the value of a load, or 50 cubit feet, of timber, at all prices, from 6 pence to 2 fhillings a foot. When I at the beginning of any line is accounted 1, then the in the middle will be 10, and the 10 at the end 100; and when the I at the beginning is accounted 10, then I in the middle is 100, and the 10 at the end 1000; and so on. And all the smaller divifions are altered proportionally. Ι PROBLEM I. To Multiply Numbers together. Suppose the two numbers 24 and 13.-Set 1 on B to 13 on A; then against 24 on в ftands 312 on A, which is the required product of the two given numbers 24 and 13. Note. In any operations, when a number runs beyond the end of the line, feek it on the other radius, or other part of the line, that is, take the 10th part of it, or the 100th part of it, &c, and increase the refult proportionally 10 fold, or 100 fold, &c. In like manner the product of 35 and 19 is 665, and the product of 270 and 54 is 14580. PROBLEM II. To Divide by the Sliding Rule. As fuppofe to divide 312 by 24.-Set the divifor 24 on в to the dividend 312 on A ; then against I on B ftands 13 the quotient on A. a. Alfo 396 divided by 27 gives 14·6, PRO PROBLEM III. To Square any Number. Suppofe to fquare 23.-Set 1 on в to 23 on A; then against 23 on в ftands 529 on A, which is the fquare of 23. I Or, by the other two lines, fet 1 or 100 on c to the 10 on D, then against every number on D ftands its fquare in the line c. So against 23 ftands 529, against 20 ftands 400, against 30 ftands 900, and fo on. If the given number be hundreds, &c, reckon the 1 on D for 100, or 1000, &c; then the correfponding I on c is 10000, or 1000000, &c. So the fquare of 230 is found to be 52900. PROBLEM IV. To Extract the Square Root. Set 1 or 100, &c, on, c to I or 10, &c, on D; then against every number found on c, ftands its fquare root on D. So, against 529 ftands its root 23, PROBLEM V. To find a Mean Proportional between two Numbers. As fuppofe between 29 and 430.-Set the one number 29 on c to the fame on D; then against the other other number 430 on c, ftands their mean proportional III on D. Alfo, the mean between 29 and 320 is 96.3, and the mean between 71 and 274 is 139. PROBLEM VI. To find a Third Proportional to two Numbers. Suppofe to 21 and 32.-Set the first 21 on в to the second 32 on A; then against the fecond 32 on B, ftand 48.8 on A, which is the third proportional fought. Alfo the 3d proportional to 17 and 29 is 49'4, and the 3d proportional to 73 and 14 is 2.5. PROBLEM VII. To find a Fourth Proportional to three Numbers. Or, to perform the Rule-of-Three. Suppofe to find a fourth proportional to 12, 28, and 114.-Set the firft term 12 on в to the 2d term 28 on A; then against the third term 114 on B, ftands 266 on A, which is the 4th proportional fought. Alfo the 4th proportional to 6, 14, 29, is 67.6, and the 4th proportional to 27, 20, 73, is 540. CHAPTER II. Of the different Measures ufed by different Artificers. 144 fquare inches a fquare foot, 9 fquare feet 63 fquare feet 100 fquare feet 272 fquare feet perch, or fquare pole. = a fquare yard, =304 fquare yards a rod, The The above denominations are those by which most kinds of work are valued ; but fome particular articles are valued by the foot running, or lineal measure. A Table for changing hundredth Parts of Feet into Inches and Parts, and the contrary; by Means of which, Dimenfions taken in one of thefe, may be readily changed to the other. If it be required to change 44 centefms into inches and 12ths. Against 4 and 40 in the first column, ftand ftand respectively 6 parts, and 4 in. 10 pts, in the fecond; then the fum of these two is 5 inches 4 parts, the number required. EXAMPLE II. If it be required to change 5 inches and or 6 eighths to centefms. Against 6 eighths and 5 inches, in the third column, ftand refpectively 6 and 42 in the laft column; the fum of which is 48 centefins. The reason why I have fet 8ths in the third column, and not 12ths, is that the measurers who calculate by 12ths take the dimenfions in 8ths, and change them into 12ths; because the inches upon the rule are divided into 8ths, and not 12ths. Note. You may convert centefms into inches and parts, and the contrary, without the table, by the following rule, viz. Multiply centefins by 12 for inches, cutting off two figures; and multiply these two figures by 12 again for parts, cutting off two figures here alfo. And divide 8ths or 12ths, with two cyphers annexed by 8 or by 12 for inches; and divide inches by 12 for centefms. EXAMPLE I. Thus, taking the first example above. 12 Inches 5-28 That is 44 centesms = 12 Parts 3.36 5 inches 3 parts. |