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Thursday July 10, 2014, 2:15-3:45 PM, CFPL
Welcome to Workshop III, of The Thoreau Society’s 2014 Annual Conference

“Thoreau’s Illustrated Atlas” and “Thoreau’s Field Notes of Surveys”
Plus Charles Davies “Elements of Surveying and Navigation” as aids to decipher a letter to Thoreau from William Davis Tuttle concerning “Wheeler’s Lot” 1854

By Allan H. Schmidt

Summary:

This paper discusses surveying procedures for measuring land areas published by Charles Davies in the 1840’s and known to Thoreau and other surveyors.

Davies’ procedures are described in the context of an Excel spreadsheet and compared to Thoreau’s and Tuttle’s land area measurements of Wheeler’s Lot in 1854.

Thoreau’s likely use of a pantograph for copying maps at varying scale is discussed.

Thoreau’s use of a surveyor’s compass capable of recording angular measurements with greater precision than described in Davies’ tables provide an unique means for identifying surveys recorded by Thoreau.

 

The Correspondence of Henry D. Thoreau: Volume 1: 1834 – 1848
Edited by Robert N. Hudspeth
“This is the inaugural volume in the first full-scale scholarly edition of Thoreau’s correspondence in more than half a century. When completed, the edition’s three volumes will include every extant letter written or received by Thoreau–in all, almost 650 letters, roughly 150 more than in any previous edition, including some that have never before been published.
Correspondence 1 contains 163 letters, ninety-six written by Thoreau and sixty-seven to him. Twenty-five are collected here for the first time; of those, fourteen have never before been published. These letters provide an intimate view of Thoreau’s path from college student to published author. At the beginning of the volume, Thoreau is a Harvard sophomore; by the end, some of his essays and poems have appeared in periodicals and he is at work on A Week on the Concord and Merrimack Rivers and Walden. The early part of the volume documents Thoreau’s friendships with college classmates and his search for work after graduation, while letters to his brother and sisters reveal warm, playful relationships among the siblings. In May 1843, Thoreau moves to Staten Island for eight months to tutor a nephew of Emerson’s. This move results in the richest period of letters in the volume: thirty-two by Thoreau and nineteen to him. From 1846 through 1848, letters about publishing and lecturing provide details about Thoreau’s first years as a professional author. As the volume closes, the most ruminative and philosophical of Thoreau’s epistolary relationships begins that with Harrison Gray Otis Blake. Thoreau’s longer letters to Blake amount to informal lectures, and in fact Blake invited a small group of friends to readings when these arrived.
Following every letter, annotations identify correspondents, individuals mentioned, and books quoted, cited, or alluded to, and describe events to which the letters refer. A historical introduction characterizes the letters and connects them with the events of Thoreau’s life, a textual introduction lays out the editorial principles and procedures followed, and a general introduction discusses the significance of letter-writing in the mid-nineteenth century and the history of the publication of Thoreau’s letters. Finally, a thorough index provides comprehensive access to the letters and annotations.”
Source: front flap,”Volume 1, Thoreau Correspondence 1834-1848”
Robert N. Hudspeth is Research Professor of English at the Claremont Graduate University and professor emeritus of English at Redlands University. He is the editor of The Letters of Margaret Fuller and the author of Ellery Channing.
Review:
“Thoreau’s letters unquestionably enlarge understanding of his character. The personality who emerges is not just cold, impassive, and stoic but also witty, playful, and sociable, not just reclusive and idealistic but also engaged and practical.”—Choice

Vol. 1 “Thoreau Correspondence” 1834-1848 includes “the stagecoach letter”:
Concord, April 6, 1840
“Dear Haskins,
I improve this the first opportunity by sending your cloak by the Accommodation Stage.
…..
Yours,
Henry D. Thoreau”
Ref. The Correspondence, Volume 1: 1834-1848, page 65
The Writings of Henry D. Thoreau
2013
Princeton University press
Note:
The Concord Accommodation Stage made the seven hour round trip between Concord and 11 Elm Street, Boston, each day.
In his A HISTORY OF THE TOWN OF CONCORD, Lemuel Shattuck wrote, “Public Stages were first run out of Boston into the country through Concord, in 1791, by Messrs. John Vose & Co. There are now (1833), on an average, 40 stages which arrive and depart weekly, employing 60 horses between Boston and Groton, and carrying about 350 passengers; 150 have passed in one day.” William Shepherd (owner of Shepherd’s Hotel on Main Street) ran a line of stages between Concord and Boston from 1817. Stages also stopped at the Middlesex Hotel.
The railroad came to Concord in 1844. Until train travel became the dominant form of transportation, stagecoach lines and the hotels that served them did good business here

The project described below relates to a letter to Thoreau from William Davis Tuttle concerning “Wheeler’s Lot”. It began in response to a question I received from Beth Witherell, formerly President of the Thoreau Society (1996-2000) and currently Editor-in-Chief of Princeton University Press Editorial Board for The Writings of Henry Thoreau. Including (Three volumes of “Thoreau Correspondence”

