accurate solution of geodetical problems vast areas and long distances are necessary, and these none of the European countries possess except Russia with its Asiatic dependencies. It has therefore been found necessary, in the interest of science, that the various countries combine together so as to have reliable observations extending over a vast area of territory which could be put together and aid in the solution of the problem that most interests the modern geodete—the exact form and size of the earth.
Although one by one the triangulations of each continental country were connected with those of the countries immediately surrounding it, there was no uniformity in the whole work until the proposal was made that all the countries combine together and act on a uniform scientific plan.
In the United States no geodetical work was done before the year 1831. The only arc measurement executed previous to that date was made by Mason and Dixon in the eighteenth century. It is a part of the line now separating the States of Maryland and Delaware, the direction of which is almost exactly north to south. The length of the arc was not over one and one half degree, and was measured directly with long wooden rods.
More recently the United States Coast and Geodetic Survey have been actively engaged in completing the measurement of an arc north to south and another east to west, the work done so far on the first bringing its length to twenty-two degrees, while the parallel arc across the continent will have when completed a length of forty-nine degrees. The advantages which these measurements in the United States have as scientific results are their great length, and, being executed by one authority, their uniformity in the methods of execution.
Although the principle is always the same, the methods of execution in geodetical work may show slight variations from one country to another. The following description of the field-work that has to be done is therefore of a general character, being intended to give the reader who is not familiar with mathematical studies, and with methods of measurement, an insight into the thoroughness with which geodetical work has to be executed, and the minuteness with which all the details of the work have to be carefully considered.
If the length of one side of a triangle is known, the length of the other two sides can be calculated, provided that at least two of the angles of the triangle can be measured by direct or indirect observation. It is therefore indispensable that a straight line be carefully measured, and the length of this line can be used as a basis by means of which all the distances between the various points or stations of the net can be calculated. This straight line that is actually measured in the field is used as the side of one of the triangles, and the other two sides are calculated with the help of the angles which can be measured by means of angular observations. The two sides of the first triangle, the lengths
