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An Exegesis on the Status of Mensuration in 1805 based on the works of James Thompson

An Exegesis on the Status of Mensuration in 1805 based on the works of James Thompson. A tale of gentle madness leading to new insights John A Kershaw, Jr. Professor of Forest Mensuration, Faculty of Forestry University of New Brunswick.

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An Exegesis on the Status of Mensuration in 1805 based on the works of James Thompson

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  1. An Exegesis on the Status of Mensuration in 1805 based on the works of James Thompson A tale of gentle madness leading to new insights John A Kershaw, Jr. Professor of Forest Mensuration, Faculty of Forestry University of New Brunswick 2005 Western Mensurationists Meeting, Hilo, HI - July, 4 - 7

  2. exegesis \ˌek-sә-jē-sәs\ - A margin note or footnote expanding on the text, particularly in ecclesiastical contexts such as in canon law; to explain, interpret : EXPOSITION, EXPLANATION; esp : an explanation or critical interpretation of a text

  3. So, what do we know about the birth and early development of North American Forest Mensuration?

  4. A Centennial View • Early 1900’s mark the birth of “professional” or “scientific” forestry • Borrowed from European practice • Summarized existing North American practice (mostly log rules) • Developed new techniques Photos: Forest History Society

  5. The 1800’s • Proliferation of log rules • Summarized in the ever popular “Ready Reckoners”

  6. Comprehensive and Informative Review Photo: John Bell and Associates

  7. Additional Glimpses of the 1800’s • Harris Collingwood, Library of Congress 1952. The Lost Identity of Doyle and Scribner. Journal of Forestry. 50:943-944. • Harold Belyea, NYS College of Forestry 1953. A Postscript on the lost identity of Doyle and Scribner. Journal of Forestry. 51:326-329.

  8. Limitations of the Ready Reckoners • Methods not always clear or even presented • Focus • May present only one aspect (i.e., log rule) • Or an omnibus of tables (logs, wages, interest, yard cloth, grain volumes, etc.) • Plagiarism • Tables reprinted under a “new” name • Parts of two rules combined to give advantage to buyers or sellers

  9. Early Mensuration Works • Edward Hoppus • Practical measuring made easy to the meanest capacity. 1761 (6th edition) • Charles Hutton • A Treatise on Mensuration, Both in Theory & Practice. 1770 • The Compendious Measurer; Being a Brief, Yet Comprehensive, Treatise on Mensuration, and Practical Geometry. With An Introduction to Decimal and Duodecimal Arithmetic. Adapted to Practice, and the Use of Schools. Illustrated With the Plan of a New Field-Book Engraven on Copper Plate. 1790 (2nd edition) • Alexander Ewing • A synopsis of practical maethematics. Containing plain trigonometry; mensuration of heights, distances, surfaces, and solids; surveying of land, gauging, navigation, and gunnery. With tables of the logarithms of numbers, and of sines and tangents. For the use of schools and men of business.1779 (2nd edition)

  10. A Little Gem of Mensuration

  11. Purpose • Focus on timber mensuration • Concise and Affordable Volume • Application of mathematics to subject • Understandable to those without mathematics training • Instrumental Arithmetic • Correct the “common” or “false” methods

  12. A Practical Approach Full Examples Tabular Results Purpose (cont.)

  13. Plagiarism well Established

  14. Contents • Decimal and Duodecimal Arithmetic • Numeration of decimals • Addition, subtraction, multiplication and division • Decimal applications to measurement unit conversion • Decimal Tables • Squares, Cubes and Roots • Applications to mensuration • Instrumental Arithmetic • Gunter’s Scale and Compasses • Slide Rule • Mensuration of Timber • Board Measure • Reduction of Scantlings to Board Measure • Content of Squared Timber • Content of Round Timber

  15. Gunter’s Scale Photo: Bruce Babcock

  16. What were the Issues? • What do we Find in the Book? • Emphasis on individual boards, scantlings, squared logs, and round logs • Board measure (bd. ft.) firmly established • Comparison of “true” methods based on geometric solids with “common” or “false” methods • Results summarized into Standardized (1-foot) Tables

  17. What were the Issues? • “common” or “false” methods • Primarily aimed at simplifying mathematics • Hoppus measure (¼-girth string rule) widely used • Applied to both round and squared timber • Midpoint measurement or average dimensions

  18. What were the Issues? • Thompson’s “true” methods • Advocated measurements at both ends • Frustum of pyramid for squared timber • Frustum of cone for round timber • Inconsistencies • Reverted to average dimensions when equally spaced measurements available

  19. What were the Issues? • What don’t we find in the book? • No mention of measuring stacks of lumber, cants, or logs • No mention of measurement of standing timber • No log rules

  20. Who was James Thompson? • Lived in/near Troy, NY • Lumber Broker? (1790 tax list, Troy NY) • Patriot? (1840 Rev. Pensioners list, Troy,NY) 83 Years Old – b. 1757 • Mensurationist

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