Beth Witherell’s letter to me relative to The Correspondence, Volume 2 included a question about Thoreau and surveying.
From: Beth Witherell <witherell@library.ucsb.edu>
Date: Sun, Nov 3, 2013 at 6:03 PM
Subject: Questions about Thoreau and surveying
To: allanhschmidt@gmail.com
Dear Mr. Schmidt,
I’m the head of the Princeton Edition of Thoreau’s writings, and I’m a big fan of your work on Thoreau. The surveys have much more significance than most readers and scholars of Thoreau have realized, and between your Illustrated Atlas and the Field Notes and Pat Chura’s book they have become more accessible. I wish I had been able to get to the last couple of Annual Gatherings to hear you talk and to meet you. For a long time I went every year, but in the last five or six years family matters have kept me from traveling.
I’ve worked on Thoreau since 1974 and studying his manuscripts, in person and using photocopies, has given me an opportunity to see the wide range of his interests and competencies. I’ve also come to understand the interlocking relationships among the contents of the various manuscripts that are now physically separate, which you don’t have a way to think about if you have access only to published versions.
For example, a (particularly full) day’s work for Thoreau might include writing up several days’ worth of notes as Journal entries, beginning a survey, reading and copying extracts from part of the Jesuit Relations, and writing a letter to the Harvard librarian accompanying a couple of books he was returning via a friend. The Journal passages would be in a MS volume of the Journal, now at the Morgan Library; the survey notes would be recorded in his Field Notes of Surveys, now at the Concord Free Public; the Jesuit Relations extracts would be in one of his MS Indian Books, now at the Morgan; and the letter might now be in the Houghton.
The parts of Thoreau’s work for that day all affected one another; sometimes the cross-pollination is visible, as when he mentions a survey or the title of a book in his Journal, and sometimes it’s not. One of my goals in annotating the Journal and Thoreau’s letters is to reveal these relationships when they’re relevant, to show the cross-pollination.
We’re working on Thoreau’s correspondence right now–the first volume of three was published August 1–and the annotations are sometimes interesting and quite complicated. I’m writing now to see if you can help me explain the contents of a letter to Thoreau from William Davis Tuttle which I am assuming is about the work Thoreau records on p. 105 of his Field Notes. On that page, above and to the right of a plan of a plot of land, Thoreau writes:
P. M.
John Fletcher^ Acton Mass
Area of his “Wheeler Lot” calculated
from minutes
Furnished by
him. Dec 22nd
1854
13A. 112 rods

To see the Image of Thoreau’s plot of Wheeler’s Lot in “Thoreau’s Field Notes of Surveys” go to http://allanhschmidt01742.wordpress.com/ and scroll down to page 105.

103

 

Tuttle’s letter to Thoreau follows–only one leaf of it survives:

“made a very small plan of it
(about 2 rods to an inch I should judge)
& cast it up making 14 A 22rods
The plan was so small (& so unskillfully drawn) that I told Mr. W that very
little reliance could be placed upon it in computing areas.
Since then I have computed the area
several times by the aid of traverse tables finding
the Lat & Dep both in chains & decimals of a chain
& in rods & dec of a rod & obtaining answers
the bearing of the 3d course N 57 E & taking out
the Lat & Dep in rods & decimals of a rod I made
the area to be 13a 109,57r. I find but little
(,01 of a rod) diff between the Eastings & Westings & but ,19
of a rod between the Northings & Southings. & in balancing
the survey I subtracted the Diff between the North &
Southings from the Southing of the 7th course.
Will you have the kindness to inform me by what
method you computed the Lat in question: if by
plotting to what scale your plan was drawn, or if by
the traverse table whether you took out the distances
in chains or rods & to how many decimal places
you found the Lat & Dep. of each course
What is your general method of computing
areas & what is the present variation of the needle in Concord?
Yours very respectfully,
Wm D. Tuttle”

I think Thoreau’s plan in the Field Notes (for 12/22/1854) and Tuttle’s letter is about the same lot because:
1) Tuttle indicates that if he uses “N 57 E” as the bearing of the third course he gets an area of 13 acres 109.57 rods, which is quite close to the area as Thoreau calculates it–13 acres 112 rods
2) In Thoreau’s drawing, the third dimension from the NE corner of the lot is labeled “N 57 E”. I’ve assumed that that third dimension is the same as Tuttle’s “3d course”
3) Tuttle refers to “Mr. W” and Thoreau says this is Fletcher’s “Wheeler Lot”
Last month, in Boston, Bob Hudspeth, the editor with whom I’m working on this volume, found the record for a transaction that I think involves this parcel: On December 14, 1854, James Wetherbee Wheeler of Acton sold a tract of woodland containing 14 acres, 28.5 rods to John Fletcher and Cyrus Dole of Acton. The price was $664.50.
I’d like to be able to date Tuttle’s letter, at least approximately, but I’ll have to use circumstantial evidence because the portion of the letter that survives doesn’t show a date. So my first question is whether I can reasonably assume that Thoreau’s record in his Field Notes and Tuttle’s letter and the record of the transaction are all about the same piece of land.
If they are, then I think I can assume that Tuttle worked for Wheeler (“Mr. W”), who supplied him with “a very small plan of [the lot] (about 2 rods to an inch I should judge)” which someone had “cast . . . up making 14 A 22 rods.” So that’s what Wheeler thinks the area is. In his letter Tuttle notes, “The plan was so small (& so unskillfully drawn) that I told Mr. W that very little reliance could be placed upon it in computing areas.” (I don’t think Tuttle went out and measured the lot–he mentions using traverse tables, which I think means that he used the data Wheeler gave him. Is that right?) Thoreau is working for Fletcher, who has furnished him with “minutes” that Thoreau has used to make his own calculations. Based on that data, Thoreau calculates the area to be smaller than Wheeler thinks–13 acres 112 rods. Tuttle wants to know how Thoreau arrived at his result.
In terms of dates, the sequence of events would be:
Before December 14, 1854, Wheeler engages Tuttle to calculate the area of the lot based on a small plan.
On December 14, Fletcher and Dole purchase the lot from Wheeler.
Between December 14 and December 22, Fletcher engages Thoreau to recalculate the area of the lot.
On December 22, Thoreau does that recalculation and records the result in his Field Notes.
After December 22, either Thoreau or Fletcher communicates Thoreau’s figures to Tuttle and Tuttle writes to explain how he made his calculations and to ask Thoreau how he did his.
Following this sequence, I’d date Tuttle’s letter “After December 22, 1854″. Does that seem supportable to you?
So that’s one set of issues this letter raises. Another is that Tuttle’s letter is packed with the vocabulary of surveying, which Thoreau obviously understood but which baffles me and will baffle most of our readers. I’ve found definitions of traverse tables and latitude and departure and chains and rods, but they don’t help me to understand the overall meaning of Tuttle’s letter. I think the best way to explain that would be to provide a brief explanation of what Tuttle is describing to Thoreau and asking Thoreau about. Could you write such an explanation to be used an annotation for this letter?
I’m sorry to say that I can’t offer you anything but credit for this work (I can send you a copy of Correspondence 1 now, and make sure you get Correspondence 2 and 3, which will save you several hundred dollars if you were planning to buy the books, but it’s not the same as a consultant’s fee, I know). You would be named as the author in the annotation itself, which will follow the letter, and you’d be listed in the Acknowledgments for Correspondence 2.
Thanks very much for persisting to the end of this long message. Whether it’s possible for you to respond to my questions or not, I do look forward to meeting you sometime.
Best,
Beth Witherell, Editor-in-Chief
The Writings of Henry D. Thoreau
http://thoreau.library.ucsb.edu/

