Due to the run away success of Dava Sobel’s book, *Longitude*, finding the solution of how to determine the longitude of one’s position on the surface of the Earth, in the pre-GPS world, is probably the best known example in history of the application of science to solve a real life problem. Should any readers of this blog have missed it, scholars from Cambridge University under the supervision of Simon Schaffer and others from the National Maritime Museum in Greenwich under the supervision of Whewell’s Ghost’s very own Rebekah “Becky” Higgitts are conducting a major research project into the history of The Board of Longitude the institution that in Great Britain financed and supported that search. They have an interesting blog covering their activities and are already producing results.

The problems involved in determining ones position on the surface of the Earth were well known to the Greeks in antiquity, the first people to produce mathematical cartography. Determining latitude, that is one position north or south relative to the poles or the equator, is a comparatively simple mathematical-astronomical procedure that is basically also the same procedure as that for determining local time. Local time is determined to be noon or mid-day when the sun is at its highest point in the sky. Determining longitude, that is ones position east or west of a given fixed point on the equator (Ptolemaeus the father of mathematical cartography used the meridian through the Canary Islands as his fixed point), is not so simple. The Greeks already knew that if one could determine the local time simultaneously for two different points then one could also determine their longitudinal separation. As the equator is a circle divided into 360° (a standard introduced by the Greeks) and the Earth rotates once in 24 hours then four minutes difference in time is equivalent to one degree difference in longitude (360° longitude is equivalent to 24 X 6o minutes time). The problem is that one can’t be in two places at once!

During the Renaissance three different methods where proposed that enabled sailors, cartographers and surveyors to get around this problem and to be able to accurately determine their longitude, in what follows I will sketch those three methods and their proposers.

The first method to be proposed was the lunar distance method and it was put forward by the Nürnberger priest and mathematicus Johannes Werner (1468 – 1522) in his *In hoc opere haec continentur* *Nova translatio primi libri geographiae Cl’ Ptolomaei *… (Nürnberg 1514), that is his translation of the *Geographia* from Ptolemaeus. Werner who was born in Nürnberg was a student at the University of Ingolstadt from 1484, which was then one of the leading German speaking universities for the study of mathematics. When he settled as a vicar in Nürnberg he became part of a tight knit circle of mathematical practitioners in Nürnberg, Ingolstadt, Vienna and Tübingen who were largely responsible for establish mathematics as a discipline in the central European universities. I will write more on Werner’s mathematical activities more fully another time for now it suffices to say that he was the originator of the lunar distance method. This method however only really became known through the writings of another member of this circle the Ingolstadter mathematicus Peter Apian (1495 – 1552) who explained it more fully in his *Cosmographia* (Landshut 1524).

The principle behind the lunar distance method is fairly simple, one needs to compile accurate tables of the moon’s position relative to one or more of the fixed stars at all times for one location. Then the moons position is determined relative to the same stars at the place for which one wishes to determine the longitude noting the local time. In the tables it is possible to determine the time when the moon occupied this position at the point of origin and thus to calculate the time and longitudinal differences. Apart from the not insubstantial practical problems of making the necessary accurate astronomical observation to determine the local lunar distance, particularly on a moving ship this method has a very major drawback. Due to the fact that the moon is a fairly large gravitational body in a gravitational system involving it, the Earth and the Sun its orbit is to say the least more than somewhat erratic as it is constantly being pulled in several different directions. Determining the moon’s orbit and producing those desired tables proved to be a problem that defeated the best of astronomers including Isaac Newton. In fact it was Newton’s failure to solve this problem that led to his falling out with the Astronomer Royal John Flamsteed, Newton blaming his failure on Flamsteed’s inability, as he saw it, to provide him with adequate observational data. The first person to actually succeed in producing adequately accurate lunar tables was Tobias Mayer (1723 – 1762) who did so whilst working as a cartographer in Werner’s hometown, Nürnberg.

