300 1. P. Косн. 
а method often resorted to is to choose the observation stations оп 
coast mountains, to determine the altitude of the station, for instance 
by means of barometric levelling, and to use this altitude as the 
basis for distance measuring at points situated along the coast line. 
This simple and serviceable method, which has, for instance, been 
widely used in Greenland, has been made the subject of scientific 
treatment by C. BORGEN and R. COPELAND, the astronomers of the 
Germaniaexpedition!). On the strength of their researches BORGEN 
and COPELAND have further prepared a table as a help to the com- 
putation of distances. 
In testing the accuracy of the method BORGEN and COPELAND 
set up a differential equation which looks as follows: 
dD = adz + Бан, 
where D is the distance, z the zenith distance and H the altitude of 
the telescope above the level of the sea. As an example I shall 
state that the co-efficients a and b of the differential equation are 
computed for the distance measuring at a definite coast point from 
Station Kap Bremen. Н is here determined at 1008.3 m, = at 91°06’20”.3; 
the refraction constant is estimated at 0.2. The differential equation 
in this case looks as follows: 
dD = — 29.48 dz + 91.21 dH. 
After this it is said: 
“If the zenith distance is supposed to be encumbered by an 
error of 10” and the altitude of the station by an error of 2m, one 
will thus by an altitude of 1000 m be able to determine a distance 
of 66 kilometres, without greater errors in the latter than at most 
500 m.” 
This gives a most misleading idea of the accuracy of the method. 
The example shows quite clearly that BORGEN and COPELAND, as 
sources of errors in the zenith distance, only reckon with the errors 
due to the measuring operation itself, but pay no attention at all to 
the variations of the refraction. These may, however, cause errors 
in the zenith distance of several minutes, so that dz in place of 10” 
ought rather to be put at 2’ (see the section on Terrestrial Refraction) 
in which manner the error in the 66 kilometres, computed in the 
example, would amount to nearly 4 kilometres. 
That one must, in numerous cases, put up with a much greater 
uncertainty than 2m in the altitude of the station is also known by 
everyone who has gone in for practical geographical survey. 
!) Zweite Deutsche Nordpolfahrt II, Küstenaufnahme mittels Depressionswinkeln, 
p. 878— 883. 
