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

by Henry Smith Williams; Edward Huntington Williams

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.

THE NAUTICAL ALMANAC

Had the earth chanced to be poised in space with its axis exactly at right angles to its plane of revolution, many computations of the astronomer would be greatly simplified. Again, were the planetary course circular instead of elliptical, and were the earth subject to no gravitational influences except that of the sun and moon, matters of astronomical computation would be quite different from what they are. But as the case stands, the axis of the earth is not only tipped at an angle of about twenty-three degrees, but is subject to sundry variations, due to the wobbling of the great top as it whirls.

Then the other planets, notably the massive Jupiter, exert a perverting influence which constantly interferes with the regular progression of the earth in its annual tour about the sun. A moment's reflection makes it clear that the gravitation pull of Jupiter is exerted sometimes in opposition to that of the sun, whereas at other times it is applied in aid of the sun, and yet again at various angles. In short, on no two successive days—for that matter no two successive hours or minutes—is the perturbing influence of Jupiter precisely the same.

What applies to the earth applies also, of course, to the varying action of Jupiter on the moon and to the incessantly varied action of the moon itself upon the earth. All in all, then, the course of our globe is by no means a stable and uniform one; though it should be understood that the perturbations are at most very slight indeed as compared with the major motions that constitute its regular action and lead to the chief phenomena of day and night and the succession of the seasons.

Relatively slight though the perturbations may be, however, they are sufficient to make noteworthy changes in the apparent position of the sun and moon as viewed with modern astronomical instruments; and they can by no means be ignored by the navigator who will determine the position of his ship within safe limits of error. And so it has been the work of the practical astronomers to record thousands on thousands of observations, giving with precise accuracy the location of sun, moon, planets, and various stars at given times; and these observations have furnished the basis for the elaborate calculations of the mathematical astronomers upon which the tables are based that in their final form make up the Nautical Almanac, to which we have already more than once referred.

These calculations take into account the precise nature of the perturbing influences that are exerted on the earth and on the moon on any given day, and hence lead to the accurate prediction as to the exact relative positions of these bodies on that day. Stated otherwise, they show the precise position in the heavens which will be held at any given time by the sun for example, or by the important planets, as viewed from the earth. How elaborate these computations are may be inferred from the statement that the late Professor Simon Newcomb used about fifty thousand separate and distinct observations in preparing his tables of the sun. Once calculated, however, these tables of Professor Newcomb are so comprehensive as to supply data from which the exact position of the sun can be found for any day between the years 1200 B.C. and 2300 A.D., a stretch of some thirty-five centuries.