Things that I have found quite interesting

Measuring the World


“Weights and measures may be ranked among the necessaries of life to every individual of human society.
They enter into the economical arrangements and daily concerns of every family.
They are necessary to every occupation of human industry; to the distribution and security of every species of property; to every transaction of trade and commerce; to the labors of the husbandman; to the ingenuity of the artificer; to the studies of the philosopher; to the researches of the antiquarian; to the navigation of the mariner, and the marches of the soldier; to all the exchanges of peace, and all the operations of war.
The knowledge of them, as in established use, is among the first elements of education, and is often learned by those who learn nothing else, not even to read and write.
This knowledge is riveted in the memory by the habitual application of it to the employments of men throughout life.”

JOHN QUINCY ADAMS - Report to the Congress, 1821


Many early measuring systems were based on the use of parts of the body and man's natural surroundings as measuring instruments.
Ancient Indian measurements related to the body are correlated to the finger measure of 1⅜ inch.
This measure is found throughout the human body in increments.
It is the measure used to build ancient temples and is precisely related to the Indus Valley measuring devices.

Early Babylonian and Egyptian records and the Bible indicate that length was first measured with the forearm, hand, or finger.
When it was necessary to compare the capacities of containers such as gourds or clay or metal vessels, they were filled with plant seeds which were then counted to measure the volumes.
When means for weighing were invented, seeds and stones served as standards.

For instance, the carat, still used as a unit for gems, was derived from the carob seed.
Carob seeds in the pods are of such uniform size and weight that they were used by ancient peoples as a measure for precious metals and stones.
We still use the name carat today for valuation of gold and diamonds.

The carob plant

The Egyptian cubit and the Mesopotamian cubit were used in the 3rd millennium BC and are the earliest known units used by ancient peoples to measure length.
The common cubit was the length of the forearm from the elbow to the tip of the middle finger.

An Egyptian cubit measuring rod

It was divided into the span of the hand (one-half cubit), the palm or width of the hand (one sixth), and the digit or width of the middle finger (one twenty-fourth) and the span or the length between the tip of little finger to the tip of the thumb.

Here is my absolute favourite among many available diagrams showing the relationship between different systems of measurement.


Just look at the names!
Barleycorn, peppercorn, nail, palm, pace, finger, spindle......
There is material for a few articles there!

In this article I want to think about the chain, first invented in 1620 and still in use today.

GUNTERS CHAIN is a measuring device still used for land survey.
It was designed and introduced in 1620 by English clergyman and brilliant mathematician Edmund Gunter (1581–1626), long before the development of the theodolite and other more sophisticated equipment, enabling plots of land to be accurately surveyed and plotted, for legal and commercial purposes.


Edmund Gunter (1581 – 1626), of Welsh descent, was born in Hertfordshire.
He was educated at Westminster School, and in 1599 was elected a student of Christ Church, Oxford.
He took orders, became a preacher in 1614, and in 1615 proceeded to the degree of bachelor in divinity.
Mathematics, particularly the relationship between mathematics and the real world, was the one overriding interest throughout his life.
In 1619 the wealthy but earnest Sir Henry Savile put up money to fund Oxford University's first two science faculties, the chairs of astronomy and geometry.
Gunter applied to become professor of geometry but Sir Henry was famous for distrusting clever people, and Gunter's behavior annoyed him intensely.

As was his habit, Gunter arrived with his sector and quadrant, and began demonstrating how they could be used to calculate the position of stars or the distance of churches, until Savile could stand it no longer.

"Do you call this reading of Geometric?" he burst out. "This is mere showing of tricks, man!" and, according to a contemporary account, "dismissed him with scorne."

He was shortly thereafter championed by the far wealthier Earl of Bridgewater, who saw to it that on 6 March 1619 Gunter was appointed professor of astronomy in Gresham College, London.
This post he held till his death.


Gunter is principally renowned for developing a metallic measuring chain made up of 100 links.
These, the chain and the link, have become units of their own.


Gunter’s chain is equal to 4 rods, 22 yards, 66 feet, 1⁄80 of a mile or 20.1168 metres.
A rectangular area with edges of one chain and one furlong (10 chains) respectively (ten square chains) is one acre, therefore the chain is sometimes called an acre-breadth.
The length of a cricket pitch ( exactly 22 yards ) is based on this dimension.

Gunter's metal chain is divided into 100 links, marked off into groups of 10 by brass rings with tags which simplify intermediate measurement.
Each link is 7.92 inches long, with 10 links making slightly less than 6 feet 8 inches.
The full length of the chain is 66 feet.
Here you see the tags


Gunter's measuring chain was uniquely able to reconcile two seemingly incompatible systems: the traditional English land measurements, based on the number 4, and the newly introduced system of decimals based on the number 10.
Because an acre measured 10 square chains in Gunter's system, the entire process of land measurement could be computed in decimalized chains and links, and then converted to acres by dividing the results by 10.


The method of surveying a field or other parcel of land with Gunter's chain is to first determine corners and other significant locations, and then to measure the distance between them, taking two points at a time.
Two people are needed; the surveyor is assisted by a chainman.
A ranging rod (usually a prominently coloured wooden pole) is placed in the ground at the destination point.
Starting at the originating point the chain is laid out towards the ranging rod, and the surveyor then directs the chainman to make the chain perfectly straight and pointing directly at the ranging rod.
A pin is put in the ground at the forward end of the chain, and the chain is moved forward so that its hind end is at that point, and the chain is extended again towards the destination point.
This process is called ranging, or in the US, chaining; it is repeated until the destination rod is reached, when the surveyor notes how many full lengths (chains) have been laid, and he can then directly read how many links (one-hundredth parts of the chain) are in the distance being measured.
The whole process is repeated for all the other pairs of points required, and it is a simple matter to make a scale diagram of the plot of land.
The process is surprisingly accurate and requires only very low technology.

