152 I. P. Косн. 
everything is arranged in such a manner as to create the most 
favourable conditions possible for the observations (protection against 
wind and sun, a particularly solid foundation), the personal estimate 
of the observer as regards the reading on circle and level come to 
exercise a comparatively great influence. The accuracy attained is 
therefore probably smaller with the small instrument than would be 
indicated by a mean-error computation. Add to this, that an esti- 
mate of the reliability of the refraction co-efficient, based exclusively 
on a determination of the mean error of the zenith distances mea- 
sured, would leave out of consideration the most important source 
of the error, that is the error of the presupposition, on which the 
formula k — 1 + (z, +2, + 180°) is based. The hypothesis forming 
the basis of this formula is that the line of vision between the two 
telescopes in A and B may be considered as coinciding with the 
circular arc touching the two sights AB and BA in the reticule of 
the telescopes. This presupposes the refraction to be the same in 
all points of the line of vision. However, as a general rule, this is 
only the case with a more or less rough approximation, and in the 
following we will see that cases must often occur where the refrac- 
tion is widely different in the various parts of the line of vision. We 
have, however, no better hypothesis to go upon in computing the 
co-efficient of refraction, k, and so we must be content with it. 
If the zenith distances z, of A from В and z, of В from A have 
been measured simultaneously, and if the altitude above sea level 
of A and B are h, and h, respectively, we get, the line of vision 
being considered as a circular arc 
her =D (1 An ne) tan 1 (21 —2,). 
From this it will appear that the hypothesis of the line of vision 
being considered a circular arc demands that the difference between 
the reciprocal simultaneous zenith distances should be constant for 
the two stations. By making these differences one gets a term for 
the uncertainty of the determination of k, and this term not only 
includes the uncertainty of the surveying operations, but also the 
inaccuracy of the hypothesis. 
Below are given the results of eight reciprocal simultaneous zenith 
distance observations from the Observatory (z,) and Cairn X (z,). 
The column z, — 2, shows very great oscillations, which are 
principally due to the variations of the zenith distances (z,) mea- 
sured at Cairn X. This might indicate a great inaccuracy in the 
survey work done by means of the small instrument, as would also 
