# The Practical Surveyor

## Research

### Institutions

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

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.

Stone
Butterfield
EratosthenesEgypt230 B.C.3795.84608.9
PosidoniusEgypt and Rhodes100 B.C.4389.4
AbelsedaArabia8273804.6
AlbazenArabia11003774.4
FernalFrance15284006.9
SnellHolland16173789.83823.3
NorwoodEngland16353984.63984.6
Ricolli and FirmaldiLombardy16584265.9
PicardFrance1669-16723957.63959.3
CassiniFrance1681-17183984.23961.9
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.

### Tables of Measure

On the second and third pages of The Practical Surveyor, there are four tables. All of these match tables in the eighth edition of Geodæsia by John Love, published in 1768. At least three of these tables are in the second edition of Geodæsia, published in 1715. Additionally, a few sentences in Chapter 7, Sect. 3 also match text in Geodæsia. It is possible that both books copied the tables from another work.

### Astronomy

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.