In researching information related to *The Practical Surveyor*, the
following institutions were helpful.

- The New York State Library, for the first and second editions of Wyld's book on microfilm, and for the use of various other reference materials.
- The Boston Public Library, for allowing
access to a first edition of
*The Practical Surveyor*in their Rare Books room. - The Rensselaer Polytechnic Institute Library, for general reference and a somewhat battered fourth edition of the book.
- The New York State Museum, for access to the Charles E. Smart collection of surveying instruments.

In Mr. Wyld's book, he provides a first-order Taylor series expansion to approximate the effects of the Earth's curvature on level measurements. In this formula, the radius of the Earth is taken to be a value of 3992 miles. This is neither the modern value nor exactly any of the values that were calculated by geodecists that preceded Samuel Wyld. Although it is possible the Mr. Wyld produced this formula himself, I believe it to be more likely that he copied it from another source. I would like to locate the original source and the original radius measurement.

In modern geodesy, the Earth is approximated as an oblate spheroid, also referred to as an ellipsoid. The WGS1984 ellipsoid uses an equatorial radius of 6378137 meters (3963.19 miles), and a polar radius of 6356752 meters (3949.90 miles). Historically, although the Earth was suspected of not being spherical, no measurements had yet been made with sufficient accuracy to verify in what way it varied from a sphere.

As of 1725, there had been many different measurements of the length of an arc along the surface of the Earth. These ranged from rough calculations of the ancient Greeks. to the careful work of Cassini. The table below was calculated by converting the arc measurements to a radius in miles.

Geodicist | Location | Year | Radius (miles)Stone |
Radius (miles)Butterfield |
---|---|---|---|---|

Eratosthenes | Egypt | 230 B.C. | 3795.8 | 4608.9 |

Posidonius | Egypt and Rhodes | 100 B.C. | 4389.4 | |

Abelseda | Arabia | 827 | 3804.6 | |

Albazen | Arabia | 1100 | 3774.4 | |

Fernal | France | 1528 | 4006.9 | |

Snell | Holland | 1617 | 3789.8 | 3823.3 |

Norwood | England | 1635 | 3984.6 | 3984.6 |

Ricolli and Firmaldi | Lombardy | 1658 | 4265.9 | |

Picard | France | 1669-1672 | 3957.6 | 3959.3 |

Cassini | France | 1681-1718 | 3984.2 | 3961.9 |

3952.4 |

These values were calculated based on the information in two very
different books. The first column is from the Appendix of *The
Construction and Principal Uses of Mathematical Instruments* by Edmund
Stone, printed for J. Richardson in Pater-Noster Row, London in 1758. The
second column is from *A History of the Determination of the Figure of the
Earth from Arc Measurements* by Arthur D. Butterfield, published by the
Davis Press in Worcester, Massachusetts in 1906. Despite the later work's
seemingly learned study of geodesy, I suspect Mr. Stone's to contain the
more accurate account of the geodetic measurements. The differences are
attributed to conversion between different units. For example, Butterfield
cites that the length of an Arabian mile is unknown, whilst Stone states that
an Arabian mile is 6000 Arabian feet, each of which is the length of 96
barley-corns, and he finds that 23 barley-corns is equal to three English
inches.

As the table shows, none of the measured values match the value used in formula used by Mr. Wyld. Since one of the attractions to the formula is its simplicity (it is easy to calculate by hand), it is likely that the radius of the earth was rounded to a convenient value for ease of calculation. It is still quite accurate for any distance that a surveyor is likely to need.

Although I have not proved it, based on the vintage of the astronomical tables (see below), I suspect that the formula for calculating the effects of curvature were originally based on Norwood's measurements.

*The Practical Surveyor* includes astronomical tables so that true
north can be found using Polaris. Due to the relative motion of the stars,
any astronomical tables will eventually become out of date. However, these
tables appear to have been crafted for the year 1656 (give or take a few
years). This suggests that they were copied verbatim from another work.

The year of the original tables and the set of modern astronomical tables were computed with the aid of Steve Moshier's Astronomical Ephemeris Calculator. Due to the limited precision of the original tables, the exact year isn't certain.

There are several surveying books from around 1656. My intent is to
eventually track down some of these books and check if they are an earlier
source of these tables. I know that the information was not taken from
William Leybourn's *Planometria* of 1657, as that work does not contain
any astronomy.

Samuel Wyld's book ran through seven editions in the course of 55 years.
It was distributed in both Britain and America. There are at least two
references to the book in the *Viginia Gazette*. It is mentioned on
both November 25, 1775 and December 30, 1775 as a part of "A Catalogue of
BOOKS for Sale by Dixon and Hunter at the Printing-Office, at a very low
Advance, for ready Money." In both cases, *The Practical Surveyor* is
listed alphabetically by author in the section of Octavos. John Dixon and
William Hunter were the publishers of the *Viginia Gazette*.

Several people aided me in the research for the Notes that accompany
*The Practical Surveyor*. I thank William J. Manthey and James Lynch
for help with translating the Latin phrases, Reb Manthey for continual
encouragement and helpful suggestions, and the people at the Invisible
College Press for making the printing process easy.

- David Manthey

The Practical Surveyor · by Samuel Wyld · with Notes by David Manthey

ISBN 1-931468-06-0 · Copyright © 2001 by David Manthey ·
6x9", 244 pages.

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