170 
that nowhere an extrapolation of the clock rate takes place; the 
night’s work therefore should always begin and end with a number 
of fund. stars. 
In the second place it is necessary that the fund. stars, or rather 
their groups, be at a sufficient distance from each other, so that 
the accidental errors in the times of transits shall have as little 
influence as possible. 
Theoretically it is always possible to fulfil these requirements by 
a well chosen programme of observations. Only on nights interrupted 
by clouds it les outside the power of the observer to fulfil them. 
It is, therefore, necessary to examine more closely the accuracy 
of the times of transits obtained. 
The clock corrections as derived from the separate stars are affected 
by two kinds of errors, accidental and systematic. 
Of the influence of the first an idea can be obtained by computing 
the mean error of the time of transit derived from the transits of 
the separate threads (in Leyden numbering eleven). Generally speaking 
this error will not exceed + 0.024. If we had two groups of four 
fund. stars separated by an interval of two hours, the mean error 
of the clock rate, due exclusively to the accidental errors would 
thus be about 
V 0.012? + 0.012? 
— = + 05.00014. 
120 
The second category of errors plays, however, at least as impor- 
tant a part and it is therefore necessary to make the times of transit 
as completely independent of them as possible. 
Under these errors we include: 
1. The magnitude equation. 
By a suitable use of gratings it is possible to confine this error 
within narrow limits. What remains must be removed as much as 
possible by deriving the magnitude equation of the various observers 
and correcting for it. 
2. The errors in the assumed positions of the fundamental stars. 
Since it is practically impossible to confine oneself to the small 
number of accurately established fundamental stars, it is necessary 
to use as fund. stars some that are of doubtful value, so that these 
errors must have a great influence not only on the mean clock 
correction, but even more on the rate of the clock as derived from 
the observations (see the large probable errors given by Boss’ P.G. C. 
for various stars for the epoch 1910,0). 
3. Personal errors of the different observers. 
Assuming that the error mentioned under 1. be removed, I shall 
