In a previous issue of the Caius Engineer (Vol 7 Michaelmas 1995) we included an article on Professor Robert Willis who was believed to be the first Caian Engineer. He was certainly the first member of the University to give lecture courses on Engineering topics (from around 1837 on).
Recently, a new claimant to the honour of being the first Caian Engineer has been found. He is Edward Wright, who was a Fellow between 1587 and 1596. He may have originated the New River Project and was certainly actively involved in it. He is widely recognised as one of the major contributors to the development of cartography. In Professor Brooke's book 'A History of Gonville and Caius College' another interesting aspect of his career is mentioned. Edward Wright was, as far as we know, the only Fellow of Caius ever to be granted sabbatical leave in order to engage in piracy! He is clearly a claimant worth investigating.
According to the College records (the Biographical History of Gonville and Caius College) he was born at Garveston in Norfolk in October 1561. We do not know what his father's occupation was, but he appears to have been only moderately well off. We do know that Edward had an elder brother Thomas who also was student in Caius. Thomas unfortunately died in his second year and is buried in St Michael's Church. Edward entered the College in 1576 as a sizar, to read Mathematics. A sizar was, in those days, a category of student who worked as a part time College servant instead of paying fees. This was the way in which relatively poor students were catered for before the days of grants and scholarships. Edward Wright obtained his B.A. in 1581 and his M.A. in 1584. He was elected to a College Fellowship in 1587.
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Wright was mainly interested in applied mathematics and specialized in surveying and map-making. This led to the work for which he has become famous. After the discovery of the sea route to India and the Far East, and the subsequent discovery of America by Columbus, navigation and mapmaking had become major topics. The only reliable navigational instrument available was the magnetic compass and while it was known that the earth was approximately spherical and great circle paths were the shortest routes between two points such paths, apart from those along the equator had continually varying compass bearings. Since it was very difficult for sailors to estimate how far they had travelled, it was much easier for them to stick to constant compass bearings when out of sight of land. The difficulty was that they did not know which compass bearing they ought to choose. In 1569 a German cartographer, Gerardus Mercator, published a map of the World designed to handle this problem. On a Mercator projection map all paths representing fixed compass bearings are straight lines, now called rhumb lines. Thus a navigator merely had to draw a straight line between his point of departure and the point at which he wished to make landfall, note its compass bearing, and then try to stick to it. (Maintaining a correct compass bearing was another problem, which we will not go into here!) Another problem was that Mercator did not reveal; how he was producing these maps, so no one else could either produce them or check his work. (In fact, it later transpired that his original maps were not quite correct, since the rigorous Mercator projection involves logarithms, which had not been discovered by Napier at that time!)
Wright had been interested in this problem and finally published an explanation of the Mercator projection in 1599.
The following account of the theory of the Mercator projection has been extracted from an internet article by Norris Weimer of the University of Alberta. See his article for the full details and a demonstration.
The Mercator projection is often illustrated as a projection from the center of a globe onto a cylinder wrapped around the globe. However, that cylindrical projection is not the Mercator projection. If you see them side by side, you will see they don't look the same. The cylindrical projection does not have the property that Mercator was seeking; the rhumb lines are not straight lines. They do have the general form in common: meridians of longitude and parallels of latitude are straight, parallel lines. Also, since the meridians don't get closer together towards the poles (as they do on a globe), that means the scale must increase as the latitude increases.
The book Dutton's Navigation and Piloting has a couple nice illustrations of this (sections 304 and 305).
The insight which is key to the Mercator projection (and indeed all conformal projections) is that if you want to avoid distorting angles (like courses and bearings), you have to keep the scale the same in both dimensions (north-south and east-west) on the map. Whatever the horizontal scale is at a point on the map, the vertical scale should be the same. (See also orthomorphic and conformal ). Mercator figured out how to make such a map using only compass and protractor.
