NO. 6.| INTRODUCTION. LATITUDE AND LOCAL TIME. XV 
the factor , where ¢ is the centrigrade temperature; consequently 
273 
273 + t 
two values & and k’ corresponding to the temperatures ¢ and ¢’ are connected 
by the equation 
k_ %3+¢ 
kK 213 + ¢ * 
The tables in use among our sailors, which are adapted to a certain 
curvature g’ and a certain mean temperature ¢’, give D = 600” for a height 
of 100 feet (norw.) = 31.37 metres; consequently k’ may be deduced from 
the equation 
mr (=k). 
600 = s]/ 
Supposing @’ to give the average curvature for latitude 50° (log 9’ = 
6.8049), this equation gives 
koa 0M39> 
and supposing further this value to be adapted to a temperature ¢/ = 10° C., 
the value corresponding to = — 20°, which may be taken as a mean tem- 
perature in the polar regions, is 
DBS 3 yo 
Taking finally the curvature for 80° of latitude (log @ = 6.8060) the 
expression for the normal dip of the horizon in the polar regions will be 
Di = H06Z0 | height in metres, 
from which a table was formed. Casual irregularities may of course con- 
siderably surpass the difference between this and the mean value for tempe- 
rate regions. Observations of the midnight Sun in 1894, as compared with 
southern altitudes taken over an artificial horizon, seem to indicate a smaller 
value of the dip. 
During the voyage along the coast of Siberia the Sun’s altitude was 
sometimes measured from a coast line at a given or estimated distance. 
Supposing the depression of this coast line, as seen from the height H, to 
be the sum of the dip for an eye’s height H’ having the coast line in the 
apparent horizon, and the angle between the two straight lines, issuing from 
