349 
In that ease, i.e. if the times of transit over all the threads are 
estimated in the same way, independently of their position and order, 
the condition for each thread would be: 
[A] Cl. West + [A] Cl. East = 0. 
It was already mentioned, that more than once at Leiden syste- 
matie differences were found, so that this relation did not hold 
accurately. Such differences: have especially occurred with the extreme 
threads and are most probably due to the first thread being observed 
in an abnormal manner (we are referring here to chronographic 
observations). Hereby the sums for the two extreme threads became 
different from zero by the amount of the anomaly. As an instance, 
in Dr. PANNEKOEK’s observations of the years 1899—1902 the sums 
for the extreme threads were — 08032 and — 08035 respectively, 
whereas for the other threads the greatest value of the sum was 
0s025, and as a rule it was much smaller. 
In the present investigation of the thread-intervals we confined 
ourselves to such stars as had been observed on all 7 threads and 
even with this restriction, at least for the four largest periods 1, II, 
V and VI, abundant material was available. As in this communi- 
cation it is our object more especially to bring forward some general 
conclusions, we shall exclusively investigate the results of those 
+ periods which are the only ones suitable for that purpose. We 
shall not communicate the results as originally derived, but imme- 
diately apply two special modifications which were found to be 
advisable to the second of us in the course of a preliminary investi- 
gation. These modifications consist in the first place in confining 
ourselves to such stars as were observed during the night and had 
also been observed in declination, and secondly in dividing the 
Vth period into two sub-periods Va and Vb, the division being 
formed by a cleaning of the reticule on January 29, 1866. Although 
it appeared later on that Vb and VI could be united, we shall 
for the moment keep these periods separated. 
As mentioned above, for each observation the quantities |4| were 
formed and subsequently the sums [A]|y + [Als, when the totally 
unexpected results were obtained which are contained in the following 
table. The quantities are expressed in thousandtbs of a time second, 
the number of observations used in each position being added 
each time. 
The sums will be seen to reach unexpectedly large values and 
to be roughly the same for all threads and also for both observers. 
A considerable part of the oscillations which appear may be ascribed 
