=======+==============================+=====================
| CENTER (1875.0) | NUMBER
FIELD +--------------------+---------+-------+-----+-------
| α | δ | Known | New | Total
-------+--------------------+---------+-------+-----+-------
I | 1ʰ 0ᵐ 30ˢ | +31°44′ | 21 | 57 | 78
II | 1 42 20 | 32 0 | 3 | 81 | 84
III | 11 3 54 | 29 27 | 8 | 178 | 186
IV | 13 37 10 | 56 21 | 21 | 52 | 73
V | 14 57 10 | 23 47 | 3 | 49 | 52
VI | 17 11 22 | 43 50 | 5 | 43 | 48
VII | 23 14 16 | 7 27 | 15 | 52 | 67
+--------------------+---------+-------+-----+-------
Total| | | 76 | 512 | 588
-------+--------------------+---------+-------+-----+-------
If very faint stellar images could be used for reference, this error
could be largely reduced. It was necessary, however, to use stars from
the catalogues of the Astronomische Gesellschaft for reference, and
with the long exposures required for the faint nebulae the images of
these stars were very large. At the edge of the plate, for instance,
the arrow-shaped image of a star of the ninth magnitude would often be
fully a minute of arc in length.
It seemed inadvisable to make an exhaustive study of this
magnitude-error, whence the alternatives were to use a restricted
portion of the field or to sacrifice accuracy in the reduced positions.
The second of these evils was chosen. The positions of the optical
centers of images at various distances from the center of the field
were determined empirically. Pairs of plates of a region were taken
with apertures of 9 inches and with the full 24 inches and were
compared in the Zeiss “blink” comparator. With the smaller aperture,
and hence the smaller focal ratio, the images near the edge of the
plates were sensibly round and small. Superimposed on the 24-inch
images, they indicated where the wires should be set in measuring the
larger distorted images. Trials were then made, measuring positions of
A.G. stars all over the 24-inch plates, until a kind of technique was
acquired. Judged by the aims in view and the results obtained, this
empirical scheme fully justified itself.
At least two plates of each field were taken. In any case the two best
plates were put on the “blink” comparator, and only those objects
clearly nebulous on both plates were marked. The better plate was then
placed on a Gaertner measuring machine. The nebulae and all the A.G.
stars fainter than the seventh magnitude were measured in _X_ and _Y_
with the same screw. After an interval of a day or two the plate was
remeasured. Settings were read to 0.01 mm, corresponding to about 0.87"
on the scale of the plate. The two measures of a nebula differed but
seldom in this unit, and if faint reference stars could have been used,
a higher degree of accuracy could have been maintained throughout the
work.
In order to orient the plate, two stars were selected with as large a
difference in right ascension and as small a difference in declination
as possible. The difference in _X_ was then computed in millimeters,
assuming a scale-value of 87.4″ per mm. The plate was placed in the
measuring machine with the meridian roughly perpendicular to the screw,
and adjusted with the tangent slow-motion until the setting on the two
stars gave the computed difference to the limit of accuracy of the
settings. This method reduced the constant of orientation of the plate
to an almost negligible quantity.
Turner’s method (_The Observatory_, 16, 373, 1893) was used as the
basis for reducing the measures. The six plate-constants for each field
were determined from the five or six A.G. stars most symmetrically
distributed about the optical center, and graphs were constructed
from which the values of _Y_-_Y₀_ and _X_-_X₀_ were corrected. The
Δα and Δδ were then added directly to the α₀ and δ₀ of the assumed
center, and final corrections to the positions were read from graphs
constructed from Turner’s formulae. Any A.G. stars not included in the
determination of plate-constants furnished checks.
Since the distribution of the stars was about the same as that of the
nebulae, it was hoped that the reduced positions of the latter would
be of the same order of accuracy as those of the stars. For the 62
A.G. stars on the seven plates measured, the average difference from
the A.G. positions was 1.0″ in either co-ordinate. The settings on the
nebulae could be made with greater precision than on the stars, hence
these results justify placing the accuracy of the nebular positions at
about 2.0″ in either co-ordinate, except for such as were near the edge
of the plates.
The positions are given for the epoch of the A.G. catalogues, 1875.0.
Two of the N.G.C. nebulae had been measured by Lorenz from photographs
made at Heidelberg. A comparison of his measures with the present
measures shows the same second of arc in declination and the same tenth
of a second of time in right ascension. The agreement is perfect to the
last units used in the present paper, but as the nebulae, N.G.C. 7619
and 7626, are situated near the center of the plate, they cannot serve
as a test of the accuracy of those near the edge. In several cases
comparisons could be made with positions from visual measures, as given
in the _Strassburg Annals_, Vols. III and IV. Here the agreement is not
so good.
In one case, on the same night, positions of four objects were measured
with reference to a certain star, which was, in turn, tied up to an
A.G. star some distance away. The objects are given as N.G.C. 3550,
3552, 3554, and a nova which is designated as K₁₂. The photograph shows
N.G.C. 3550 and 3554 properly placed with reference to the star, both
in distance and in position-angle; there is nothing at all in the place
given for N.G.C. 3552; K₁₂ is properly placed from the star, but is in
the N.G.C. position for No. 3552. The position of the reference star
is given as about 17″ too small in declination. K₁₂ is clearly N.G.C.
3552, and evidently the fourth object does not exist in the published
position. As these objects were all in the same field of view in the
telescope, one is at a loss to account for the discrepancy. A list of
the comparisons is given in Table II.
The descriptions indicate form, brightness, and size, and occasionally
the location of a neighboring star. Wolf’s classification was used.
It is, as he remarks, wholly empirical and probably without physical
significance, yet it offers the best available system of filing away
data, and will later be of great service when a significant order
is established. One class was interpolated between g and h, and was
designated g₀. Brightness was estimated in the order B, pB, pF, F, vF,
eF, eeF, and eeeF. The range is from Herschel’s Class II down to the
limit of the plates. For several of the fields diameters were estimated
to the nearest 5″. Otherwise the size was given in the order L, pL, pS,
cS, S, vS, eS.
The classification given in Table III is illustrated in Plate III,
copied from Wolf’s engraving in Band III, No. 5, of the _Publicationen
des Astrophysikalischen Instituts Königstuhl-Heidelberg_. The most
striking feature is the great predominance of the classes e and f.
These two classes form a continuous sequence from the brightest in the
list to the very limits of the plates, where they are but mere faint
markings on the films. Eleven are clearly spirals, and the spindles are
unexpectedly common. These results are typical.
The frequency of the classes e and f may merely be a way of stating
that the scale of the telescope is too small to show the ordinary
structure, but it must be remembered that many members of these classes
are pretty large and bright and that the gradation in the series is
apparently continuous. As far as telescopes of moderate focal length
are concerned, the predominant form of nebulae as we know them at
present is not the spiral, but is this same “e, f” class, described
as round or nearly so, brightening more or less gradually toward
the center, and devoid of detail. The brightest of the class are
probably Messier 60 and N.G.C. 3379. Their spectrum, as derived from
objective-prism plates, is continuous, and is probably of the same type
as those of the spirals and the globular clusters. A detailed study
on an adequate scale of the brighter members of the class will throw
considerable light on the problem of the small nebulae.