MEASURING THE EARTH'S SURFACE. 247 



accurate solution of geodetical problems vast areas and long distances 

 are necessary, and these none of tbe European countries possess except 

 Russia with its Asiatic dependencies. It has therefore been found ne- 

 cessary, 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 sci- 

 entific 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 w T hich is almost exactly north to south. The length of 

 the arc was not over one and one half degree, and was measured di- 

 rectly 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 execu- 

 tion 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 meth- 

 ods of measurement, an insight into the thoroughness with which geo- 

 detical 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 bv means 

 of angular observations. The two sides of the first triangle, the lengths 