My response of Nov/15/2014 to Beth Witherell’s letter follows:
Tuttle and Thoreau correspondence concerning “Wheeler’s Lot” 1854
Question: What is Tuttle describing to Thoreau and asking Thoreau concerning Wheeler’s Lot?
Answer: Tuttle is describing two different procedures he had used to measure the area of Wheeler’s lot and asking Thoreau’s opinion as well as Thoreau’s experience concerning a related issue of compass correction for magnetic variation in Concord.
Area measurement of a land parcel was a common statistic provided by Thoreau for the lots that he surveyed from 1837-1860. Many of the land parcels were described as “woodlots”. An area measurement could be used to calculate the amount firewood or building lumber and therefore dollar value that could be expected from a woodlot prior to its being cut.
According to a Surveyor’s Manual that was in Thoreau’s library (Davies, Charles “Elements of Surveying and Navigation”, 1846):See:
http://play.google.com/books/reader?id=KpVHAAAAIAAJ&printsec=frontcover&output=reader&hl=en&pg=GBS.PP5
There were two commonly used methods for computing land areas, given a map of known scale.
1. Divide the existing map of land lots into geometric units (e.g. squares and triangles) and then compute the area of each lot and sum their total area.
2. Noting the bearings and distances for each lot originally recorded with compass and chain, use rules of geometry and traverse tables to compute the area enclosed within the map perimeter.
(Both procedures were alluded to by Tuttle in his letter to Thoreau)
Davies notes that when using compass and chain there are two potential sources of error:
1st. Inaccuracy of the surveyor’s field observations when recording bearings and distances.
2nd. Local attractions or the derangement which a compass needle experiences when brought into the vicinity of iron-ore beds, or any ferruginous substances.
To guard against these sources of error, reverse bearing should be taken at every station: if this and the forward bearing are of the same value, the work is probably right; but if they differ considerably, they should both be taken again.
Differences between measurements taken in each direction also may be used to estimate “balancing” corrections.
THE TRAVERSE TABLE AND ITS USES
The Traverse tables that are included in Davies book, show the latitude (N-S) and departure (E-W) corresponding to bearings for each survey line segment expressed in degrees and quarters of a degree from 0 to 90°, and for every course from 1 to 100, computed to two decimal places.
By use of these tables the latitude (Y- coordinate) and departure (X-coordinate) of each course segment may be computed.
Davies describes how given a surveyor’s field measurements describing the straight line segments defining the perimeter of a property boundary, it also is possible to compute the area of the property in question and also create a graphic x-y coordinate plot of its perimeter.

Tuttle’s Letter to Thoreau follows (with my comments in italics):
Made a very small plan of it about 2 rods (i.e. 33 feet) to an inch (scale)
An enlarged copy of a map can be made by use of a pantograph, see: http://en.wikipedia.org/wiki/Pantograph
Thoreau owned such devices currently on display in the Concord museum and shown on their website. http://www.concordcolleection.org/ then do a word search in the Thoreau collection for “compass” and you will see Thoreau’s pantograph.

 Untitled-4 copy

 

 

I should judge & cast it up making 14 A 22 rods
(i.e. I manually drew an enlarged plot and divided it into geometric units (e.g. squares and triangles) then summed the area of each lot, resulting in an estimate of 14A 22 rods,= 14.14 A.)
The plan was so small (& so unskillfully drawn) that I told Mr. W that very little reliance could be placed upon it in computing areas.
Since then I have computed the area several times by the aid of traverse tables
(I next computed the area using the compass and chain technique described by Davies.)
Finding the Lat & Dep both in chains & decimals of a chain
& in rods & dec of a rod & obtaining answers
the bearing of the 3d course N 57 E & taking out
the Lat & Dep in rods & decimals of a rod I made
the area to be 13a 109,57r.
(resulting in an estimate of 13A 109.5722 rods, 13.69A.)
I find but little (,01 of a rod) diff between the Eastings & Westings & but ,19
of a rod between the Northings & Southings. & in balancing
the survey I subtracted the Diff between the North &
Southings from the Southing of the 7th course.
Will you have the kindness to inform me by what
method you computed the Lat in question: if by
plotting to what scale your plan was drawn, or if by
the traverse table whether you took out the distances
in chains or rods & to how many decimal places
you found the Lat & Dep of each course.
What is your general method of computing areas?
(i.e. Do you generally use plotting of geometric units or the Compass and chain measurements?
We know from a review of Thoreau’s Land Surveys that he used both techniques beginning with geometric units and moving on to compass and chain once he had acquired a survey compass.)
& What is the present variation of the needle in Concord?
The question concerning “the present variation of the needle in Concord” refers to difference between True North and Magnetic North that Thoreau typically included on the plots he made of his Concord area surveys, a process which Thoreau described in detail in his Field Notes of Land Surveys on Feb 7, 1851 on page 38.
For example Thoreau reported a Variation = 10’1/8W on his map of Oct. 3, 1853.
For a detailed description of how Thoreau measured the angular correction required between magnetic and geodetic north, see the discussion in chapter six of “Thoreau The Land Surveyor” by Patrick Chura. http://www.upf.com/book.asp?id=CHURA001
Charles Davies in the 1839 edition of his book points out that heat and cold affect the magnetic needle and that the same needle will at the same place indicate different line at different times of the day. The magnetic needle will continue to recede from the meridian as the day advances until about the time of highest temperature, when it will begin to return and at evening will make the same line as in the morning. This change is called the diurnal variation and varies during the summer season from one fourth to one-fifth of a degree.

Terminology references:
Traverse table operations: see p. 105 of Charles Davies “Elements of Surveying”
Traverse networks involved placing the survey stations along a line or path of travel, and then using the previously surveyed points as a base for observing the next point.
Balancing the survey see p. 109 of Davies
Fletcher’s question to Thoreau concerning methods for computing areas is indeed interesting, and two different methods for dong so are described in Davie’s book.
Thoreau’s had used gridded data for measuring the area of Isaac Watts’ Woodlot Nov. 1849.
Davies describes the use of traverse tables to estimate the area of a land parcel including corrections for surveyor error in the vector data plus procedures for traversing the survey perimeter as an error check.

