714 
greatly divergent from the average. This difficulty disappears, if the 
accidental irregularities can be abolished by reduction to one system, 
which is feasible if a great number of plates are joined so as to 
partly cover one another. With chart-plates this does not happen 
anywhere; but it does in the case of the Paris catalogue-plates, of 
which the zones 22°, 23° and 24° have been published complete. 
As in this case the centres of the one zone concur with the corners 
of an adjoining zone, each plate has a quadrant in common with 
each of the 4 surrounding plates. In this way it was possible to 
reduce all the plates of these three zones between 3'16™ and 532m 
to their average. A few particulars regarding this reduction will 
be added here. 
Two consecutive plates a and 6 of the central zone (23°) can be 
joined together by a plate of the N-zone (24°) c, which has a qua- 
drant in common with both, and also by one of the S-zone (22°) d. 
A be 
pct 
If we call the quadrants 3 the density (6): density (a) = TA 
and likewise =" x = For the logarithmic difference in density of 
An 4 
every two consecutive plates of the central zone we get therefore 
two values, the concurrence of which gives a measure of the accu- 
rateness obtainable. We must bear in mind that the quadrants on 
the adjoining plates do not accurately concur, because of the con- 
vergence of the declination-circles, and because they stretch 65’ 
from the centre. The results obtained, starting with log d (3h24m) 
— log d(3'16™) and ending with log d(5'40™) — log d (5'32™) (in 
units of the 3rd decimal), are: 
from de N. plate +046 +070 —161 +030 +216 —240 +029 +369 —002 
from de S. plate +027 +106 —335 +233 +298 —535 —115 +490 —073 
adopted +036 +088 —248 +131 +257 —387 --040 +430 —037 
+639 —816 +807 —552 +359 +094 —529 +500 —165 
+469 —856 +637 —531 +382 4-168 —588 +451 —120 
+554 —836 +722 —541 +370 +131 —558 +476 — 142 
Herefrom for every plate of the middle-zone the deviations from 
a medium-value were deduced and from these numbers the same was 
found for the N- and the S-zone; these values, with contrary sign, 
give the logarithmic reduction for each plate, the logarithm of the 
factor, by which the number of stars on that plate is to be multiplied, 
in order to count for the same average limiting magnitude. They 
are in the sequence of decreasing R.A.: 
