is the first term, and 2,100 the second; and having placed the first term over the second, (as in the last example,) to avoid any mistake in reading off, let the learner run along the line A from $250,000 till he comes to the end of the rule on the left hand, which brings him to 10,000; then beginning at A on the right, and calling the ten on the rule 10,000, let him continue the computation from A towards the left till he comes to the starting-point, when the 250,000 will count 2,500; then let him commence with the second term, 2,100, on B, and proceed in the same manner till he has made the circuit of the line B, when under the first term he will find 21, or $21, which would consequently be the tax on $2,500; and under 1,000 we find 8.4, or $8.40, for the tax on $1,000; and under 650, $5.46; under 500, $4.20; under 400, $3.36; under 250, $2.10; under 200, $1.68; under 100, 84 cents; under 75, 63 cents; under 25, 21 cents; under 8, 62 cents; and under 1,8 mills. VULGAR AND DECIMAL FRACTIONS. To reduce a vulgar fraction to its equivalent decimal expression, the proportion is, as the denominator upon A is to 1 on B, so is the numerator upon A to the decimal required on B. Set 1 upon B to 4 upon A, then against 1 upon A is .25, the answer, upon B. |