An M.S. Excel spreadsheet shown below was used to organize, analyze and display vector data as per Davies for Wheeler’s Lot for the west meridian and then the east meridian:
  Untitled-1 copy

 Untitled-3 copy

Column A numbers each survey station as a separate row in the table.
Column B is reserved for entering a course designation for a survey line between two stations
In column C enter the bearing in degrees and minutes for each course
In column D enter the distance in chains and links for each course
In column E and F enter the difference in latitude N or S from the traverse table for each course
In columns G and H enter the departure E or W from the traverse table for each course
In columns I and J enter the balanced latitude N or s for each course
In columns K and L enter the balanced departure E or W for each course
In Column M enter the double meridian distance (DMD) for each course
In columns N and O enter the area+ or area – for each course
Traverse Table Data is shown in columns Q through U taken from Davies Handbook.
Column Q contains the course number
Column R contains the Station number
Column S contains the Bearing in degrees and minutes
Column T contains the Bearing latitude
Column U contains the Bearing departure

After entering all the distances in column D, compute the sum of the distance in chains
After entering all the differences in latitude and departure in columns E-H compute the sums for each column N+, S-, E+, W-
The latitude error is equal to the difference between N/S latitude sums and
The departure error is equal to difference between E/W departure sums
(Davies p. 109)
The half error in southing and easting is found by dividing each by 2
Column I and J balanced values are found by subtracting the half error values for each N/S latitude and E/W departure course values
The resulting sums for North-South sum of courses then are equal and balanced as are the East-West sums of courses
In doing so, we have distributed the differences between the outliers in the values for each course.

After the work has been balanced, we next calculate the Double Meridian Distance (DMD) of each course. (Davies p. 112)
For this purpose a meridian line is selected that passes through the most westerly station of the survey.
The West meridian is located at Station 6 and called the Principal Station and course 1 which begins at this point, the “first course”. It is marked with an asterisk (*)
Next we look for inconsistency in the data values by checking for equivalence when tracing the values when we attempt to link the values in a clockwise order. The linking process involves computing an estimated next value based upon the current, last, and next value in the sequence which should result in a complete return to the initial value in the chain if all entries are consistent. Due to the numerous values derived from various tables and calculations this is an essential step for quality control. It also is very time consuming to perform manually.
The following rules are used in computing the DMD for each course proceeding clockwise:
The DMD of the first course is equal to its departure = (1.46)
The DMD of the second course is equal to the DMD of the first course, plus its departure, plus the departure of the second course. (1.46 +1.46 -0.71 = 2.20)
The DMD of any course is equal to DMD of the preceding course, plus its departure, plus the departure of the course itself. (2.20 -0.71 +2.99 = 4.48) Course #3
(4.48 +2.99 -0.92 = 6.55) Course #4
(6.55 -0.92 +6.95 =12.58) Course #5
(12.58 +6.95 +0.07 = 19.60) Course # 6
(19.60 +0.07 +2.08 = 21.75) Course # 7
(21.75 + 2.08 -7.94 = 15.88) Course # 8
(15.88 -7.94 -3.97 = 3.97) Course # 9
The DMD of the last course should be equal to the departure of that course.
Note that the DMD value and the departure value for last course #9 is = 3.97 and thereby closing the loop.
A verification of the work is therefore obtained by comparing the DMD with the departure of the course.

Next we apply Davies rules for computing the area given the DMD of each course. Charles Davies in his book “Elements of Surveying & Navigation” (1846) describes a procedure for calculating land area on pages 110-114 .
1. Multiply the DMD of each course by its northing or southing, observing that like signs in the multiplicand and multiplier give plus in the product and unlike signs give minus in the product.
2. Place all the products that have a plus sign in one column and all the products that have a minus sign in another.
3. Add up the columns separately and take the difference: this difference will be double the area of the land.
Data for Wheeler’s Lot using Davie’s traverse tables results in a value = 267.44 Sq. Chains, = 13.37 A.
Thoreau reported 13A+112 Sq. Rods= 13.7A.
13.7-13.37= 0.33A diff
.33/13.7*100= 0.2A diff
. Tuttle’s estimate was 13+109.57/160 i.e. 13.6848 A. or 13.69A, almost same as Thoreau.

 

