Drawing Instruments - Their History and Classroom Use

Drawing instruments - their history and classroom use in developing geometrical reasoning

No.1 The parallel ruler

Introduction

For a while drawing instruments have fascinated me. I like the cases in which they come and the beauty of the old (and new) instruments. Over the years I have tried to collect what I consider to be affordable (currently <£10) instruments within my budget. I have also managed to acquire some books about drawing instruments and at last I feel I have enough motivation to start writing some geometrical lessons about the instruments I have and how I’ve used them in the classroom to motivate my pupils. It was our meeting today that spurred me into writing something about mathematical instruments, and I hope that I have the time and energy to keep this going for a few lessons! I start with an instrument that has connections with mathematics and navigation - the parallel ruler.

Description

Five examples of parallel rulers plus a normal ruler for scale.

These come in two forms. The more commonly known parallel rulers look like two normal (usually unmarked) rulers joined with two bars of equal lengths. The smallest one I have is 6 inches long and 1 3/8 inches wide when closed. It is made of a black wood (ebony?) and joined by two brass bars. There are no markings but a small brass peg in the middle of each rule, presumably to assist moving the rule. I think this probably came from a case of mathematical instruments. The largest parallel ruler I have is 18 inches long and 2 7/8 inches wide. This is clearly meant for navigational purposes as in its closed position it can be used as a 180˚ protractor and also has compass markings along one side. The brass hinges are very similar to the ones on the small ruler and the knobs used for moving each rule are larger (and easier to grasp). This ruler is black, but from damage to the ruler it appears that the ruler is boxwood that is stained black on the surface. At the bottom of this ruler are the words ‘Capt Fields Improved’, words that also appear on the next largest ruler, which has its natural light colour. The next to smallest ruler is stained black and unmarked. This was the first parallel ruler I bought for £2. The hinges and knobs are made of steel. The edges of both the two smaller rulers have parallel chamfers so that you can run the pen or pencil along an edge that either touches the paper or is above it. The other type of ruler is a large brass one with two serrated wheels on which the ruler can run up and down a piece of paper. Both edges of the ruler can be used, and one uses the most appropriate edge when the ruler has been moved into position.

History

By 1600 parallel rulers were common. Both the bar and rolling types were known by the beginning of the nineteenth century. The older bar types used to be made in ivory or ebony with brass, silver or electrum cross-links. The rolling types were often made in metal that made them much heavier and less prone to slipping. The rules varied in length from 6 to 36 inches. The large 12 inch rolling parallel were introduced by E.G. Eckhardt and made for him by Dolland in 1770. However these rolling rulers were rather tricky to use and by 1850 the set-square and tee-square had largely superseded them. The double-barred parallel rule, illustrated below was an improvement on the plain parallel, as the ruling edge moves a greater distance from the fixed rule, and also moves in a direct line. The difference between this and the plain parallel is the addition of an extra rule and pair of bars, which are joined at reverse inclination to the first pair. As this was more difficult to make it is seldom as true as the plain parallel.

Classroom use

I’ve used parallel rulers in a few ways in the classroom. The first way was with a Year 10 (14/15 year olds) class of middle-achievers when we were studying bearings. I decided that rather than spend too much time drawing bearings from those given in a text book I would set a lesson where the class were working in groups of 3 or 4 with real maps. I borrowed maps of the Solent area (the area around Southampton) as that area is known by my pupils and asked them to plot a sailing course round the Isle of Wight, starting and ending at Lymington, a small port that is home to a large number of yachts and boats. I showed them how to use the parallel ruler to get straight lines parallel to the given north line at the side of the map so they could measure the bearings on which they would have to sail to get round the Isle of Wight. The work involved measuring angles and using a scale of 1:50,000. This was quite involved work and I asked the lower attaining pupils in the class just to plot the course round the island (roughly a rhombus in shape) as that only involved four separate stages to the route. Yes, it involved a lot of work by me and my pupils, but the rewarding part was that although some did not complete the work, all thought it a more worthwhile task than tackling questions from the textbook. One pupil, a sea-cadet, said that it was the most relevant work he had ever done in mathematics. Others said they would never use it, as they were not intending to become sailors. At least they were intrigued by the parallel rulers and had fun using them to draw parallel lines.

I’ve also used parallel rulers with Year 7 and 8 classes when we have studied parallel lines and also locus. There’s something about the movement that adds dynamism to the concept of angle. The pupils can see the corresponding angles remaining the same, and also the alternate angles. The parallel rulers work well by placing them on an OHP as the image can be projected onto a white board and any necessary additional writing done there. With locus work you can consider the locus of a point on the hinge (What can you say about its distance from the pivot?), or on the moveable rule. Using dynamic geometry software the locus can be traced out. In writing this article I now think of other questions I could have asked. Questions such as • What if the bars are of different lengths? • What if the bars are the same lengths but the line joining their centres is not parallel to the edge of the ruler? I’ll finish now - I want to see about adapting some more material for my classroom!

Hmmm… where’s all my old Meccano?

References

W.F. Stanley, Mathematical Drawing Instruments (5th edition) , Spon, New York & London, 1878 M. Hambly, Drawing Instruments, RIBA drawings Collection, London, 1982 M. Scott-Scott, Drawing Instruments, Shire Album 180, Aylesbury, 1986

Peter Ransom [email protected] The Mountbatten School and Language College Whitenap Lane Romsey SO51 5SY