160 I. P. Косн. 
has been used. From the latter it appears that there should be a 
maximum value of k corresponding to z — 90°, i.e. k — 1. The 
observations at the horizon II, however, show three cases, where 
z< 90, and to this must necessarily correspond values К > 1. 
It must be borne in mind that the computation of k rests upon 
the basis of the refraction being the same at all points of the sight 
line. In this manner the line of vision at the horizon becomes an 
arc of a circle which touches the sight line and the surface of the 
sea, and the radius of which must consequently be greater than R, 
when the sight line turns the concavity downwards. 
In Fig.12 the earth is looked 
upon as a sphere, with the 
radius R, whereas the line of 
vision is considered an arc of 
a circle with the radius о. The 
geometrical significance of k is 
k= 2; the line of vision AB 
to which the sight line AB, 
s makes a tangent, represents a 
Fig. 19. 0 normal case. 
In the case of р = the 
line of vision becomes a straight line — AC in Fig. 12. To this corre- 
sponds the value k — 0, or in the case of the zenith distance from 
the Observatory in Danmarks Havn z = 90°07'10”. In the case of 
still greater zenith distances 
k would be negative i. e. the 
line of vision would turn the 
concavity upwards. This has 
not occurred in the case of 
the levellings at the sea hori- 
zon, whereas it undoubtedly 
occurs in the case of those 
undertaken at Cairn IX. 
In the case of o < В the 
theoretical line of vision ACB 
(Fig. 13) becomes more curved 
than the surface of the earth. 
It will, however, appear at Fig. 13. 
once from Fig. 13 that the 
course of the theoretical line of vision excludes the seeing of the 
horizon. In order that this may be possible it is an absolute ne- 
cessity that the line of vision should touch the surface of the sea, 
i.e. it must е. g. have a course like the one of ASB in Fig. 13. The 
