Vol. 6, 1920 
GEOPHYSICS: W. BOWIE 
547 
longitude of each point and the bearing of each Hne based on the data 
for the initial point, at which the astronomic latitude and longitude were 
observed and the true bearing determined of one line of the triangulation. 
This is the simplest case of a geodetic survey where the whole net work 
depends on some initial astronomic station. 
In practice, we have a much more complicated situation. Geodetic 
surveys have been started from many widely separated astronomic sta- 
tions and the triangulation based on each has been finally extended until it 
meets the triangulation nets based on other astronomic stations. When 
this has been done, it is always found that the geographic positions com- 
puted from one astronomic station will differ from the geographic posi- 
tions of the same points computed from other astronomic stations. We 
have a very striking example of this on the island of Porto Rico. The 
astronomic latitude was determined at Ponce, on the southern coast, 
and at San Juan on the northern coast of the island. The distance 
across the island, in a north and south direction, between these stations, 
is approximately thirty miles. The distance between the two stations, as 
computed from their observed astronomic positions, differs by about one 
mile from the distance between the two as determined by triangulation. 
The triangulation distance is correct within ten feet. The cause of this 
difference in distance as determined by the two methods is the attraction 
of the mountain mass, forming the Island of Porto Rico, on the plumb 
line to which the astronomic observations are referred. To the north- 
ward of Porto Rico are the deepest parts of the Atlantic Ocean and just to 
the southward of the island is a vast depth in the Caribbean sea. It can 
be readily seen that the effect of this distribution of mass in the oceans 
and in the island and its base is to draw the plumb line towards the centre 
of the island. This would throw the zenith on the south shore too far 
to the south and the zenith at the north shore station too far north. The 
plumb lines projected against the celestial sphere would therefore in- 
clude a greater arc than they would under normal conditions. This angle 
is actually about 56 seconds of arc greater than normal. 
In carrying on a geodetic survey, as described above, it is necessary to 
know accurately the elevations of the base lines and triangulation stations 
above the so-called plane of reference which is mean sea level. Each 
line that is determined by the triangulation is referred to sea level, that 
is, the computed distance between any two stations is the distance, along 
the geoid or sea level surface, between the points where the plumb lines 
at the two stations pierce this surface. Accurate elevations are also 
needed in many phases of surveying, in mapping, and in other engineer- 
ing operations. They are also essential in many branches of science, 
notably in meteorology, geology, etc. 
In order that elevations may have the maximum value to engineers 
it is necessary that they all be referred to the same, so-called, plane of 