Surveyors at work 1865

Although Gunter's chain was later superseded by the steel tape, (a form of Tape measure), its legacy was a new unit of length called the chain, which measured 66 feet (or 100 links).
This unit still exists as a location identifier on British railways, as well as in some areas of Australia and America.
In the United States, for example, Public Lands Survey plans are still published in the chain unit to maintain the consistency of a two-hundred-year-old database.

The steel tape which largely replaced the chain, although it remains a recognised unit of length


With Gunter's name are associated several useful inventions, descriptions of which are given in his treatises on the Sector, Cross-staff, Bow, Quadrant and other instruments.

Gunters Quadrant

He contrived his sector about the year 1606, and wrote a description of it in Latin, but it was more than sixteen years afterwards before he allowed the book to appear in English.
In 1620 he published his Canon triangulorum.
In 1624 he published a collection of his mathematical works.
It was entitled "The description and use of sector, the cross-staffe, and other instruments for such as are studious of mathematical practise."


One of the most remarkable things about this book is that it was written, and published, in English not Latin.

"I am at the last contented that it should come forth in English," he wrote resignedly, "Not that I think it worthy either of my labour or the publique view, but to satisfy their importunity who do not understand the Latin yet were at the charge to buy the instrument."

It was a manual not for cloistered university fellows, but for sailors and surveyors in the real world.
There is reason to believe that Gunter was the first to discover (in 1622 or 1625) that the magnetic needle does not retain the same declination in the same place at all times.
By desire of James I he published in 1624 "The Description and Use of His Majesties Dials in Whitehall Garden," the only one of his works which has not been reprinted.
He was first to coin the terms cosine and cotangent.

Gunter's scale or Gunter's rule, generally called the "Gunter" by seamen, is a large plane scale, usually 2 feet (0.61 m) long by about 1½ inches broad (600 mm by 40 mm), and engraved with various scales, or lines.

On one side are placed the natural lines (as the line of chords, the line of sines, tangents, rhumbs, etc.), and on the other side the corresponding artificial or logarithmic ones.
By means of this instrument questions in navigation, trigonometry, etc., are solved with the aid of a pair of compasses.
It is a predecessor of the slide rule, a calculating aid used from the 17th century until the 1970s.


An excellent description of the use of the chain is given in ‘A Complete Treatise on Practical Land-surveying’ published in 1837 (Designed chiefly for the use of schools and private students) from which the following extracts are taken.

Victorian surveyors with equipment, including Gunters Chain


Chains, when new, are seldom a proper length; they ought always, therefore, to be examined; as should those, likewise, which are stretched by frequent use.

Note 1. In folding up the chain, it is most expeditious to begin at the middle, and fold it up double.
When you wish to unfold it, take both the handles in your left-hand, and the other part of the chain in your right; then throw it from you, taking care to keep hold of the handles.
You must then adjust the links before you proceed to measure.

Note 2. Chains, which have three rings between each link, are much better than those which have only two, as they are so apt to twist.
In addition to the instruments already described, you must provide ten arrows, each about a foot in length, made of strong wire, and pointed at the bottom.
These should be bent in a circular form at the top, for the convenience of holding them, and a piece of red cloth should be attached to each, that they may be more conspicuous among long grass, etc.

Let your assistant or chain-leader take nine arrows in his left-hand, and one end of the chain with one arrow in his right; then, advancing towards the place directed, at the end of the chain, let him put down the arrow which he holds in his right-hand.
This the follower must take up with his chain-hand, when he comes to it; the leader, at the same time, putting down another at the other end of the chain.
In this manner he must proceed until he has put down his tenth arrow; then, advancing a chain farther, he must set his foot upon the end of the chain, and call out, “change”.

The surveyor, or chain-follower, must then come up to him, if he have no offsets to take, and carefully count to him the arrows; and one being put down at the end of the chain, proceed as before, until the whole line be measured.
Each change ought to be entered in the field-book, or a mistake of 10 chains may happen, when the line is very long.
The chain-follower ought to be careful that the leader always puts down his arrow perpendicularly, and in a right-line with the object of direction; otherwise the line will be made longer than it is in reality.

The follower may direct the leader by the motion of his left-hand; moving it to the right or left, as circumstances require, and always placing his eye and chain-hand directly over the arrow which is stuck in the ground.
The leader likewise, as soon as he has put down his arrow, ought to fix his eye upon the object of direction, and go directly towards it.
This he may easily effect by finding a tree or bush beyond the station to which he is going, and in a straight line with it and himself.

In hilly ground, if the follower lose sight of the mark towards which he is going, he must stand over his arrow; and the leader must move to the right or left, till he sees the follower in a direct line between himself and the mark from which they last departed.

If the surveyor can conveniently procure two assistants, the one to lead the chain and the other to follow it, it will be much to his advantage; as he will thus be left at liberty to take offsets, note down dimensions, etc. without loss of time.

A team of land surveyors in America. The young man in central right position is carrying the chain.

GUNTER COMPARATIVES (look at the diagram above)
1 Link = 7.92 Inches
100 Links = 1 Chain = 66 feet = 22 yards
10 Chains = 1 Furlong = 40 Poles (linear measure)
8 Furlongs = 1 Mile

Units of Area (English)
1 Acre = 10 Square Chains i.e. 10 chains by 1 chain
1 Rood = One quarter of an acre 1
Perch (pole or Rod) = One fortieth of a Rood

Amazing , to think that Gunter's Measures are still in use today!

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