PREFACE. Ar the suggestion of several intelligent friends who have become acquainted with my "Compu ting Scale," I have been induced to present this simple volume to the public. The general principle on which my Scales are constructed, is now acknowledged by all scientific men, as the only one adequate to perform computations mechanically. The rapidity, certainty, and accuracy of their results are now established beyond the possibility of a doubt. The present volume can be afforded at a price which will place it within the reach of all. Those who wish to carry out their computations to a greater number of decimals, can have their wishes gratified in the purchase of "Palmer's Computing Scale," which is nearly one foot square. All the errors which have been discovered in the former editions, have been corrected in this; and the present work may be regarded as nearly perfect. I only ask a candid examination of the work, and hope it may be as useful to the public, as I have, by long and arduous labor, sought to make it. Boston, Feb. 15, 1844. AARON PALMER. DESCRIPTION OF THE SCALE. THE lines on both parts of the Scale are precisely alike. That part of the Scale which revolves is called "the circular," and the other is called the "fixed part." The lines represent the exact position of the different figures, and are generally numbered. The longest lines are numbered 1, 2, 3, &c., and represent 1, 2, 3, &c., or 10, 20, 30, &c., or 100, 200, 300, &c., or,,, &c., according to the nature of the problem to be solved. The next sized lines represent 11, 12, 13, 21, 54, &c., or 110, 120, &c., and are nearly all numbered. The shortest lines represent the amount or quantity, when it. is composed of three figures, as, 101, 102, 125, &c., or 10·1, 12·5, &c., or 1·01, 1.25, &c.; but on the Pocket Scale these lines are not numbered. To find 105 on the Pocket Scale.-Call the large 1, 100; then count five of the short lines toward 11, and you have the point for 105. To find 224.-First find 22, (the two first figures in the amount,) then count the short lines between 22 and 23; the first short line represents 223; the next short line is 224. To find 645.-First find 64, (the two first figures in the amount,) then the only short line between 64 and 65 represents 645. A TABLE OF GAUGE-POINTS USED ON THIS SCALE. I., at the diamond, is the gauge-point for Multiplication, Division, &c., &c. A. Area of a Circle. C. Circumference of a Circle. 15. For months, at 8 per cent. do. 144. For Square Timber. 9. Yards Square. years, at 7 do. 886. Square and Circle, equal in Area. 707. Inscribed Square. 577. Side of Inscribed Cube. 87. Side of Inscribed Triangle. 589. Side of Pentagon, (5 sides.) 5. Side of Hexagón, (6 sides.) 437. Side of Heptagon, (7 sides.) 383. Side of Octagon, (8 sides.) 337. Side of Nonagon, (9 sides.) 81. Side of Decagon, (10 sides.) 282. Side of Undecagon, (11 sides.) 26. Side of Dodecagon, (12 sides.) 464. Diameter of 3 Inscribed Circles. 416. Diameter of 4 Inscribed Circles. 785. Point for Area. 314 Point for Circumference. TO PERFORM MULTIPLICATION. RULE. First find the multiplier on the circular. Place it opposite 1; then opposite the multiplicand found on the fixed part, is the product on the circular. Example. What is the product of 4 by 2? Place 2 opposite 1; then opposite 4 is the product = 8. N. B.-Observe, now, that all the numbers and parts of numbers on the fixed part, are multiplied by 2, and their products are directly opposite them on the circular. So of any other multiplier. What is the product of 12 by 7? Place 7 opposite 1; then opposite 12 is 84, the answer. Of 3 by 3? Place 3 opposite 1; then opposite 3 is 9, the Place 2.5 opposite 1; then opposite 8 is 20, the answer. What is the product of 10 by 5? Place 5 opposite 1; then opposite 10 is 50, the |