Book, that the sun upon the shortest day " had Dagmálastaðr and Eyktarstaðr," this does not mean that the sun was visible until a certain hour, for they lacked the means of determining the hour, according to our understanding of the word, but it does mean that the sun was visible in certain horizontal directions which they were experienced in determining.'
Applying the passage in Kristinnréttr to the determination of the position of the sun at sunset, on the shortest day of the year in Wineland, Mr. Geelmuyden concludes that:
' Since Útsuðrsætt is the octant, which has S. W. in its centre, therefore between 22-5° and 675^ Azimuth, Eyktarstaðr must be in the direction 22-5° + 1 of 45°=52-5° from the south toward the west. Solving the latitude in which the sun set in this direction on the shortest day [in the eleventh century] we find it to be 49°55'. Here, therefore, or farther to the south the observation must have been made.'
I am indebted to Capt. R. L. Phythian, U. S. N., Superintendent of the U. S. Naval Observatory, Washington, for the following detailed computation undertaken, at my request, from a brief statement of the problem:
'As the solution of the question j'ou propose depends, of course, upon the interpratation of the data furnished, it is necessary that I should give in detail the process by which the amplitude of the sun is derived from the statement contained in your letter.
' " Eyktarstad " is assumed to be the position of the sun in the horizon when setting. The south-west octant you define to be the octant having S.W. as its centre; its limits, therefore, are S. 221° W. and S. 67^° W.
' " It is eykt when, the south-west octant having been divided into thirds, the sun has traversed two of these and has one still to go." That is, it is eykt when the point of the horizon is 30° west of S. 22^ W., or S. 52^° W. From this the sun's amplitude when in this point of the horizon is W. 37° 30' S.
'The sun's declination on the shortest day of the }-ear 1015 was S. 23° 34' 30" [nearly].
'The simple formula for finding the sun's amplitude when in the true horizon is sufficiently accurate for the conditions of this case.
' It is sin A = sin d sec. L,
from which sec L = sin A cosec. d.
' Solving with the above data:
A =-37° 30' log. sin. -978445
d= -23° 34' 30" log, cosec. -0-39799
L= -f48 56 log. sec. 4-018244.
' If I have been in error in the process by which the amplitude has been arrived at, the substitution of its correct value in the above computation will give the proper latitude.'
This computation was undertaken independently of Mr. Geelmuyden's conclusions, and in reply to my query, evoked by the slight discrepancy in the two results, which was then first brought to his attention, Capt. Phythian writes, as follows:
'The formula by which I computed the latitude is the simplest form that can be employed for the purpose, but was, for reasons that will be mentioned later, deemed sufficiently accurate.
