XVI GEELMUYDEN. ASTRONOMICAL OBSERVATIONS. [NORW. POL. EXP. 



the points in heights H and H' to the point in question, the expression 

 will be 



C H , t t\ 



*=' + iy(i-fc) 



where y is the given distance in miles (or minutes of arc) and C is the 

 number of minutes in an arc of circle equal to the radius (3438). Using the 

 above values of k and Q and multiplying by 60, this gives 



x = 110".8 - + 25".3 y 



y 



when H is expressed in metres. 



On taking the altitude of a star with an artificial horizon it happened 

 twice that one star was combined with the reflected image of another nearly 

 in the same vertical (a and y Cygni, Castor and Pollux). These observations 

 were utilised in the following manner. As soon as it was detected which 

 stars had been observed, a preliminary calculation would give with sufficient 

 accuracy their difference of azimuth. If H and h are the true altitudes of 

 the two stars, D and d their declinations, R and r their right ascensions, 

 A and a their azimuths, and P the measured angle diminished by a quantity 

 corresponding to the sum of refractions, which could be found by the same 

 preliminary calculation, the true altitudes are given by the following equations: 



_ a 

 cos (H -\- h) = cos P + 2cos H cos h sin 2 = 



h . ) d . , . nE r , . A a 



2 



sin 



. . , . n , . 



= sin 2 g -- f- cos D cos d sin 2 ^ -- cos H cos h sin 2 



~ 



where approximate values of H and h will suffice on the right. 



The determinations of time and latitude near the observations of Lunar 

 Distances and of Solar Eclipses, the observations taken at sea in 1893 and 

 on the sledge expedition, and some few others, have been computed by the 

 writer, all the others by Mr. A. ALEXANDER, teacher of mathematics at the 

 Royal Military Academy, and Mr. A. GRAARUD, assistant at the Norwegian 

 Meteorological Institute, both in Ghristiania. 



The present volume contains all that is necessary for the reduction, 

 except the meteorological data. An approximate value of the temperature 



