Dividers

__NOTOC__A dividers, also known as a measuring compass, is a mathematical, drafting or cartographic instrument used to aid measurements of the length of irregular lines and of distances on maps or charts. It is commonly used in geometry and in nautical navigation. It is similar in appearance to a drafting compass, the difference being that the compass has a spike on one end and a pencil (or other drawing utensil) on the other which allows the drawing of circles, whereas the dividers has spikes on both ends. Often a compass can be fitted with a spike in place of the drawing utensil and thus converted to dividers.

Note that in older usage in British English, “dividers” and “compasses” are plural nouns.

Measuring the length of an irregular line

The use of dividers to measure an approximate distance "a–b" on an irregular line is as follows:
#The dividers are opened (extended) on a ruler so the points are a distance apart corresponding to a convenient unit of length on the ruler, such as an inch or a centimetre. This is known as the "sampling length" or "scale interval" .
#The dividers are placed with one spike on point "a" and the other along the line towards "b".
#The dividers are then 'walked' along the line by holding one spike in place and rotating the dividers 180º to bring the other leg further along the line.
#The number of 'steps' in the walk to reach point 'b' are counted. In practice the last step to reach "b" will be less than the sampling length.
#The dividers are then closed up to the distance of the last step, and placed on the ruler to measure its length.
#The total length is calculated as number of steps times the sampling length plus the length of the last incomplete step. If the sampling length is 1 cm and it took 12 'full' steps and one last step of 0.6 cm to reach "b", the total length of the line is about 12.6 cm.

This approximation can be improved by using a smaller sampling length (or by optically enlarging the line by a known ratio and repeating, taking into account the enlargement ratio). Each time a smaller sampling length is used, the measurement will come out slightly larger, and if the line is not fractal, the measurement will tend towards a limit. If the line is a fractal, its length measurement will theoretically increase without limit. Measurements of a coastline behave somewhere in between.

In digital mapping, measuring and navigation technology, the dividers are replaced by software tools for measuring irregular lines with very small sampling lengths assuring great accuracy.

Measuring a distance on a chart in nautical navigation

The process is similar, but a straightedge is aligned with a-b and a line is drawn between them on the chart. The straightedge is for best results but the same can be done without it if utmost accuracy is not required.
#The dividers are opened (extended) on the chart scale so the points are a distance apart corresponding to a round number, such as the equivalent of five miles on the chart scale.
#The dividers are placed as before with one spike on point "a" and the other along the line towards "b".
#The dividers are then 'walked' along the line in the same way, counting the steps.
#Suppose this is done six times, then we know we have counted 6 times 5 = 30 miles. Now we are left with a segment smaller than five miles. We close the dividers to bring the free spike to point b and we then take the dividers to the scale and measure the distance. Suppose it is 2.6 miles. We now know the total distance is 30 + 2.6 = 32.6 miles.

See also

*Compass (drafting)

External link

* [http://boatsafe.com/navigation/divide1.htm How to use the dividers]