Moving forward through history a couple of decades we meet the second method, the accurate clock. One of the first mechanical clocks in Europe was built by the mediaeval mathematicus Richard of Wallingford (1292 – 1336) Abbott of St. Albans in around 1330 but this would have been of no use for cartographers or navigators. Anybody who has seen the clocks in the cathedrals of Salisbury in Southern England or in Ulm in Southern Germany knows that they are about the size of an average living room, weigh several tons and are highly inaccurate add to this the fact that the first generation of mediaeval clocks did not have a clock face to tell time but were basically fitted with an astrolabe on the front that displayed the phases of the moon the movement of the planets etc. and one can see that we are a long way from anything with which to determine longitude. However over the centuries the technique of clock making improved and the clocks got smaller and more accurate. By the beginning of the 16^{th} century the first pocket watches began to appear in Europe. Local tradition has it that the first pocket watch was produced by the clockmaker Peter Henlein (c. 1480 – 1542) in Nürnberg in 1502 however this story is disputed by many leading horology historians. What ever the case may be by the middle of the century clock making was advanced enough that the clock method of measuring longitude was proposed.

In this method the traveller carries with him or her a very accurate clock set to the local time of his or her point of departure then to determine the longitude of his or her current position he or she needs only to measure the local time of their actual position calculate the difference to the clock time and thus the longitudinal difference to their point of departure. Anybody who has read Ms. Sobel’s book or seen the TV documentary will know how difficult it proved to be to manufacture a clock accurate enough that could withstand the rigours of a long sea voyage, vibration, extreme changes in temperature etc in order to fulfil this requirement.

By a strange warp in the fabric of history this method was also first published in Peter Apian’s *Cosmographia* but not by Apian. Apian’s *Cosmographia* was the leading textbook in the 16^{th} century for basic astronomy, surveying and cartography and enjoyed many successful edition and reprints over many decades. The first edition was written, printed and published by Apian in Landshut in Southern Germany in 1524 but for reasons that are still not known all subsequent improved and expanded edition were written and published by the Professor for Medicine at the University of Leuven in the Spanish Netherlands, the mathematicus Gemma Frisius (1508 – 1555). Frisius was born Jemme Reinierszoon in Dokkum in Friesland and hence the toponym Frisius. He remains virtually unknown in mainstream history of science but he is a very important and central figure in the histories of astronomy, globe making and cartography. Just to mention three examples, he was the first astronomer to publish comments on Copernicus’ *De revolutionibus*, he invented triangulation and he was the teacher of Mercator, yes the Mercator the invention of whose map projection you were all taught at school. As already mentioned Frisius edited and published many improved and expanded editions of Apian’s *Cosmographia* and was in the habit of adding appendices containing his newest thoughts for improving his various disciplines. One such appendix contained the concept of triangulation and another the proposal of the clock method of determining longitude.

The beginning of the 17^{th} century saw the advent of the third method, which was first proposed by Galileo Galilei (1564 – 1642) and involved using his most important astronomical discovery the moons of Jupiter as a clock. Galileo actually negotiated with the Spanish King to supply the Spanish navigators with this method but the scheme failed on its practicability. As Jupiter is very far away from the Sun and as it is very large in comparison to its four largest moons they have very regular orbits and are eclipsed by Jupiter at regular intervals. The method that Galileo proposed is very similar to the lunar distance method. An accurate set of tables of the eclipses of the moons of Jupiter for a given location would act like a clock of local time for that location. Somebody observing the same eclipse occurrence at another location could compare the local time of the occurrence with the time in the tables and thus calculate time and longitudinal differences. This method works but has a couple of major drawbacks. Observing the moons of Jupiter with a Galilean telescope is incredibly difficult at the best of times, I know I’ve tried it, and literally impossible from the deck of a moving ship (the lunar method has the advantage that the moon is a large target). Galileo tried getting round this problem by designing a special pair of binoculars mounted on a helmet to be worn by the navigator making the observations but the design never left the drawing board. The difficulties of the observations also meant that compiling the necessary tables was anything but easy and in fact Galileo abandoned his own attempt to do so. The first set of tables accurate enough for the purpose were produced by Cassini (1625 – 1712) more than fifty years later using vastly superior telescopes. Although impractical for use at sea the Jupiter moon method was used very successfully by cartographers on solid ground and vastly improved the quality of maps at the end of the 17^{th} century. This improvement led to the famous comment by the French King that he had lost more territory to the cartographers than he had ever lost in war, France having been shown to be substantially smaller than previously believed.

