It follows that meridian observation of the sun, owing to the necessary inaccuracy of such observation, is not the ideal method. In point of fact the sun may be observed for this purpose to much better advantage when it is at a considerable distance from the meridian, since then its altitude above the horizon at a given moment is the only point necessary to be determined. The calculation by which the altitude of the sun may be translated into longitude is indeed more complicated in this case; but while spherical trigonometry is involved in the calculation, the tables supplied by the _Nautical Almanac_ enable the navigator to make the estimate without the use of any knowledge beyond that of the simplest mathematics.
While these observations tell the navigator his exact location in degrees of latitude and longitude, such knowledge does not of course reveal the distance traversed unless the precise length of the degree itself is known; and this obviously depends upon the size of the earth. Now we have seen that the earth was measured at a very early date by Greek and Roman astronomers, but of course their measurements, remarkable though they were considering the conditions under which they were made, were but rough approximations of the truth. Numerous attempts were made to improve upon these early measurements, but it was not until well into the seventeenth century that a really accurate measurement was made between two points on the earth's surface, the difference between which, as measured in degrees and minutes, was accurately known.
In June of the year 1633, the Englishman Robert Norman made very accurate observations of the altitude of the sun on the day of the summer solstice (when of course it is at its highest point in the heavens); the observation being made with a quadrant several feet in diameter stationed at a point near the Tower of London. On the corresponding day of the following year he made similar observations at a point something like 125 miles south of London, in Surrey. The two observations determined the exact difference in latitude between the two points in question.
Norman then undertook a laborious survey, that he might accurately measure the precise distance in miles and fractions thereof that corresponded to these known degrees of latitude. He made actual measurements with the chain for the most part, but in a few places where the topography offered peculiar difficulties he was obliged to depend upon the primitive method of pacing.