Unresolved questions:
On December 14, 1854, James Wetherbee Wheeler of Acton sold a tract of woodland reportedly containing 14.18A to John Fletcher and Cyrus Dole of Acton.
Who created the survey “minutes” and rough sketch describing Wheeler’s Lot before it was sold to Fletcher? Who provided the area measurement recorded with the lot sold by Wheeler to Fletcher?
I suspect Tuttle initially surveyed the nine points needed to establish the minutes and chain measurements for Wetherbee Wheeler.
From that Tuttle would have been able to create a crude sketch from which he estimated the total area by use of a grid to initially compute the area for Wheeler as 14.14A. That data could have been used as a basis for recording and selling Wheeler’s lot to Fletcher.
After Fetcher purchased the land, he may have asked for a second more accurate opinion about the lot area from Tuttle.
We do not know when Tuttle was initially contacted by Wheeler but it appears to be prior to Tuttle’s letter to Thoreau. Tuttle initially computed the area from a grid giving 14.13A. Subsequently Tuttle computed the area using traverse table area to be 13.69A. Tuttle clearly had an interest and experience in estimating the area of Wheeler’s lot by a variety of methods.
Shortly thereafter Thoreau estimated the area to be 13.70A.
Tuttle provided an estimate of 13.69A.using traverse table data, and he asked Thoreau what procedure he used to compute a value of 13.70A. Tuttle’s letter suggests he was aware of Thoreau’s interest in Wheeler’s lot area and seeking to compare results and procedures.
Thoreau implies that his estimate was calculated for Fletcher “from minutes furnished by him”, It is not known how Fletcher initially had obtained the minutes, possibly from Tuttle.
If Tuttle worked for Wheeler before he sold the property Tuttle may have computed the area and the minutes that appear on the deed that Fletcher acquired at the time of sale.
After the sale, Fletcher hired Tuttle to measure the property with greater accuracy at which time Tuttle computed the minutes from a field survey and computed the area. Fletcher then asked Thoreau for his opinion and gave Thoreau the minutes computed by Tuttle. Tuttle was aware of Davies’ procedures for measuring land.
Thoreau’s measurements always appear to have had at least one measurement finer than ¼ degree so they could not be used with Davies Traverse tables for measuring land areas. Thoreau’s measurements were to the precision of his instrument, not to the less precise requirements of Davies’ Traverse tables with angles no finer than ¼ degree.
Therefore, Thoreau’s field survey entry of Fletcher’s “wheeler’s Lot” for 12/22/54 was probably a description of Tuttle’s original data “from minutes furnished by him” i.e. furnished by Tuttle to Fletcher who furnished them to Thoreau. Thoreau was aware of Davies procedures and presumably could have applied them to compute the lot area with the coordinates he was given rather than coordinates he (Thoreau) had measured in the field. I doubt that the coordinates shown were measured by Thoreau.
Thoreau’s measurement of Fletcher’s lot by use of minutes is the only example I have found of a map attributed to Thoreau that would qualify for use of Davies traverse tables because all of Thoreau’s other maps included at least one coordinate measurement finer than ¼ degree increment, e.g. 1/8th, 3/8th, 5/8th, or 7/8th of a degree. Davie traverse data tables included coordinates only in ¼ degree increments.
The first example of a land survey by Thoreau that included survey coordinates appears to have been R. W. Emerson’s Woodlot and meadow by Walden Pond (that part contained within the Lincoln bounds) the woodlot being a part of what was known in 1746 as Samuel Heywood’s pasture “and deeded as such to his son Jonathan Taunier Surveyed March 1850 with unusual accuracy”. (Perhaps because this appears to be his first use an instrument that allowed Thoreau to record his coordinate’s measurements to 1/8th of a degree.)
http://www.concordlibrary.org/scollect/Thoreau_surveys/33.htm
Thoreau also notes the lot area to be13 Acres, 1.0 rods and 7 perches. (40 perch = 1 rod)
Although he obviously did not use Davies traverse tables, Thoreau may have plotted the area using a fine grid.
Tuttle’s letter to Thoreau indicates that Tuttle used Davie’s traverse table data but we cannot tell whether Thoreau used traverse table data or merely plotted a fine grid to estimate the Fletcher’s lot area.
As Tuttle said:
“Will you have the kindness to inform me by what method you computed the Lat in question: if by plotting to what scale your plan was drawn, or if by the traverse table whether you took out the distances in chains or rods & to how many decimal places you found the Lat & Dep of each course. What is your general method of computing areas?”
That is the question being asked of Thoreau by Tuttle.
Thoreau’s response is unknown.
If Thoreau were to use Davie’s traverse tables he would have needed to extrapolate values from the existing tables to be compatible with his measurements that included 1/8 degree values. Or Thoreau would have had to compute the traverse table values in a manner with which I am unfamiliar.
Thoreau and Tuttle worked jointly on one or more projects involving work by Thoreau in May 1859 and by Tuttle five years later in 1864.
see for example http://www.concordlibrary.org/scollect/Thoreau_surveys/150a.htm
The map was likely obtained from Tuttle and included in the Concord Public Library collection of Thoreau’s maps when they were assembled by his sister after Thoreau’s passing.
N.B. Notice the two parts of the survey with and without a 1/8th degree value as an indication of Thoreau’s and Tuttle’s contribution.(Thoreau’s work is on the north side of the road and Tuttle’s on the south.)
Thank Beth Witherell for suggesting and supporting this project.
Thank also Adrienne Donohue, Concord Museum Registrar & Collections Manager, for her assistance.
Thank the concord Free Public Library for providing space, equipment and access to Thoreau’s records.
The above comments will be posted on my blog, Thoreau’s Chronological Atlas http://aschmidt01742.wordpress.com/

Tuttle and Thoreau correspondence concerning “Wheeler’s Lot” 1854

Question:  What is Tuttle describing to Thoreau and asking Thoreau concerning Wheeler’s Lot?

Answer:  Tuttle is describing two different procedures he had used to measure the area of Wheeler’s lot and asking Thoreau’s opinion as well as Thoreau’s experience concerning a related issue of compass correction for magnetic variation in Concord.

Area measurement of a land parcel area was a common statistic provided by Thoreau for most of the lots that he surveyed from 1837-1860.   Many of the land parcels were described as “woodlots”.  An area measurement was used to calculate the amount firewood or building lumber and therefore dollar value that could be expected from a woodlot prior to its being cut.

According to a Surveyor’s Manual that was in Thoreau’s library (Davies, Charles “Elements of Surveying and Navigation”, 1846):See:

http://play.google.com/books/reader?id=KpVHAAAAIAAJ&printsec=frontcover&output=reader&hl=en&pg=GBS.PP5

There were two commonly used methods for computing land areas, given a map of known scale.

“1. Divide the existing map of land lots into geometric units (e.g. squares and triangles) and then compute the area of each of each and sum their total area.

2. From an existing map or field notes of the bearings and distances for each lot originally recorded with compass and chain, compute the area of each lot summing their total area.

(Both procedures were alluded to by Tuttle in his letter to Thoreau)

When using compass and chain there are two sources of error:

1st.  Inaccuracy of the surveyor’s field observations when recording of distance or angle.

2nd,. Local attractions or the derangement which a compass needle experiences when brought into the vicinity of iron-ore beds, or any ferruginous substances.

To guard against these sources of error, reverse bearing should be taken at every station: if this and the forward bearing are of the same value, the work is probably right; but if they differ considerably, they should both be taken again.

Differences between measurements taken in each direction also may be used to estimate “balancing” corrections.

THE TRAVERSE TABLE AND ITS USES

These tables which are included in the Davies book,  show the latitude (N-S) and departure (E-W) corresponding to bearings for each survey line segment expressed in degrees and quarters of a degree from 0 to 90°, and for every course from 1 to 100, computed to two decimal  places.

By use of these tables the latitude (angle) and departure (distance) of a course segment may be computed to any desired degree of accuracy.