We have arrived at the beginning of the 17^{th} century where the English Board of Longitude was called into being in 1714 charged with finding an accurate method of determining longitude. Although many often crazy schemes were proposed only two serious proposals were in the running, the lunar distance method of Johannes Werner and the clock method of Gemma Frisius and you can follow how these methods faired in the hands of the Board of Longitude in the 18^{th} century by checking in regularly at The Board of Longitude Blog. I will be there will you?

Pingback: Where the fuck are we? | Whewell's Ghost

This is fucking great.

Many thanks Thony for the plug! Thanks also for setting out the back story so clearly and thoroughly. I’ve linked it in a brief post over at the Longitude Project Blog. I’ve also highlighted there the other seriously-persued longitude solution: magnetic variation.

Best title for a blog post on longitude ever.

Interesting blog, Thony. Something to add is that one of Galileo’s observing-helmets (he called it a ‘celatone’) was made and tried out at sea in 1617. There’s a short animation about it on the Museo Galileo website. Giovanni de’ Medici thought it was ‘more important than the discovery of the telescope itself’, although it turned out not to work.

Interestingly every Dutch school child learns that Christiaan Huygens improved the pendulum clock so that it could be used on ships to determine longitude, but not that it was Frisius who first published about this method.

Pingback: Weekly Roundup | The Bubble Chamber

I enjoyed your post Thony. Thanks for highlighting that the Jupiter’s satellite method is a serious contender. It is also interesting how long it sticks around, even in the eighteenth century with the Board of Longitude. I’ve discussed this in a short postover on our blog.

I enjoyed your post Thony. Thanks for highlighting that Jupiter’s satellites remain a contender for solving the longitude problem. It’s also interesting how long the idea sticks around, even into the eighteenth century and the Board of Longitude. I’ve discussed this in a short post over on our blog.

Sorry that link didn’t work. Here it is

Excellent! Exactly the kind of blogging I am looking for! !

http://emergent-hive.com/about

This is an excellent new blog, but it is in desperate need of an RSS feed. I follow hundreds of blogs: if I can’t subscribe using my RSS reader, I will simply forget to keep checking for updates. (I know this for a fact, because I have been aware of the blog since it launched, but only remember to check it out, as I did just now, when some other blogger with an RSS feed which I am following links to it.)

Ah, yes. Indeed. It’s been raised with the NMM IT folks a number of times but nothing as yet. Just be glad at people can finally comment!

I’ll ask again but have a horrible feeling that it’ll be left until we move platforms later in the year. Please don’t abandon us though! I tweet all the new posts on @beckyfh #histsci.

So much for this website for me, due to allowed language which I find offensive/

My blog my language! You don’t like it, nobody is forcing you to read it.

Offence is taken, not given. Onward and upward, Thony!

Pingback: Upon reflection: The Hadley brothers. | The Renaissance Mathematicus

Pingback: zum 250. Todestag von Tobias Mayer « mathematik, bücher & meer

Pingback: How far the moon? | The Renaissance Mathematicus

Pingback: The weather and the stars | The Renaissance Mathematicus

Pingback: The specialist in causing pain. | The Renaissance Mathematicus

Pingback: Hans Holbein and the Nürnberg–Ingolstadt–Vienna Renaissance mathematical nexus. | The Renaissance Mathematicus

Pingback: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time | The Renaissance Mathematicus

Pingback: Marine chronometer, lunar distance method or something else altogether? | The Renaissance Mathematicus

Pingback: The Renaissance Mathematicus – A users guide | The Renaissance Mathematicus