To find the rebate or discount on any sum, at any rate per cent. per annum. Note. Rebate or discount is an allowance generally made for the ready payment of money before it becomes due, or upon advancing it for notes, bills, &c. which are payable at a future day. RULE. Find the interest for the given sum, at the given rate per cent. then find the interest on the first found interest, subtract the lesser from the greater, the remainder will be the rebate, (nearly,) which sum subtract from the principal and the remainder will be the present worth. EXAMPLE. What is the rebate or discount on 100 dollars, payable one year hence, discount to be made at 6 per cent? For the rate per cent. take NO. 6, then under N. take 100, the number of dollars, against which stands $ C. Then against N. $6 or 600 cents, stands 36 subtract. The Rebate $5 64 the Ans. To find the rebate for any number of months less than a year. RULE. Find the rebate by the preceding rule, then divide by any even part of a year that will make the time required, and the quotient will be the rebate, which, subtracted from the principal, will give the present worth. A Table of aliquot or even parts, to divide by. To find the rebate for one month, divide by 12 What is the rebate on $100, payable 6 months hence, rebate being made at 6 per cent? 2. Find the rebate of $100, at 7 per cent. per annum, payable 6 months hence, and the present worth of the principal; under NO. 7, and opposite N. 100, stands 7 dollars; then against N. 7, stands 49 cents, which cents, subtracted from $7, leaves $6 51cts. the rebate per annum. By the table of even parts I find this 6 dollars and 51 cts. must be divided by 2, which gives $3 25cts. 5m. then $3. 25cts. 5m. subtracted from $6 51cts. gives $3 25cts. 5m. which is the rebate; then by subtracting the rebate from the principal, gives $96 74cts. 5m. for the present worth. Note. This rule will find the rebate and present worth of any sum, within a few mills of the truth, tho' it is not introduced on a principle to serve those who are acquainted with, and have leisure to use, the Rule of Three, for this purpose. To Measure Superfices. RULE, Find NO. the length, then under V. find the breadth, against which stands the superficial contents, which will be of the same name with NO. EXAMPLES. 1. What is the superficial contents of a wall that is 14 feet by 8? Under NO. 14 find N. 8, against which stands 112, the superficial contents in feet. 2. What is the number of square rods contained in a piece of land in the form of an oblong square, 98 rods long, and 73 rods wide? Take NO. 98, the length, then find N. 73, the breadth, against which stands 7154, the number of square rods, which being divided by 160 will give the number of acres. Of Cubical Measure. RULE. Call NQ, the height, N. the breadth, against which stands stands the superficial contents; then take NO. for the length and M. for the superficial contents, against which. stands the answer. EXAMPLES. What is the cubical contents of a pile of wood that is 4 feet high, 4 wide, and 8 feet long? Find NO. 4, the height, then find N. 4, the breadth, against which stands 16; then find NO. 8, the length, and N. 16, against which stands 128, the answer in feet. 2. What is the cubical contents of a pile of wood that is 6 feet by 9, and 98 feet long? NO. 6 and N. 9 give 54, then NO. 98 and M. 54 give 5292, which is feet; then divide by 128, the number of square or cubical feet in a cord, will give the number of cords. Note. As these tables are calculated on a plan that obliges reduction to bring any odd numbers, as feet and inches, into one denomination before the superficial or cubical contents can be found. I think it will not be improper to give some short arithmetical rules for that purpose-cross multiplication, or duodecimals, I think the most proper for accomplishing my design in this business. NOTATION TABLE. 9 feet 8 inches 7 seconds 6 thirds 5 fourths 4 fifths, &c. TABLE OF PARTS. 1. What is the superficial contents of a board that is 9 feet 7 inches long, and 2 feet 3 inches wide? FI FI! 97 23 19 2 24.9 2169 Here I begin with the left hand figure of the multiplier, and multiply the right hand figure of the multiplicand, and say 2 times 7 is 14, which is 2 above twelve, set down the 2 under the 7, then take the next figure 9 and say 2 times 9 is 18 and 1 that I carry makes 19, set it down under 9; then I take the right hand figure of the multiplier and 3 times 7 make 21, which is 9 above 12, (and, remembering that inches multiplied by inches give seconds,) I set down the 9, one period to the right hand; then I say 3 times 9 make 27, and one that I carry makes 28, which is twice 12 and 4 over, I set down the 4 and carry 2 to the next period; then I add them up, beginning at the right hand figure, their sums, 21F61 9 seconds, or twelfths of an inch, the answer. say 2. What is the contents of a wall that is 14 feet 3 inches long, by 6 feet 7 inches high? 3. What is the contents of a board that is 21 feet inches long, and I foot 9 inches wide. Of Feet Inches and Seconds. 1. What is the contents of a board that is 16 feet 4 inches 4. What is the contents of a joist that is 7 inches by 4, and 11 feet 9 inches long? What is the cubical contents of a pile of wood that is 4 feet 3 inches 2 seconds by 3 feet 9 inches 1 second, and 8 feet 2 inches long? Next follows a Table of Simple Interest, which is sufficiently explained in the introduction to the Table; I have only to remark that the interest for days is set down to the nearest mill. Next follows a Table of the several currencies of the United States, reduced to an equivalent value of federal currency, from one farthing to one hundred pounds. The next Table shews the value of federal currency, from one cent to two thousand dollars. |