XVI GEELMUYDEN. ASTRONOMICAL OBSERVATIONS. — [NORW. POL. EXP. 
the points in heights H and H’ to the point in question, the expression 
will be 
_ CH = 
ere + ty (1—h) 
where y is the given distance in miles (or minutes of are) and C is the 
number of minutes in an are of circle equal to the radius (8438). Using the 
above values of # and @ and multiplying by 60, this gives 
a = 1108 - +. 9543 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, A 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 
2 
cos (H + h) = cos P + 2cos H cos h sin? = 
ee i 
SS aaa 
2 
Yr pil 
— cos H cos h sin? —_— 
d + cos D cos d sin? 3 
= 
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. Avexanprr, teacher of mathematics at the 
Royal Military Academy, and Mr. A. Graarup, assistant at the Norwegian 
Meteorological Institute, both in Christiania. 
The present volume contains all that is necessary for the reduction, 
except the meteorological data. An approximate value of the temperature 