Wright improved on the method and wrote a book which provided tables and explanations. The following intuitive explanation is his. Make a globe out of a spherical balloon. Place it in a larger glass cylinder. Blow it up slowly so that it first touches at the equator. Continue blowing it up slowly. Each point on the balloon globe is blown up until it is pressed against the wall of the glass cylinder. Higher latitudes are blown up more. The final result is a Mercator projection. Wright explained that the scale factor varied with the secant of the latitude.
Some sailors still use the methods of Mercator and Wright, but all sailors still use Mercator charts, although perhaps not for the same reasons. The fact that the meridians are parallel makes it easy to measure angles, especially when you have a large chart table and parallel rules. However aircraft pilots do not use it because it is not suitable for radio navigation. For that it is better to use a chart which shows great circles as straight lines. Surveyors do not use it because neither distances nor bearings are accurate over longer distances. Others dislike it because it greatly exaggerates the size of regions near the poles.
In mathematics a projection is a function which takes points on one surface and transforms them into points on another surface. For making maps, the projection goes from the sphere or the ellipsoid (eg, the earth) to a plane (the map). There is no geometric projection to produce a Mercator chart.
The Mercator projection "is not perspective and the parallels cannot be located by geometric projection, the spacing being derived mathematically." (Bowditch).
The Mercator projection takes a point (Latitude, Longitude) on the ellipsoid and returns the point (Easting, Northing) on the plane. These values can be scaled and plotted on a map.
Note the following formulas are shown for the northern hemisphere. For the southern hemisphere, use the absolute value of L and adjust the sign of N.
Note: there are many mathematically equivalent ways to express these formulas. As usual, not all of them are computationally equivalent.
L = latitude in radians (positive north) Lo = longitude in radians (positive east) E = easting (meters) N = northing (meters)
For the sphere
E = r Lo N = r ln [ tan (pi/4 + L/2) ] where r = radius of the sphere (meters) ln() is the natural logarithm=
For the ellipsoid
E = a Lo N = a * ln ( tan (pi/4 + L/2) * ( (1 - e * sin (L)) / (1 + e * sin (L))) ** (e/2) )
e
-
pi L 1 - e sin(L) 2
= a ln( tan( ---- + ---) (--------------) )
4 2 1 + e sin(L)
where
a = the length of the semi-major axis of the ellipsoid (meters)
e = the first eccentricity of the ellipsoid
Note: the equation for northing does not have a closed form inverse.
The inverse can be calculated by iteration; it converges rapidly.
The expression which is used in the Mercator projection is also used as the starting point for other map projections. In this case, it is regarded as transforming the geodetic latitude L into the isometric latitude q. The isometric latitude is then used instead of the geodetic latitude in the projection. Note that this can produce isometric latitudes greater then 90°.
pi L e 1 - e sin(L)
q = ln( tan( ---- + ---)) + --- ln (--------------)
4 2 2 1 + e sin(L)
The N value calculated above is essentially the same thing as Meridional Parts, except that Meridional Parts are in units of nautical miles instead of meters.
Meridional Parts are used to calculate the Mercator Sailings (ie, to do navigation as if on a Mercator chart, but by calculation instead of by plotting).
At the equator, one Meridional Part is equal to one nautical mile (but not elsewhere). Nautical miles are convenient for a sailor because one nautical mile is almost exactly the same as one minute of latitude, and the latitude scale is used to measure distance on the Mercator chart, which is necessary since the Mercator chart does not have a fixed distance scale.
Bowditch provides a table of Meridional Parts: Table 5 in volume 2; also see the explanation of Table 5 and section 1007 "Mercator Sailing". See also Bowditch volume 1: section 305 Mercator Projection, section 306 Meridional Parts, and section 307 Mercator Chart Construction.
The Discoverers: A history of Man's Search to Know his World and
Himself
Daniel J. Boorstin, 1985
ISBN 0-394-72625-1
Mathematics Magazine vol.60, no.3, June 1987, pages 151-158
A Curious Mixture of Maps, Dates, and Names, by J.M. Sachs.
