N03: Using Latitude and Longitude

There is no more precise way of knowing your position on the surface of the planet than with a knowledge of latitude and longitude. It has been a longstanding tradition to use Greek geometry to define circles and spheres in everyday three dimensions. In this system, a circle has 360 degrees, written as 360o, where the symbol (o) means 'degrees'. Although we talk about degrees, we can divide a degree into sixty parts, which we call minutes. Now, the symbol (') means minutes. We can also divide a minute into another sixty parts, which we call seconds, symbolised by ("). So, a latitude and longitude specified to degrees (o), minutes (') and seconds (") - north or south - is a very precise statement of your position on Earth.

Determination of latitude is easy because it depends on the position of the sun and the time of day in the place you happen to be. However, the determination of longitude is much harder because longitude is defined relative to the position of Greenwich and can only be found out by knowledge of the exact time at Greenwich. Sailors often had to use what they called Dead Reckoning, a method by which they used knowledge (often guesses) of wind and currents to calculate their speed. Then, with knowledge of time travelled in a given direction, they could estimate their position. However, mistakes were very common and some terrible shipwrecks have occurred, with great loss of life, because navigators thought they were in one place and they were actually somewhere else!

One of the worst examples of this was in 1707 when Admiral Sir Cloudesley lost four large ships (including his own) and the lives of 2000 sailors in a terrible disaster in the waters around the Isles of Scilly, Cornwall, UK. It is said that the fleet was out of position because of navigational errors of longitude.

The problem of longitude was solved by the English instrument maker, John Harrison, who in 1730 designed his first, accurate timepiece. It was designed to maintain a precise record of the time at the Greenwich meridian, whatever a sailor's potition on the globe. These clocks (called chronometers) were carried in ships and never changed: they always showed the time at Greenwich. From this it was possible to use knowledge of latitude and other measurements to calculate longitude.

Today, of course, satellite technology enables this to be done instantly and with amazing accuracy. The specification of latitude and longitude has changed somewhat from previous times to accommodate modern digital instrumentation. The basics are the same, but instead of using minutes and seconds to improve the accuracy, it is now common to use a simple decimal specification of the number of degrees north or south, and east or west. Let us take an example.

Consider the Eddystone lighthouse, for which the specified latitude and longitude is [50o 10.84' N; 4o 15.94' W]. This specification is in degrees and minutes to two decimal places. Now, since there are 60 minutes in one degree, 10.84 minutes converts to 0.18067 degrees, and 15.94 minutes converts to 0.26567 degrees, so the fully decimal position of the Eddystone lighthouse is 50.18067 o N and 4.26567 o W. However, we can go further and transform the specification fully into two numbers, i.e. dropping the NSEW labels. This is done by using the mathematical convention that North and East are positive and that South and West are negative. We can therefore say that the Eddystone position is just [50.18067, -4.26567]. Using this method, there is no practical limit to the accuracy with which a position on the planet can be specified.

Readers who use Google Maps should note that this system is used by Google to specify positions.

As we saw in the previous section, we can also use latitude and longitude to calculate distances between two points.