А COMPLETE TREATISE ON THE Mensuration of Timber : CONTAINING, Besides all the rules usually given on the subject, PARTICULARLY THE NEW, EXPEDITIOUS, AND VERY ACCURATE METHOD OF CALCULATING THE CONTENTS OF SQUARE & ROUND TIMBER : ....WITH .... THE DESCRIPTION OF THE So far as they relate to this Art. THE WHOLE BEING ILLUSTRATED WITH EXAMPLES AT PRACTICAL TIMBER MEASURER. BY JAMES THOMPSON. TROY, (N. Y.) FOR THEMSELVES AND THE AUTHOR. 1805, DISTRICT OF NEW-YORK, N. DE IT REMEMBERED, that on the eighth day of October, in the twenty-ninth year of the Independence of the United States of America, James Thump son, of the said District, hath deposited in this Office the title of a book, the right whereof he claims as author, in the words following, to wit : “ A complete treatise on the mensuration of timber-Contain“ ing, besides all the rules usually given on the subject, some new and interesting improvements, particularly the new, ex" peditious, and very accurate method of calculating the contents " of square and round timber..... With the description of the « sliding rule and gunter's scale, so far as they relate to this art, “ The whole being illustrated with examples at full length, and “ is well adapted to the practical timber measurer. “ BY JAMES THOMPSON. In conformity to the act of the congress of the United States, entitled “ An act for the encouragement of learning, by securing " the copies of maps, charts, and books, to the authors and pro" prietors of such copies, during the time therein mentioned.” Edward Dunscomb, Clerk of the District of New-York. IN order to prevent the Publick from being imposed upon, by any spurious imitations of the following Treatise, or of the Tables contained therein--I have thought proper to distinguish such copies as are correct and genuine, by subscribing my name, James Thompistas PREFACE. THERE is not wanting a great variety of mathematical works wherein the menfuration of timber is fully explained ; but thus it happens, that there is not extant a separate treatise on the art, in every respect adapted to the use of the merchant, and to the general capacities of those who are otherwise concerned in the measurement of timber. The following is meant as an attempt of this kind, comprehending in a small pocket volume, of moderate price, all the practical rules, in an easy, obvious manner fo that they may be sufficiently intelligible for common practice, even to those who have not had the advantage of a mathematical education. As the mensuration of timber requires the application of decimal arithmetick in all its parts, it has therefore been treated of, together with the extraction of the square and cube roots, a3 fully as is needful-and at least, as plainly as in any other book of the kind : Immediately after, is explained at considerable length, the use of the line ci numbers, on the gunter's fcale and Niding ruleboch instruments being useful for finding the contents of timber, and is performed with great expedition. And as the method of calculating by duodecimals is very short in some cases, (whereas by decimal fractions the same would be somewhat tedious, on account of repetends,) I have examplified all the rules in the multiplication of feet and inches; which is all that the timber measurer requires. Having discussed the above mentioned branches, the subject then comes to be purely practical, and commences by treating, ifly, of board measure; 2dly, of reducing fcantling to board measure; 3dly, of square timber ; 4thly and lastly, of round timber. In all the cases in each problem, there is at least one example wrought according to all the approved and common rules ; and the operations are inserted at full length, in order that it may conspicuously appear, which is the shortest, plainest, and most accurate. The customary, or false method, is particularly pointed out ; and on comparing it with the true method, it will be found to give the contents above the truth, on rectangular square timber whose breadth is greater than its thicknefs ; and under the truth, on tapering square timber ; and about one fourth part under the truth, on round timber. There are also other examples, with their anfwers according to the true and false methods. Following the problem of board measure, there is a table exhibiting the superficial contents of boards from 3 to 30 inches in breadth, and from 7 to 30 feet in length. -Following the problem of reducing fcantling to board measure, there is an original table of the areas in fuperfi. cial feet of squares and parallelograms, for all fizes from 3. by 3, to 12 by 12 inches.-Following the problem of square timber, there is an original table of the areas of squares in feet, or it is a table of the folid contents of prisms from 3 to 30 inches square, and I foot in length.-And following the problem of round timber, there is an original table of the areas of circles in feet ; or, it is a table of the folid contents of cylinders from 10 to 141 inches in circumference or girt, and I foot in length. These tables are extended to fix decimal places ; but in common practice, two or three will be fufficiently accurate ; which will render the calculation of the contents: of timber very easy, and as expeditious as by any inftrıment-and at the same time much more to be depended At the end are added a number of questions, intenda ed for practical exercises to the learner, that he may farther improve himself in the problems and in the characters which are generally used in works of this nature. In the exe on of this little treatise, I have received areat affiftance from a number of mathematical works, particularly from those of Hutton, Ewing, Pyke and Mac Gregor, besides many other good writers on decimal arithmetick; the gunter's scale and Niding rule have been consulted, and in several things, found of no small use. The several parts of the art have been handled more or less fully, according to their apparent practical imper on. tance ; and it is hoped nothing is omitted which is either necessary to the practitioner's understanding the reafons of his various operations, or materially useful for his affiftance in performing them.-At least, this was the end proposed, and pains have not been spared in order to attain it : but with what success, the candid judgment of the publick must determine, |