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Roy's Roads. Linked information
Circumferentor
It is not known which type of measuring chain was used for the military survey, but we know it was not the Ramsden Chain (Engineers' Chain: 100 ft) since that was commissioned by Roy himself, later in his life.
It seems very likely therefore that the instrument used was Gunter's Chain. This device was invented in 1620 and was in universal use from the 17th to the 19th centuries as the main measuring tool for land survey. It was employed extensively through the Americas, India and Australia as the empire expanded.
Gunter was a 17th century clergyman and mathematician. His invention was ahead of its time. In his day a long rod (or Pole) had been used to measure out land and compute area. This was of of Roman origin. It had had been standardised and we now know it was 16.5 feet long. It was cumbersome and unwieldy. So Gunter constructed a linked chain which was 4 Poles in length and thereby much more useful. It could be folded and carried. The key element was that the chain had 100 links; he further determined that 10 chain lengths would henceforth equal one furlong.
Lengths could be summed in furlongs and expressed to three decimal points: simplicity for anyone measuring long distance. Furthermore a strip one furlong long and one chain wide would be set to be one acre. Thus an acre could be divided into ten square chains. This, then, was the first decimal system, 150 years ahead of its time.
A Chain happens to be 22 yards long, and a furlong was one eighth part of a mile, but these conversions were of little relevance. All distances and areas could be expressed in furlongs , chains and links. It is interesting that a cricket pitch is 22 yards long and many road widths and block-lengths in erstwhile colonies are also 22 yards wide. Each link in a chain was about 8", this being the smallest unit of land measured length. On a Gunter's Chain there is a small metal label called a Tally, which denotes each 10 links: hence the phrase "tally-up".
The chain was operated by two 'chain men' who stretched it as tightly as possible and inserted serial pegs on the outer border of the handle. They attempted to keep it as level as possible but there were well used calculations to compensate for inclines and offsets.
Distance EF (the offset) = CD(sin c)(sin d)/ sin (c+d).
Roy had no optical device for measuring angles, but relied on a 'gun sight' on the circumferentor. The angles would be very inaccurate. Furthermore, a single simple chained-measurement of distance ( CD) lacks precision and would have compounded the error. Despite this, the time and effort saved would be incalculable. However "closing the traverses" was necessary before the return to base: this was the process by which surveyed material from adjacent traverses was linked together, probably in a loop. This loop process would have imposed a measure of control. It is probable that the locations of shared features, measured from both traverses, would have been pivotal to these adjustments.
Roy had no optical device for measuring angles, but relied on a 'gun sight' on the circumferentor. The angles would be very inaccurate. Furthermore, a single simple chained-measurement of distance ( CD) lacks precision and would have compounded the error. Despite this, the time and effort saved would be incalculable. However "closing the traverses" was necessary before the return to base: this was the process by which surveyed material from adjacent traverses was linked together, probably in a loop. This loop process would have imposed a measure of control. It is probable that the locations of shared features, measured from both traverses, would have been pivotal to these adjustments.
The Circumferentor was an early theodolite. It was a large compass with a swivelling dial. A metal gunsight groove was used for sighting on distant objects or on progress lines. The dial could be adjusted to record a bearing from magnetic north and then to determine the angles to sighted objects. The instrument was mounted at eye-level on a pole; a ball-and-socket joint eased the swivel. It was a very innacurate instrument
The triangulation calculation, which invokes the sine rule, had been understood for more than 2000yrs. It provides a means of determining the offset-distance to a point without having to measure it out. Dutch and German cartographers had referred to the calculation in the 16th century and the practice had been used in Germany, Austria, Holland and Sweden. In England there had been several references in books on the practice of surveying including William Bourne's Rules of Navigation (1571) and John Norden's Surveyor's Dialogue (1607). François Viète had first published European sine lookup tables in 1579.
The Dutch mathematician, Willebrod Snell, had extended the calculation to create small-scale triangulation networks on the landscape, with carefully measured distances to reference points, marked in concrete. This conferred a huge measure of referential integrity to subsequent mapping, and in 1745 the French Cassini family were preparing for a full-scale triangulation-network in France. The Atlas of France was not completed until 1789. It has to be emphasized that Roy, in 1747, certainly did not use such triangulation networks for his military survey; he had neither the resources nor the skills. However Arrowsmith confirms that Roy employed measured traverses across the countryside and that bearings were taken to the left and right. It therefore seems inconceivable that he would not have profited from the simple triangulation calculation. Furthermore, he completed his map in 5 years ; a feat almost impossible without recourse to such help.
The principle then is as follows-: A traverse across a countryside, perhaps through a glen, is being carefully surveyed and measured with a measuring chain and serial pegs. The length of a single section ( CD) is then recorded with care. A feature E lies to one side of the measured line, at some distance, but still in sight. It would be laborious and inconvenient to measure-out the offset-distance to E: a calculation can be used instead.
The Dutch mathematician, Willebrod Snell, had extended the calculation to create small-scale triangulation networks on the landscape, with carefully measured distances to reference points, marked in concrete. This conferred a huge measure of referential integrity to subsequent mapping, and in 1745 the French Cassini family were preparing for a full-scale triangulation-network in France. The Atlas of France was not completed until 1789. It has to be emphasized that Roy, in 1747, certainly did not use such triangulation networks for his military survey; he had neither the resources nor the skills. However Arrowsmith confirms that Roy employed measured traverses across the countryside and that bearings were taken to the left and right. It therefore seems inconceivable that he would not have profited from the simple triangulation calculation. Furthermore, he completed his map in 5 years ; a feat almost impossible without recourse to such help.
The principle then is as follows-: A traverse across a countryside, perhaps through a glen, is being carefully surveyed and measured with a measuring chain and serial pegs. The length of a single section ( CD) is then recorded with care. A feature E lies to one side of the measured line, at some distance, but still in sight. It would be laborious and inconvenient to measure-out the offset-distance to E: a calculation can be used instead.
Measuring Chain
Triangulation