The periodicity of the errors (assuming the difference between the
Greenwich and Oxford results to be due to errors in the latter) is very
obvious, butj before discussing it, it is necessary to bear in mind that
different refraction-constants have been used at the two Observatories.
At Greenwich BesseFs constant, used in the Tabula RegiomontaneB,
is employed, while at Oxford this constant has been reduced in the
ratio of I : o'9967, or is nearly that of the Fundamenta.
I will therefore discuss the errors on two suppositions, namely, first,
as they stand, or as obtained by the use of the diminished constant ;
and secondly, as they would stand if Bessel's constant had been used
undiminished.
Now a single glance at the table exhibiting the errors will shew

e



XIV



SECOND RADCLIFFE CATALOGUE OF STABS.
that they follow a very simple law, and they could be represented by a
formula of this shape,

a + 6Sin4N.P.D.
For example, the errors vanish after passing from positive to nega,tive
near the pole, and again between the 14th and 15th group, or at an
interval of 90°; and the -maximum negative is attained when the
N.P.D. is about 18° and the maximum positive when it is about 6^°,
or at an interval of nearly 45°.
Assuming then this law, the following table will give the elements
for the solution of the equations for determining the constants a and 6,
on the two suppositions which have been named, weights being
assigned very nearly in proportion to the number of observations.
05:

3 P
1 2,


Excess of
Greenwich

uncor-
rected for
Refraction.
Cor-
rection
for

Re-
fraction.
Excess
cor-
rected.
1


4N.P.D.
Nat.
Sine.
Coefficient
of a
multi-
plied by
Weight.
Coeff'.
of 6

multi-
plied by
Weight.
