Longitude Revealed

Defining Navigation

Navigation refers to the science by which the exact location of a ship on the sea is determined. This then allows obstacles in known positions but not visible to be avoided and the course to be set (Stebbing, 1956:A and Quill, 1966). Given that the earth is now known to be spherical, the ship actually moves on the surface of a sphere and positions, courses and charts have to refer to spherical shape. Two angular coordinates are used to specify position: latitude, an angle in the plane containing poles and place; and longitude, an angle in the plane parallel to the equatorial plane and containing the place (Stebbing, 1956:2-4.)

Definition of Latitude and Longitude

The line on the surface of the earth through the place and both poles is called the meridian of the place: it is a half-circle since the earth is spherical. The angle subtended at the earth's centre by the arc of the meridian between the place and equator is the latitude of the place. It is measured in degrees, minutes and seconds from 0 degrees at the equator to 90 degrees north or south at the respective poles. The angle between the plane of the meridian of the place and the plane of a prime or reference meridian is the longitude. It is measured in degrees, minutes and seconds, and runs from 0 degrees at prime to 180 degrees east or west according to the direction taken from prime (Williams, 1992:11). Thus 180 degrees east and 180 degrees west coincide; this meridian is co-planar with prime (0 degrees) and is the International Date Line along most of its length. Latitude is conventionally quoted first in giving position, but north/south and east/west label them unequivocally. (Some nautical tables etc may speak of latitude as a distance, but the coordinates actually refer to angles as above. Two places a degree apart in latitude are 70 miles apart north-south wherever they are on the globe between equator and pole; but for single degree differences in longitude the distance apart varies (maximum at the equator to zero at the pole).

Thus latitude alone defines all the points where a plane parallel to the equatorial plane meets the surface of the earth. Longitude along defines all the points along a meridian. Both are needed to specify a single point (Stebbing, 1956:1-7).

The problem for all navigators is that the sun and stars can be used to calculate the latitude north or south of the equator but not the easterly or westerly position that is, the longitude (Berthon and Robinson, 1991:117).

The Ease of Determining Latitude

The means to calculate latitude were mastered during ancient times. For example, Pytheas (c.300BC) was able to calculate the latitude of his home town Marseilles to an accuracy of approximately a quarter of a degree (Williams, 1992:9).

Sailors have long been able to determine latitude fairly easily and with comparative accuracy (Williams, 1992:9). In the northern hemisphere the Pole Star is in line with the earth’s axis, that is, it is always north at every point and latitude can then be calculated by the observation of this star. Other bodies had to be observed un the southern hemisphere when European mariners crossed the equator.

The Difficulty of Determining Longitude

In contrast to latitude, the means of accurately calculating longitude at sea was long elusive. Not until 1714 was there an accurate way of determing longitude even on land, let along at sea where waves made accurate measurements difficult. The best that sailors could do was to calculate their displacement east-west by using a process of intelligent guess work called "dead-reckoning." Given that this ‘reckoning’ had to be adjusted for the effects of wind and sea in carrying a ship off-course and that these effects (called leeway and drift respectively) could not be accurately and reliably measured it was, as Quill (1966:2) observes, "a most hazardous way of navigating."

As the earth rotates, each meridian passes directly beneath the sun, which has maximum altitude at noon each day along the whole of that meridian. Noon is thus earliest at 180 degrees east and latest at 180 degrees west, these meridians being considered, for this purpose, to be not quite coincident. There is in fact 24 hours difference: the earth takes 24 hours to rotate, that is, describe 360 degrees, so it covers 1 degree in 4 minutes, 15 degrees in each hour and 360 degrees in 24 hours (Quill, 1966:4). Thus degrees of the angle, that is longitude, can be rendered as periods of time, the difference between local and prime time (the time at the reference or zero meridian).

Clocks at prime and the unknown place can be used to measure longitude. Observed noon at the place serves as one clock and the other, an actual clock carried on board, gives the simultaneous time at prime provided it has kept accurate time since being set. Time difference in hours/24 x 360 = longitude in degrees.

This simple conversion was to solve the problem of determining longitude, but it called for accurate timepieces, so it was only theoretically possible for centuries.