171 
endeavour to avoid as much as possible those mentioned under 2. 
and 3., beginning with 3. From the whole of the observations of 
all the observers, freed from their individual personal errors, it will 
then perhaps be possible to estimate those given under 2. 
A brief account of the Leyden programme may precede. The stars 
of the programme are, as far as possible, divided into zones, whence 
in view of the somewhat restricted material (1600 stars distributed 
over 24 hours of right ascension and declination —2°. to 52°, and 
the distribution in R.A. still very irregular) it was impossible to 
take the zones very narrow. 
In general the zones are chosen with the limiting declinations of 
0°— 20°, 20°—30°, 30°—40° and 40°-zenith, but it was often neces- 
sary to include in a zone stars of slightly different declination. The 
fund. stars are so chosen that they lay below, in and above the 
zone so that their mean declination was as much as possible at the 
middle of the zone. 
As, therefore, fundamental stars differing by 25° in declination 
are sometimes observed on the same night, the question arises, 
whether the different observers registered stars with such different 
declinations, i.e. of different velocities, all in the same way. 
If a systematic difference of this kind existed, it would be desi- 
rable to reduce the times of transit of the separate stars to a hypo- 
thetical star with a declination equal to the mean declination of 
the fund. stars used. The times of transit of the programme stars 
could then be reduced also to the same hypothetical star, and by 
a purely differential reduction the results of the programme stars 
would be freed from this systematic error. 
For this purpose the separate nights of the different observers are 
treated in the following way : 
Let observer X on one night observe n fund. stars. 
Times of transit 7... 7,, mean 7 
Declinations d,...dn, mean d 
Clock correction derived from each star a,...a», mean a. 
As unknowns may be taken the rate of the clock = 2° per 
minute and the possible influence of the declination on the time of 
transit = +y* per 1° deviation from the mean declination. 
Every night gives n equations of the form: 
(T — Tj) as + (d— dj) ys = (a8 —a;8) Bae | Pde le BPs n 
From these » equations the unknowns # and y have been solved 
by least squares. 
The x as found in this solution can be regarded asa first approx- 
imation to the rate of the clock. 