Dutton's Navigation and Piloting
G.D.Dunlap and H.H. Shufeldt
Naval Institute Press
Bowditch, American Practical Navigator
Pub. No. 9
Defense Mapping Agency
GPS Satellite Surveying
Alfred Leick
Geodesy
G. Bomford
CAM - Cartographic Automatic Mapping Program Documentation
CIA
Map Projections: Their Development and Use in New Zealand (Seminar
Notes)
J. Hannah
Professional Development Committee
New Zealand Institute of Surveyors, Auckland NZ, August 1984
[This booklet contains a very clear and concise mathematical derivation of the
conformality conditions (the Cauchy-Riemann equations). It also contains an excellent
short discussion of the types of possible distortions in a map projection, and pratical
formulae for calculation, especially for the New Zealand mapping grid.]
Feedback welcome: norris.weimer@ualberta.ca
28 July 1998
The mathematical part of Weimer's article shows how logarithms and exponentials enter the Mercator projection. It is not clear how much Wright knew about Napier's work on logarithms by the time he published his analysis in 1599, but Napier had apparently been working on them since about 1590 (although his work was not finally published until 1614). I think it is probable that Wright did know about this work.
Wright had been interested in the problem of marine navigation long before he finally solved the Mercator projection problem and this was apparently well known. As a result of this, when, in 1589, the Earl of Cumberland organised an expedition to the Azores to capture Spanish Galleons, Queen Elizabeth requested that Wright be sent on this expedition to carry out Navigational studies. In effect, she ordered Caius College to grant him leave of absence for this purpose. (The College records put this a little more delicately, stating that he was granted sabbatical leave 'by Royal Mandate'.) Clearly a young man involved in an expedition in which the participants were going to share part of the spoils was going to make the most of his opportunities.
Since the 14th century the supply of drinking water to
London had been a growing problem. Initially water was taken from the Thames, the rivers
feeding it and a few wells, but there was no effective control of sewage or waste disposal
so waste and sewage were dumped in these same rivers. As London's population grew these
problems became worse and the pollution spread into the ground water and hence to the
wells. By the end of the 16th century London's population was approaching
200,000 and the problems were becoming critical. The city authorities apparently saw no
hope of stopping the pollution of the existing rivers. In view of the large amount of
fresh water needed the only solution would be to get supplies from uncontaminated sources
well outside the city. This in turn posed some practical problems. The Elizabethans did not have the technology to design or operate large pumps, so any supplies had to flow by gravity through canals or aqueducts. (Large pipes were also beyond the existing technologies.) Two possible sources were identified, the river Colne to the west of London and springs near Hertford. A scheme for this latter source was eventually adopted. This was dependent on the fact that a practical route from the springs into London was discovered. There is a certain amount of mystery over this. Records in Caius College suggest that Edward Wright actually discovered the practical route and was the original proposer of this scheme. Other records state that a former army captain, Edward Colthurst, made the original proposal. It is certain the Edward Wright, who we have already mentioned was a highly competent surveyor was responsible for the detailed planning of the route for this canal, which came to be known as the 'New River'.
Choosing the route did in fact call for very accurate surveying. The crucial point was that there was a 100 foot contour from a point just below the springs all the way into London near Islington. Provided the Islington end of the river was not too far below this level it would then be easy to feed large parts of London by gravity through small pipes or aqueducts. However, the 100 foot contour was not anywhere near straight. Although the direct distance from the springs to Islington was little over 20 miles, the practical router for gravity feed was nearly forty miles. The plans called for a drop of only 18 feet over this distance, equivalent to only 5.5 inches per mile. This clearly required high precision in surveying the actual route and the fact that the surveyors of that time considered (correctly, as it turned out) that they were capable of achieving this is a testimony to their skills. In particular, Wright, who apart from the calculations and planning, had been involved in the design of surveying instruments must have been responsible for much of this expertise. The New River still supplies drinking water to London, 390 years after its construction.
It does appear that Edward Wright was a major contributor to at least two major practical developments at the end of the 16th century and there is therefore certainly a good case for naming him as the first Caian Engineer. Whether he was also the first Caian Pirate is more uncertain - but it's a good story!
Derek Ingram.
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