Every-day Science: Volume 7. The Conquest of Time and Space

by Henry Smith Williams; Edward Huntington Williams

MEASURING A DEGREE OF LATITUDE

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.

The modern surveyor, equipped with instruments for the accurate measuring of angles, not differing largely in principle from the quadrant of the navigator, would consider Norman's method of measurement a very clumsy one. He would measure only a single original base line of any convenient length, but would make that measurement with very great accuracy, using, perhaps, a rod packed in ice that it might not vary in length by even the fraction of an inch through changes in temperature. An accurate base line thus secured, he would depend thereafter on the familiar method of triangulation, in which angles are measured very accurately, and from such measurement the length of the sides of the successive triangles determined by simple calculation. In the end he would thus have made the most accurate determination of the distance involved, without having actually measured any portion thereof except the original base line. Notwithstanding the crudity of Norman's method, however, his estimate of the actual length of a degree of the earth's surface was correct, as more recent measurements have demonstrated, within twelve yards—a really remarkable result when it is recalled that the total length of the degree is about sixty nautical miles.

Inasmuch as the earth is not precisely spherical, but is slightly flattened at the poles, successive degrees of latitude are not absolutely uniform all along a meridian, but decrease slightly as the poles are approached. The deviation is so slight, however, that for practical purposes the degree of latitude may be considered as an unvarying unit. But obviously such is not the case with a degree of longitude. The most casual glance at a globe on which the meridian lines are drawn, shows that these lines intersect at the poles, and that the distance between them is, in the nature of the case, different at each successive point between poles and equator. It is only at the equator itself that a degree of longitude represents 1/360 of the earth's circumference. Everywhere else the parallels of latitude cut the meridians in what are termed small circles—that is to say, circles that do not represent circumference lines in the plane of the earth's center. Therefore while all points on any given meridian of longitude are equally distant in terms of degrees and minutes of arc from the meridian of Greenwich, the actual distances from that meridian of the different points as measured in miles will depend entirely upon their latitude.

At the equator each degree of longitude corresponds to (approximately) sixty miles, but in the middle latitudes traversed for example by the transatlantic lines, a degree of longitude represents only half that distance; and in the far North the meridians of longitude draw closer and closer together until they finally converge, and at the poles all longitudes are one.

It follows, then, that the navigator must always know both his latitude and his longitude in order to estimate the exact distance he has sailed. We have seen that a single instrument, the sextant, enables him to make the observations from which both these essentials can be determined. We must now make further inquiry as to the all important guide without the aid of which his observations, however accurately made, would avail him little. This guide, as already pointed out, is found in the set of tables known as the Nautical Almanac.