Davies notes that given a surveyor’s field measurements describing the straight line segments defining the perimeter of a property boundary, it is possible to compute the area of the property in question and also create a graphic plot of its perimeter.

Tuttle’s Letter follows (with my comments in italics):

Made a very small plan of it about 2 rods (i.e. 33 feet) to an inch (scale)

An enlarged copy of a map can be made by use of a pantograph, see: http://en.wikipedia.org/wiki/Pantograph

Thoreau owned such a device currently on display in the Concord museum and shown on their website.

http://www.concordmuseum.org/henry-david-thoreau-collection.php

Within the Concord Museum Collection, go to: Catalog #:   TH0012E, Object Name:                Compass

I should judge & cast it up making 14 A 22 rods

(i.e. I manually drew an enlarged plot and divided it  into geometric units (e.g. squares and triangles)then  summed the area of each lot, resulting in an estimate of 14A 22 rods,.)

The plan was so small (& so unskillfully drawn) that I told Mr. W that very little reliance could be placed upon it in computing areas.

(I next computed the area using the compass and chain technique described by Davies.)

Since then I have computed the area several times by the aid of traverse tables

Finding the Lat & Dep both in chains & decimals of a chain & in rods & dec of a rod & obtaining answers

the bearing of the 3d course N 57 E & taking out the Lat & Dep in rods & decimals of a rod I made

the area to be 13a 109,57r. (resulting in an estimate of 13A 109.57 rods,.)

I find but little (,01 of a rod) diff between the Eastings & Westings & but ,19 of a rod between the

Northings & Southings. & in balancing the survey I subtracted the Diff between the North & Southings

from the Southing of the 7th course.

Will you have the kindness to inform me by what method you computed the Lat in question:

if by plotting to what scale your plan was drawn,

or if by the traverse table whether you took out the distances in chains or rods & to how many decimal places you found the Lat & Dep. of each course.

What is your general method of computing areas?

(i.e. Do you generally use the geometric units or the Compass and chain measurements?

We know from an review of Thoreau’s Land Surveys that he used both techniques beginning with geometric units and moving on to compass and chain once he had acquired a survey compass.

& What is the present variation of the needle in Concord?

The question concerning “the present variation of the needle in Concord” refers to difference between True North and Magnetic North that Thoreau typically included on the plots he made of his Concord area surveys, the procedure for which Thoreau described in detail in his Field Notes of Land Surveys on Feb 7, 1851 on page 38.

For example Thoreau reported a Variation = 10’1/8W on his map of Oct. 3, 1853.

Terminology references:

Traverse table operations: see p. 105 of Charles Davies “Elements of Surveying”

Departure ibid. p. 105

Balancing the survey see p. 109 of Davies

THE TRAVERSE TABLE AND ITS USES. ibid. p 19. This table shows the latitude and departure corresponding to bearings that are expressed in degrees and quarters of a degree from 0 to 90°, and for every course from 1 to 100, computed to two places of decimals. The following is the method of deducing the formulas for computing a traverse table; by means of these formulas and a table of natural sines, the latitude and departure of a course may be computed to any desirable degree of accuracy. P.105

Traverse (surveying)

Traverse is a method in the field of surveying to establish control networks. It is also

used in geodetic work. Traverse networks involved placing the survey stations along a

line or path of travel, and then using the previously surveyed points as a base for

observing the next point. Traverse networks have many advantages of other systems,

including:

1.  Less reconnaissance and organization needed.

2.  While in other systems, which may require the survey to be performed along a

rigid polygon shape, the traverse can change to any shape and thus can

accommodate a great deal of different terrains.

3.  Only a few observations need to be taken at each station, whereas in other survey

networks a great deal of angular and linear observations need to be made and considered.

4.  Traverse networks are free of the strength of figure considerations that happen in triangular systems.

5.  Scale error does not add up as the traverse is performed.

http://www.hbp.usm.my/hilmy/traverse.pdf

Fletcher’s question to Thoreau concerning methods for computing areas is indeed interesting, and two different methods for dong so are described in Davie’s book.

Balancing   the survey’s 7th course to which he refers likely reflects the fact that the 7th course is also the longest at 12.81 chains of the 9 courses and potentially subject to variation over its length compared to other shorter courses.

Although both Thoreau and Wheeler arrive at approximately the same area measurement value i.e. 13.7 A and 13.5 A respectively, Davies procedure for area measurement suggests a more precise value to be 13.45 A.

Wheeler’s first measurement by casting up or enlarging a small map and then summing a grid overlay resulted in a value of 14A+22R. = 14.13A

Wheeler’s second measurement applying Davies’ procedures produced 13A+109.57R=13.68A

Thoreau’s measurement of 13+112R = 13.70 may have been derived from the work done by Wheeler, we will never know but Thoreau and Wheeler reported the same value and both are different from Davies’ presumed correct value by an identical amount.

The reason for the approximately 2% difference I suspect is due to the time required to carry out Davies procedures manually with pencil, paper, traverse tables and logarithms rather than computers and spreadsheets.

Although additional precision was possible the 98% accuracy level was adequate.

If Thoreau ever responded to Wheeler we do not have a copy.

Thoreau may have accepted Wheeler’s measurements and included them in his Field Notes of Surveys.

T said 13A + 112R = 13.7A, a difference of only +2R more than Wheeler but +40R over Davies

13.7A-13.45A=.25A        .25/13.45=.018 =+1.8% T greater than D

W said 13A + 110R = 13.68A

D said 13A +72R = 13.45A

Note: R = 1 square rod, 160 R = 1 A

Tuttle December 22, 1854

-6.66Letter from William Davis Tuttle to Thoreau dated December 22, 1854

Area of Wheeler Lot initially measured by Tuttle on an enlargement by plotting produced 14 A. 22R.

Area of Wheeler’s Lot subsequently measured by Tuttle using traverse table produced smallest value of 13A 11.9 R plus other values up to 13A 106.5 R.

Thoreau calculated the area of John Fletcher’s of Acton,” Wheeler Lot” from minutes  furnished by Fletcher, Dec. 22, 1854 and who estimated the area to be 13A 112 R.

Tuttle’s initial estimate by plotting = 14A 22R.

Tuttle’s several estimates by traverse table range from 13A 11.9R to 13A 109.57R.

