Tag: maps

Book review: The Measure of All Things by Ken Alder

TheMeasureOfAllThingsThe Measure of All Things“ by Ken Alder tells the story of Pierre Méchain and Jean Baptiste Joseph Delambre’s efforts to survey the line of constant longitude (or meridian) between Dunkerque and Barcelona through Paris, starting amidst the French Revolution in 1792.

The survey of the meridian was part of a scheme to introduce a new, unified system of measures. The idea was to fix the length of the new unit, the metre, as 1/10,000,000th of the distance between the North Pole and the equator on a meridian passing through Paris.

At the time France used an estimated 250,000 different measures across the country with each parish having it’s own (uncalibrated) weights and measures with different measures for different types of material i.e. a “yard” of cotton was different from a “yard” of silk, and different if you were buying wholesale or selling to end users. These measures had evolved over time to suit local needs, but acted to supress trade between communities. Most nations found themselves in a similar situation.

Although the process of measuring the meridian started under the ancien regime, it continued in revolutionary France as a scheme that united the country. The names associated with the scheme: Laplace, Legrendre, Lavoisier, Cassini, Condorcet, leading lights of the Academie des Sciences, are still well known to scientists today.

Such surveying measurements are made by triangulation, a strip of triangles is surveyed along the line of interest. This involves precisely measuring the angles between each each vertex of the triangles in succession: given the three angles of a triangle and the length of one side of the triangle the lengths of the other two sides can be calculated. It’s actually only necessary to measure the length of one side on one triangle on the ground. Once you’ve done that you can use the previously determined lengths for successive triangles. All of France had been surveyed under the direction of César-François Cassini in 1740-80, the meridian survey used a subset of these sites measured at higher precision thanks to the newly invented Borda repeating circle. As well as this triangulation survey a measure of latitude was made at points along the meridian by examining the stars.
The book captures well the feeling of experimental measurement: the obsession with getting things to match up via different routes; the sick feeling when you realise you’ve made a mistake perhaps never to be reversed; the frustration at staring at pages of scribbles trying to find the mistake; the pleasure in things adding up.

Méchain and Delambre split up to measure the meridian in two sections: Delambre taking the northern section from Dunkerque to Rodez and Méchain the section from Rodez to Barcelona. Méchain delayed endlessly throughout the project, trusting little measurement to his accompanying team. Early on in the process, at Barcelona, he believed he had made a terrible error in measurement, but was unable to check whilst Spain and France were at war. He was wracked by doubt for the following years, only handing over doctored notes with great reluctance at the very end of the project. He was to die not long after the initial measurements were completed, leaving his original notes for Delambre to sift through.

At the time the measurements were originally made the understanding of experimental uncertainty, precision and accuracy were poorly developed. Driven in part by the meridian project and similar survey work by Gauss in Germany, statistical methods for handling experimental error more rigorously were developed not long afterwards. I wrote a little about this back here. Satellite surveying methods show that the error in the measurement by Méchain and Delambre is equivalent to 0.2 millimetres in a metre or 0.02%.

In the end the Earth turns out not to be a great object on which to base a measurement system: although it’s pretty uniform it isn’t really uniform and this limits the accuracy of your units. The alternative proposed at the time was to base the metre on a pendulum: it was to have the length necessary to produce a pendulum of period 2 seconds. This is also ultimately based on properties of the Earth since the second was defined as a certain fraction of the day (the time the Earth takes to rotate on its axis) and the local gravity which varies slightly from place to place, as Maskelyne demonstrated.

Following the Revolution, France adopted, for a short time, a decimal system of time as well as metric units but these soon lapsed. However, the new metric units were taken up across the world over the following years – often this was during unification following war and upheaval.

The definition of the basic units used in science is still an active area. The definition of the metre has not relied on a unique physical object since 1960, rather it is defined by a process: the distance light travels in a small moment of time. However, the kilogram is still defined by a physical object but this may end soon with some exquisitely crafted silicon spheres.

I must admit to being a bit wary of this book in the first instance, how interesting can it be to measure the length of a line? However, it turns out I like to read history through the medium of science and the book provides an insight into France at the Revolution. Furthermore measuring the length of a line is interesting, or it is to a physicist like me.

Thanks to @beckyfh for recommending it!

Footnotes
1. The full-text of the three volume “Base du système métrique décimal” written by Delambre is available online. The back of the second volume contains summary tables of all the triangles and a diagram showing their locations.
2. The author’s website.
3. Some locations in Google Maps.

