2005 Western Mensurationists Meeting, Hilo, HI - July, 4 - 7

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 ForestryUniversity of New Brunswick

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

So, what do we know about the

birth and early development of North American Forest

Mensuration?

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

The 1800’s

Proliferation of log rules

Summarized in the ever popular “Ready Reckoners”

Comprehensive and Informative Review

Photo: John Bell and Associates

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.

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

Early Mensuration WorksEdward 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)

A Little Gem of Mensuration

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

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

Plagiarism well Established

ContentsDecimal 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

Gunter’s Scale

1 2 3 4 5 6 789 1 2 3 4 5 6 789

10

Photo: Bruce Babcock

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

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

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

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

Who was James Thompson?

Lived in/near Troy, NY

Mensurationist

Lumber Broker? (1790 tax list, Troy NY)

Patriot? (1840 Rev. Pensioners list, Troy,NY)

83 Years Old – b. 1757