XXXII 
PRELIMINARY GENERAL CATALOGUE OF STARS FOR 19OO 
derived from the residuals for that star alone, but are computed from the weights 
resulting from the least-square solution, the probable error of the unit of weight 
having been verified from the residuals in the solutions of hundreds of stars. As 
with probable error in general, it may happen that abnormal residuals, or a favor¬ 
able “run of luck, ” may cause the probable error computed from the residuals for a 
given star to be greater or less than the mean probable errors printed in this Cata¬ 
logue ; but it is believed that, in the long run, the latter are more reliable. It should 
be borne in mind, however, that probable error is not probable uncertainty. This 
latter may be as much as, or more than, four times the probable error. Computa¬ 
tion shows that we ought to expect that 43 out of the 6188 stars of the Catalogue will 
ultimately prove to be affected by errors equal to four times the printed probable 
error of position, and similarly for the probable errors of motion. But these will be 
the extremely unlucky cases, and, after all, they will be only about one star in 140. 
Not quite one-fifth of all the stars should be found to have errors equal to twice their 
probable errors; and about one in twenty-three stars should turn out to have a real 
error three or more times the probable error assigned to it in this Catalogue. 
Then there are the mistakes, as distinguished from mathematical probable 
error. These may be classified for convenience as follows: 
(1) Mistakes in the star-positions as printed in the original catalogues of 
observation. 
(2) Mistakes of computation in course of preparing the data for this General 
Catalogue. 
(3) Mistakes occurring in the combination of data from these computations in 
order to form this Catalogue as printed. 
Doubtless all the catalogues contain undetected errors that may be termed 
mistakes, some of which have been discovered in the course of this work. The 
presence of such errors, notably in catalogues like Pi 1900, Madr 35, Arm 40, 
Madr 75, and others, has been frequently indicated to us by abnormal residuals. 
When it appeared that these might be five times as large as the computed probable 
error of the catalogue-positions for the particular number of observations employed, 
the residuals were rejected; but, since satisfactory probability that a discordance 
was really to be attributed to a particular catalogue would often be wanting in the 
case of many of the weaker stars, it must have happened in numerous instances 
that the catalogue-places as actually employed in these computations are still 
injuriously affected by undetected, material errors of observing record or of com¬ 
putation. The effect of such undetected errors, and of other well-known practical 
considerations, must have been to make the probable errors assigned to the weaker 
stars relatively less accurate than for the stronger stars, from which abnormal 
errors are more completely, though not entirely, eliminated. In considering this 
first point, however, it should be noted that, in computing the weights of observed 
star-positions (App. Ill) some of the effect of mistakes in the individual cata¬ 
logues is naturally included. 
As to errors in the computation for this work, very great care has been exercised 
to reduce the number of these to the lowest possible limit. The greatest part of 
this work has been absolutely duplicated, and all of it has been carefully checked. 
