OF NEBULJE AND CLUSTERS OF STARS. 
3 
greater errors than those which probably affected her results. This I have accordingly 
done. But to do it effectually, and at the same time to effect a thoroughly correct 
identification of the objects in my catalogues with those of the older series, involved, 
as a necessary preliminary step, the reduction to 1830-0 of the whole of her catalogue, 
an operation in which I received the assistance of my sons ; the computations being 
executed for each nebula in duplicate and checked by myself, and which, taken 
leisurely, zone by zone, as time and circumstance permitted, proved less onerous and 
wearisome than might have been expected. The Catalogue thus reduced to the same 
epoch as my own, afforded the means of detecting and rectifying a great many errors of 
nomenclature in the latter. And it was in the course of this part of the inquiry, in 
which many cases of considerable intricacy and difficulty occurred (as will be evident on 
a perusal of the notes appended to this Catalogue), and in which it became necessary to 
recur both to the original sweeps and to a series of registered extracts from them (the 
nature of which will be more distinctly stated hereafter), that I learned fully to appre- 
tiate the skill, diligence, and accuracy which that indefatigable lady brought to bear on 
a task which only the most boundless devotion could have induced her to undertake or 
enabled her to accomplish. 
Arrived at this stage — that is to say, the mean results of all the observations in my 
own Catalogues taken, and all the deficient or imperfectly observed nebulae in my 
Father’s list supplied, as above stated, and the whole arranged, not in zones, but in 
general order of right ascension, — it then became necessary, in order to produce a work 
available for future observation, to bring the whole up to a still more advanced epoch. 
The work required for this purpose, calling no longer for any discussion, or collation of 
the original observations or registers, but being one of simple arithmetical computation 
from a definite formula — the Royal Society, at my application, very liberally undertook 
to supply, from the funds at their annual disposal, the amount necessary to procure its 
execution by an experienced computer (Mr. Kerschner, one of the occasional computists 
for the Royal Observatory of Greenwich). This work the Astronomer Royal most 
obligingly offered to superintend, affording at the same time his advice as to the general 
principle on which the computation should be conducted. The plan suggested by him 
and adopted in effect was this. Each object in the Catalogue was first roughly brought 
up to the year 1880 by the application of approximate precessions in R.A. and P.D. 
The places so obtained were then employed to compute the exact precessions in both by 
the usual formulae, with coefficients for the year 1880-0, viz. 
Precession in R.A. = 3 s -072-|-l s -337. sinR.A. cotan P.D. 
Precession in P.D. = — 20"-06 cosR.A. 
And the precessions, so calculated, were then used to bring up the places from 1830 to 
1860, the epoch of the Catalogue ; so that, the places being given for 1860 and the pre- 
cessions for twenty years in advance, the application of those precessions to those places 
shall give dependable places for any year up to the year 1930, at which time the small 
error in excess or defect of the true precession consequent on using the fifty years’ 
b 2 
