NO. 6.] INTRODUCTION. LATITUDE AND LOCAL TIME. XV 



273 

 the factor ^^ . . , where t is the centrigrade temperature; consequently 



two values k and k' corresponding to the temperatures t and t' are connected 

 by the equation 



k_ _ 273 + f 



k' 273 + < ' 



The tables in use among our sailors, which are adapted to a certain 

 curvature Q' and a certain mean temperature t', give D = 600" for a height 

 of 100 feet (norw.) = 31.37 metres; consequently k' may be deduced from 

 the equation 



Supposing Q' to give the average curvature for latitude 50 (log Q' = 

 6.8049), this equation gives 



1 fc' = 0.139, 



and supposing further this value to be adapted to a temperature t' = 10 G., 

 the value corresponding to t = 20, which may be taken as a mean tem- 

 perature in the polar regions, is 



* = 15 * = - 156 

 zoo 



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 



D = 106".0 |/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 



