GEODESY. The science of measuring large portions of the earth's surface, continents, countries, etc., with a view to determining the form and dimension of our globe and of mak ing maps of extended regions of its surface, differs from surveying (q.v.) in the wider re gions which its scope includes, and in the cor responding necessity of more delicate and re fined instruments and methods. As an example of the problem it involves: If a map of the United States is to be made, one of the many questions arising would be that of the exact distance on the earth's surface between two cities. This is obviously impossible of measure ment in the familiar way with the tape line. To carry out such measurements the method of tri angulation must be applied. To do this, two points must be found a few miles apart so sit uated that the distance between them can be directly measured on the ground, and that from each of them several different points in the region to be surveyed are visible. Let AB be the two points chosen and C, D, E, F, etc., some of the distant points: The line AB is called the base line of the triangulation, and is measured by means of rods closed in wooden cases to protect them from rapid changes of temperature, which arc successively placed end to end from the point A to the point B. Re cently it has been found that steel tape can be used much more expediently and with all the precision that is required for the purpose. Having found the exact length of the base line, a theodolite is mounted at A and vertical rods or signals are erected at B C, so that the angle BAC can be measured with the greatest pos sible exactness. Then the theodolite is carried to the point B and the angle is measured in like manner. If practicable the theodolite may also be mounted at C in order to measure the re maining angle of the triangle. The sum of the angles should come out 180°, this being the sum of the angles of any plane triangle. These three measurements will show any error in the measurement of the angles. Knowing the three angles and of the side of the triangle, the com putation of the two remaining sides is a very simple one in trigonometry.
Commonly there will be a number of points, C, D, E, F, etc., which can be determined at the same time. Having done this, any of the lines from A or B to C, or between any two of the other known points, may be used as a new base line and the distance of vet other visible points measured in the same way. These, again, can he used as new base lines, and so on indefinitely. This method is especially expeditious in moun tainous regions, where observations can be made from peak to peak at distances sometimes ex ceeding 100 miles.
A fundamental point in which geodesy dif fers from surveying is in the combination of measurements of the earth's surface, with ob servations of the stars; the object of the com bination is the determination of the curvature of the earth's surface and the size of our globe.
The principle involved will be readily seen iv a little careful thought. It is obviously im possible to determine with any exactness the degree on the earth's surface. This distance can be determined between any two points which are connected by a geodetic measurement. The difference of longitude may also be determined astronomically by telegraph and by geodetic measurement of the earth's surface. The rela tion between the two measures shows the curva ture in the east and west direction.
One of the most difficult questions connected with the figure of the earth is that of the exact ellipticity or flattening of our globe. The pre cise figure of the earth itself does not admit of definition on account of the irregular outlines of the mountains. Hence, as a basis of all exact statements, geodesy takes, as a standard body representing the earth. the figure that would he formed by the surface of the ocean if the continents were removed so that the curvature of the earth's surface by observations made solely on that surface. But the surface of the ocean, which is taken as the basic one, is everywhere perpendicular to the plumb-line. It follows that the angle between the directions of the plumb-line at two points will be equal to the curvature of the ocean surface between the points. By skilful astronomical observa tions it is possible, on any part of the solid earth where an instrument can be mounted, to determine the exact declination in the celestial sphere from which the plumb-line points, which is, in fact, the zenith. The declination of the zenith is the latitude of the place; it follows, that if the latitude of two points north and south of each other is accurately determined, and found to be one degree, for example, the distance between them is the measure of one ocean would cover the whole globe. It is clear that if the earth did not rotate on its axis, the form assumed by an ocean covering it would be that of a sphere. But, owing to the rotation, the equatorial regions of the earth are expanded and' the polar regions contracted so that the ideal form is that of an ellipsoid. If all parts of the earth were of the same density this ellip soid would be easily determined; but owing to the inequality of density of different parts of the earth, the figure of the ocean itself is not an exact ellipsoid. The best that can be done is to make the calculations assuming it to be such, and to make the best allowance that we can for such small deviations as may be discovered.