Book review: The World of Gerard Mercator by Andrew Taylor

Once again I have been reading, this time “The World of Gerard Mercator” by Andrew Taylor. As before this blog post could be viewed as a review or, alternatively, as some notes to remind of what I have read. Overall I enjoyed the book, it provides the right amount of background information and doesn’t bang on interminably about minutiae. I would have liked to have seen some better illustrations, but I suspect good illustrations of maps of this period are hard to come by and a full description of Mercator’s projection was probably not appropriate.

The book starts off with some scene setting: at the beginning of the 16th century the Catholic church were still keen on Ptolemy’s interpretation of world geography in fact to defy this interpretation was a heresy and could be severely punished. Ptolemy had put down his thoughts in Geographia produced around 150AD, which combined a discussion of the methods of cartography with a map of the known world. As a precedent Ptolemy’s work was excellent, however by the time of the 16th century it was beginning to show it’s antiquity. Geographical data, in Ptolemy’s time, from beyond the Roman Empire was a little fanciful, and since the known world was a relatively small fraction of the surface of the globe the problems associated with showing the surface of a 3D object on a 2D map were not pressing. Ptolemy was well aware of the spherical nature of the world, Eratothenes had calculated the size of the earth in around 240BC, he stated that a globe would be the best way of displaying a map of the world. However, a globe large enough to display the whole world at sufficient detail would have to be very large, and thus difficult to construct and transport.

Truly global expeditions were starting to occur in the years before Mercator’s birth: Columbus had “discovered”  the West Indies in 1492, John Cabot made landfall on the North American landmass in 1497. Bartolomeu Dias had sailed around the Southern tip of Africa in 1488, Vasco da Gama had continued on to India in 1497, around the Cape of Good Hope. The state of the art in geography could be found in Waldseemüller’s map of 1507, showing a recognisable view of most of our world. Magellan‘s expedition would make the first circumnavigation of the globe in the early years of Mercator’s life (1519-1522).

Mercator was born in Rupelmonde in Flanders on 5 March 1512, he died 2 December 1594 in Duisburg in what is now Germany at the age of 82. This was a pretty turbulent time in the Netherlands, the country was ruled by Charles V (of Spain) and there appears to have been significant repression of the somewhat rebellious and potentially Protestant population. Mercator was imprisoned for heresy in Rupelmonde in February 1543, remaining in custody until September, many in similar circumstances were executed, however Mercator seems to have avoided this by a combination of moderately powerful friends and a lack of any evidence of heresy.

Mercator’s skill was in the collation and interpretation of geographical data from a wide range of sources including his own surveys. In addition he was clearly a very skilled craftsman in the preparation of copperplate engravings. He was commercially successful, manufacturing his globe throughout his life, as well as many maps and scientific instruments for cartographers. He also had a clear insight into the power of patronage.

His early work was in the preparation of maps of the Holy Land (in 1537) and Europe (in 1554), along with a globe produced in 1541. The globe seems to be popular amongst reproducers of antiquities, you can see details of it on the Harvard Map Collection Website.

Mercator is best known for his “projection”, in this context a projection is a way of converting the world – which is found on the surface of a 3D sphere into a flat, 2D map. Mercator introduced his eponymous projection for his 1569 map of the world, illustrated at the top of this post. The particular feature of this projection is that if you follow a fixed compass bearing you find yourself following a straight line on the Mercator projected map. This is good news for navigators! The price you pay for this property is that, although all regions are in the correct places relative to each other, their areas are distorted so those regions near the poles appear much larger than those near the equator. Mercator seems to have made little of this discovery, nor described the method by which the projection is constructed – this was done some time later, in 1599, by Edward Wright. Prior to maps following Mercator’s projection navigation was a bit hit and miss, basically you headed up to a convenient latitude and then followed it back to your destination – an inefficient way to plan your course. If you’re interested in the maths behind the projection see here.

In terms of it’s content the 1569 map shows Europe, Africa and a large fraction of Asia much as we would see it today, certainly in terms of outline. The Eastern coast of North and South America is fairly recognisable. The map fails in it’s representation of the West coast of America – although to give credit where it is due, it at least has a west coast. The landmasses indicated at the northern and southern poles are close to pure fantasy. The Southern continent had been proposed by Ptolemy as a counterbalance to the known Northern continents – with no supporting evidence. Exploration of the far North was starting to occur during Mercator’s life, with expedition such as that of Frobisher.

Mercator is also responsible for the word “atlas” to describe a book containing a set of maps, in this instance he coined the term to describe the volumes of maps he was preparing towards the end of his life, the last of which was published published posthumously by his son, Rumold, in 1595.

Following my efforts on Joseph Banks, I thought I’d make a map of significant locations in Mercator’s life. You can find them here in Google Maps, zoom out and you will see the world in Mercator projection – a legacy from a man that lived nearly 500 years ago.