Thoreau’s estimate calculated from minutes = 13A 112R. (largest of Traverse estimates)

Davies’ traverse table procedure says area correct value = 13A 72R.  See: https://docs.google.com/spreadsheet/pub?key=0AroG1WG-7zJ-dDN2emNRWGF0UDdJQk9WeUZLQkM4bEE&output=html

Thoreau’s area estimate is 1.8% or a quarter acre greater than Davies’.

Note that resulting Thoreau’s estimate of 13A 112R is within 98.2% of Davies rules as described by him and incorporated in an Excel spreadsheet above.

The data Thoreau used from Davies Tables are only given to two decimal places.

Thoreau could not assume greater precision in his result than in his data and if he were to compute all of the values required by Davies Rules it would be time consuming process involving pencil, and paper,  reference tables,  and logarithm tables.

I assume Thoreau had many other interests he pursued and the time required to compute the Area value to an additional decimal that required would not be warranted.

Davies’ tables were only given for quarter angle increments and would not have been applicable to most of Thoreau’s because every survey with exception of the Wheeler Lot shown above that involve a quarter angle specification by Thoreau in the Bearing specification.

However Thoreau may have computed the values required using the same equations Davies used in preparing the tables.

Measurements with chains were said to be precise to plus or minus one link in 100 (the length of the chain). I.e. 1 %

Credits for the above research project go to Beth Witherell witherell@library.ucsb.edu who suggested and funded the project.

Concord, April 6, 1840

“Dear Haskins,

I improve this the first opportunity by sending your cloak by the Accommodation Stage.

…..

Yours,

Henry D. Thoreau”

 Ref. The Correspoondence, Volume 1: 1834-1848, page 65

The Writings of Henry D. Thoreau

2013

Princeton University press

Note:

The Concord Accommodation Stage made the seven hour round trip between Concord and 11 Elm Street, Boston, each day.

In his A History of the Town of Concord, Lemuel Shattuck wrote, “Public Stages were first run out of Boston into the country through Concord, in 1791, by Messrs. John Vose & Co. There are now (1833), on an average, 40 stages which arrive and depart weekly, employing 60 horses between Boston and Groton, and carrying about 350 passengers; 150 have passed in one day.” William Shepherd (owner of Shepherd’s Hotel on Main Street) ran a line of stages between Concord and Boston from 1817. Stages also stopped at the Middlesex Hotel.

The railroad came to Concord in 1844. Until train travel became the dominant form of transportation, stagecoach lines and the hotels that served them did good business here.

 

A copy of “ John Fletcher Acton Mass area of his “Wheeler Lot” calculated from measurements furnished by him.  Dec 22, 1854 (includes sketch)” has been posted in the online edition of Thoreau’s Illustrated Atlas.

103

Thoreau perambulated Concord’s 1851 boundaries as required by the Commonwealth since 1692.

 

In October 1, 1860 Thoreau reported the results for his  ” Measured Area of Concord, Carlisle, Lincoln, Boxborough, Acton, Littleton, Stow, Bedford”

See : http://www.concordlibrary.org/scollect/Thoreau_Surveys/23.htm

It also appears as Gleason’s zone # 23 in Thoreau’s Illustrated Atlas

See:  http://allanhschmidt.wordpress.com/page/2/

The above url begins with January 1860 surveys. 

To find the October 1 map for Thoreau’s map of Concord Town boundaries with adjacent towns the reader must scroll through the 1860 survey map set.

The above notes help explain the context of a recent inquiry:

 

From Juilien Negre to Allan Schmidt:

 

Julien NEGRE

September 30th 2013 at 08:56

Hello Allan,

 

I am doing some research into the history of the “perambulation” of Concord’s boundaries (in which Thoreau took part in September, 1851). I am trying to determine if it was an annual duty and when it was suspended (I am assuming it is no longer performed nowadays!). Do you have any information on the subject or could you suggest a source where I could learn more? Thank you very much!

 

Julien Nègre

Paris Diderot University – France

 

Allan Schmidt

September 30th 2013 at 15:12

Hello Julien,

 

Thoreau’s 1851 “perambulation” of Concord’s boundaries i.e. perform an official inspection of (a boundary) on foot was likely a one-time event that took place when the town’s boundaries were changing as Concord expanded and contracted its various parts in relation to surrounding towns.

The only reason to walk the boundary would be to inspect the physical boundary markers.

Once the boundaries had been established and mapped by Thoreau or some other surveyor each adjacent town would share a common legal description of their boundaries.

I hope this is of help to you.

Regards,

 

Allan H. Schmidt

 

allanhschmidt.wordpress.com

 

Julien NEGRE

Julien NEGRE

October 1st 2013 at 06:28

Allan, thank you for your answer. Actually I received an answer from the Concord Town Clerk who explained that the perambulation is still required by Massachusetts State Law and has to be performed at least every 5 years! The selectmen or their designates usually drive or hike to the markers and then send a formal letter to the neighboring towns. The procedure has been part of the law in Massachusetts since 1692 (with several amendments). A very old and fascinating history. Thank you for your help.

Best regards,

 

Julien

 

Friday July 12, 2013, 1-2:30 PM, CFPL

Welcome to Workshop V, of the Thoreau Society’s 2013 Annual Conference

Thoreau’s Illustrated Atlas Project

(A continuation of my 2012 talk http://allanhschmidt2.wordpress.com/)

 

1. Thoreau’s exposure to surveying courses at Harvard (then and now)

During his initial year (1833) at Harvard College, Henry Thoreau was subjected to a “thorough course” of “Plane Trigonometry, Analytic Geometry, and Algebra with practical application to Heights and Distances, and Surveying and Navigation.”

This course on navigation is still being offered and happens now to be the longest continuously running subject-matter offered there! “It’s the most practical course you can take at Harvard,”

According to Dan Justicz ’91, alum, “You find your way by watching the movements of the sun and stars. You even construct your own navigation instruments. There’s a minimum of lecturing.”

Harvard Catalog 2013

Astronomy 2 – Celestial Navigation (2179)

Faculty of Arts and Sciences    Fall 2012-2013

Philip M. Sadler

S M T W T F S

Tuesday 11:30 a.m. – 1:30 p.m.; Tuesday 11:30 a.m. – 1:30 p.m.; Tuesday 7:00 p.m. – 10:00 p.m.; Tuesday 7:00 p.m. – 10:00 p.m.

