546 
GEOPHYSICS: W. BOWIE 
Proc. N. a. S. 
Almost every country of the world that pretends to any standing has 
organized a service for the purpose of carrying on what are called geodetic 
surveys. As a matter of fact, any survey of the land in which the shape 
and size of the earth are taken into consideration can be called geodetic; 
thus, the hydrographic surveys along the coast made for a sailing chart 
are really geodetic surveys and, similarly, a topographic survey of a large 
area may be considered to be a geodetic survey; but what I have in mind 
in speaking of geodetic surveys, are triangulation, base measurements, 
precise leveling, etc. 
By means of base measurements and triangulation, the geographic 
positions of places are determined which are of immense value in the 
permanent establishment of boundary lines between nations and political 
sub-divisions of a nation, for the control of various classes of surveys and 
maps, and for other engineering purposes. 
Practically the whole of Europe has been covered by a system of points 
whose latitudes and longitudes have been determined by triangulation. 
This is also the case in Japan and in India. Australia, portions of Africa, 
and some of the countries of Central and South America have made good 
starts towards extending triangulation over their areas. In the United 
States excellent progress has been made in this w^ork. There is triangula- 
tion around the entire border and there are many arcs in the interior of 
the country from which triangulation of precise or lower grades may be 
extended into every area in which detailed surveying and mapping opera- 
tions are to be carried on. 
It will be of interest to outline briefly the methods for carrying on tri- 
angulation or trigonometric surveys. 
In the first place a spheroid of reference must be adopted which will 
approximate the actual shape and size of the earth. Then there must 
be an initial point whose astronomic latitude and longitude have been 
observed. Next is needed the azimuth or true bearing of a line of which 
the station occupied forms one end. After these data are available it is 
necessary to measure with extreme accuracy the distance between two 
inter^dsible points on the earth's surface to serve as a base. After the length 
of the base is known, additional stations are selected with a view to form- 
ing triangles by lines which are clear of obstructions and thus intervisible 
between their ends. It is, of course, a well known mathematical princi- 
ple that when a side and the angles of a triangle are known, the other 
sides can be computed. When these sides have been computed from the 
base, either one of them can be used as the base for a new triangle. In a 
similar manner we may extend the computations through a long chain 
of triangles extending in some cases hundreds of miles across a country. 
When the base has been measured and the angles observed and the com- 
putations of the triangles have given the lengths of the sides of the tri- 
angles, then computations can be made which will give the latitude and 
