158 I. P. Kocx. 
This formula was used to compute the deviations of the co- 
efficient of refraction from the mean value. These deviations are 
entered in the table under 4k in units of the third decimal place. 
In the case of Cairn X and the “Skerry” the correction of the 
values of the co-efficient of refraction, which had already been deter- 
mined by means of reciprocal, simultaneous observations, was like- 
wise computed from the formula dk — 15 In order that this 
might occur, the values which had been determined by reciprocal 
observations of the zenith distances of the reticule of the little in- 
strument, had to be conveyed to the centre of the wooden disc at 
Cairn X and to the top of the rocky knoll on the “Skerry”, by means 
: 1.51 m + 0.73 т 
Me 19 [44 = = [ vr 
of the correction — 1'24”.8 and +o 19986 m + 16.5. 
Besides the two thus determined values of the co-efficient of 
refraction we further — as given in the following — computed a 
value corresponding to a point of the sea horizon. As mean values 
of the observations to Cairn X, to the “Skerry” and the said point 
of the sea horizon we have: 
for Cairn X k* — 0.160, 
[77 = LE] BS) 
= thes, Skerry. ice 0.516, 
- Horizon I КИ = 0.584. 
m 
| 
Absolute determinations at the sea horizon. 
The levellings at the sea horizon were undertaken in three dif- 
ferent fixed azimuths. The distance to the points observed may be 
computed from the known formula 
However, one may deduce a still simpler term in which k is not 
included, through the following argument: 
If the levelling at the sea horizon is considered as the one ob- 
servation in a reciprocal, simultaneous zenith-measuring, it follows, 
as a matter of course, that the other imaginary levelling gives a zenith 
distance equal to 90°. 
For the difference of altitude between two points, in which a 
reciprocal, simultaneous observation of the zenith distance is under- 
taken one gets: 
“hy +h, = Dtan$(z, +z,)! 
Е : h, +h 
1) Approximation for В, +h, = D (1 + ne) tan 4 (z, 22): 