Description: Never be lost again! Find your way on sea, land, or air by employing celestial and terrestrial techniques. Acquire expertise in using navigators’ tools (sextant, compass, and charts) while learning the steps to the celestial dance of the sun, moon, stars, and planets. This 108-year-old course (1905?) continues to rely on practical skills and collaborative problem-solving, while utilizing historical artifacts (instruments, maps, captains’ logs) and student-built devices. Culminating in a day-long cruise to practice navigation skills.

Credits: Half course

Location: Observatory A Building A-101, Observatory D Building Phillips Auditorium

2. Thoreau Surveying while living at Walden Pond (1845-1846)

http://www.concordlibrary.org/scollect/Thoreau_surveys/133a.htm

http://www.concordlibrary.org/scollect/Thoreau_surveys/133b.htm

map orientation

http://www.concordlibrary.org/scollect/Gleason/Map_Large.jpg

3. Thoreau visits Brister’s Spring while traveling to Walden Pond

https://aschmidt01742.wordpress.com/2009/04/24/how-could-thoreau-not-have-known-or-did-he/

4. Thoreau’s trails and t-rails to Walden Pond

http://aschmidt01742.wordpress.com/2007/11/09/how-%E2%80%9Cthoreau%E2%80%99s-t-rail%E2%80%9D-got-its-name/

5. Surveying textbooks in Thoreau’s library include 1852 edition of Charles Davies Element of Surveying

http://books.google.com/books/reader?id=nJw9AAAAYAAJ&authuser=0&printsec=frontcover&output=reader&pg=GBS.PP3

Harvard 1851 edition originally published 1830; copy in CFPL is 1852 from Thoreau’s library

6. Thoreau’s surveying work after Walden Pond

http://allanhschmidt.wordpress.com/

7. Thoreau’s Field Notes of Surveys 1849-1861

http://allanhschmidt01742.wordpress.com/

Over 100 Land building Surveying products created by Thoreau 1839-1861

1. Isaac Watt’s Woodlot

http://www.concordlibrary.org/scollect/Thoreau_surveys/135.htm

3. Emerson’s Woodlot & Meadow

http://www.concordlibrary.org/scollect/Thoreau_surveys/33.htm

7. Sawmill Brook

http://www.concordlibrary.org/scollect/Thoreau_surveys/34.htm

8. Haverhill

http://www.concordlibrary.org/scollect/Thoreau_surveys/30.htm

10. Yellow House Lot

http://www.concordlibrary.org/scollect/Thoreau_surveys/129.htm

13. Daniel Shattuck Cottage

http://www.concordlibrary.org/scollect/Thoreau_surveys/108.htm

32. Barns

http://www.concordlibrary.org/scollect/Thoreau_surveys/80a.htm

http://www.concordlibrary.org/scollect/Thoreau_surveys/80b.htm

http://www.concordlibrary.org/scollect/Thoreau_surveys/80c.htm

http://www.concordlibrary.org/scollect/Thoreau_surveys/80d.htm

87. Lead pipe

http://www.concordlibrary.org/scollect/Thoreau_surveys/84.htm

91. 94.  John B. Moore

http://aschmidt01742.files.wordpress.com/2010/09/survey-feb081853.jpg

http://www.concordlibrary.org/scollect/Thoreau_surveys/94a.htm

04/1860 John B. Moore

http://www.concordlibrary.org/scollect/Thoreau_Surveys/94b.htm

05/1860 Concord River

http://www.concordlibrary.org/scollect/Thoreau_surveys/107a.htm

(see below)

10/1860 Multi-town

http://www.concordlibrary.org/scollect/Thoreau_Surveys/23.htm

(see below)

8. Bronson Alcott suggests creation of an Illustrated Atlas by Thoreau according to Marcia Moss’ Catalog of Thoreau Surveys” published by the Thoreau Society as Booklet 28, Genesco New York, 1976

http://allanhschmidt1.files.wordpress.com/2012/03/mossbinder1.pdf

9. Louisa May Alcott negotiates purchase of Thoreau residence after his death

https://aschmidt01742.wordpress.com/2011/05/21/a-chronology-of-john-thoreau%E2%80%99s-yellow-house-lot-so-called-its-purchase-by-louisa-may-alcott/

10. Today’s trails to Walden Pond 

Town Forest Trail Map

 Amble Opening Invitation and Map (1)_Page_2

11. Map design for walkers today

NYC Pedestrian maps URL http://www.nytimes.com/2013/06/25/nyregion/cant-find-north-new-york-pedestrian-maps-are-coming.html?emc=eta1

12. Thank TS (Mike Frederick) Thoreau Society and CFPL (Leslie Wilson the CFPL Special Collections Curator, & Caroline Nie, Head CFPL, Technical Services/Technology, and their staff for their resources and support.

Bio: 

Allan H. Schmidt formerly Executive Director of the Harvard Laboratory for Computer Graphics and a specialist in research, development and use of geographic information systems recently has explored the application of such technology to historical data.  He also serves as Chairman of The Mill Brook Task Force, a subcommittee of Concord’s Natural Resources Commission.

2013-05-27 # 2 Wild Calla, Everett's Meadow by Cambridge Turnpike. Concord MA JWB 2013-05-27 # 1 Wild Calla, Everett's Meadow by Cambridge Turnpike. Concord MA JWB 2013-05-27 # 1 Wild Calla, Everett's Meadow by Cambridge Turnpike. Concord MA JWB (1)

Wild Calla lilies in the Mill Brook

http://eol.org/pages/1088272/details

Wild Calla lilies currently are blooming in a tributary of the  Mill Brook along the west of side Cambridge Turnpike extending from the eastern entrance to the Concord Town Forest Trail network south toward Hawthorne Lane.

These rare native flowers are in danger of being lost due to current Cambridge Turnpike reconstruction activities and need to be recognized and protected by the Town of Concord.

J. Walter Brain made the discovery and recorded the images shown:

2013-05-27 # 4 Wild Calla, Everett's Meadow by Cambridge Turnpike. Concord MA JWB

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