This list contains 762 entries, which may be subdivided as follows, in accordance with the type of the objects: 513 spiral nebulae. 56 diffuse nebulosities. 36 globular clusters. 24 sparse clusters. 78 planetary nebulae. 8 "dark" nebulae. 47 unclassified, non-existent, etc. For many of the smaller nebulae the description reads: "No trace of spiral character," or some equivalent expression. This will, I think, mislead no one. I have, in all cases, indicated where a nebula is undoubtedly of the diffuse or the planetary type. Such indications of the lack of discernible spiral character merely mean that no whorls are visible, either because these may be very compactly arranged, or because of the small size of the object, and should not be taken to signify that the nebulae thus described are not bona-fide spirals. It is my belief that all the many thousands of nebulae not definitely to be classed as diffuse or planetary are true spirals, and that the very minute spiral nebulae appear as textureless disks or ovals solely because of their small size. Were the Great Nebula in Andromeda situated five hundred times as far away as at present, it would appear as a structureless oval about 0:2 long, with very bright center, and not to be distinguished from the thousands of very small, round or oval nebulae found wherever the spirals are found. There is an unbroken progression from such minute objects up to the Great Nebula in Andromeda itself; I see no reason to believe that these very small nebulae are of a different type from their larger neighbors. There is one fairly common type of spiral of which twenty-three examples are included in this list, and traces of the effect are seen in many nebulae. Its main characteristic is a band of matter extending diametrally across the nucleus and inner parts of the spiral. Frequently the whorls in this type form a nearly perfect ring; in other examples the whorls appear to begin at the ends of this cross-arm. The general appearance is that of the Greek letter p, and I have termed such objects p-type spirals, for lack of a better name. See figure 2, where several examples of this type are given. Varying estimates have been made as to the probable total number of the spiral nebulae. Director Keeler, early in the course of his programme of nebular photography and before photographs of many regions were available, estimated that there were 120,000 small nebulae, and regarded this estimate as a very conservative one.2 Perrine, on completing the original Keeler programme, and using the number of new nebulae found in fifty-seven of the one hundred and four regions of that programme, was of the opinion that 500,000 small uncatalogued nebulae were within reach of the Crossley Reflector. He deemed it probable that the total would ultimately be found to exceed 1,000,000. Fath,* from a series of 139 plates in the Kapteyn areas, on which 1031 nebulae were found, estimated that the number within reach of the 60-inch reflector with exposures of one hour on Lumière Sigma plates (an approximate equivalent to the exposures of the Crossley Reflector programme) was 162,000. Sanford made a number of very long exposures with the Crossley Reflector in the effort to determine whether by this means any considerable number of faint nebulae would be found which were not reached in more moderate exposures, and came to the conclusion that such long exposures would make very little change in the number recorded. The great numbers of small spirals found on nearly all my plates of regions distant 2 Ap. Jour., 11, 325, 1900, and Publ. Lick Obs., 8. 3 Lick Obs. Bull., 3, 47, 1904. 4 Astr. Jour., 28, 75, 1913. 5 Lick Obs. Bull., 9, 80, 1917. from the Milky Way long since led me to the belief that Perrine's estimate of half a million was likely to be under, rather than in excess of, the truth. The extent of existing nebular photographic material now makes possible a new determination. I have made, therefore, a count of the small nebulae occurring in all the regions covered by this list, rejecting thirty-one regions where the exposure was insufficient or the plate was flawed by developer, or was otherwise of very poor quality. The average exposure of the plates is somewhat over two hours; in general, an exposure of one and a half hours is necessary to record the very faint nebulae, and two to three hours is better. Very little is gained by lengthening the exposure beyond three hours; a cleanly developed plate in sharp focus, of one and a half to two hours exposure time, will show the faintest and smallest nebulae much better than a four-hour plate where the focus is slightly out, or the guiding poor. I have not used any counts made by others, having preferred to make the count as homogeneous as possible. For many of the earlier objects of the Keeler programme better plates have since been taken. Where possible, I have checked the count on a duplicate plate, but this has been impossible for the majority of the regions, for which no duplicate plate exists or for which the duplicate plate is of poor quality. Checks made on regions where duplicate plates exist have convinced me of the essential trustworthiness of my counts, and that few spurious objects have been recorded. The results of these counts are given at the end of the descriptions in the list, abbreviated to the form "12 s. n.", i.e., twelve small nebulae were counted in this region, over and above any objects, large or small, which are given an entry in the list. Where a nebula is followed by no data as to number of small nebulae, it means either that several N. G. C. objects are found in the one region and the number of small nebulae is given elsewhere, or that the count was not made because of rejection of the region. The greatest number found on a single plate was 304 (checked by duplicate plate); the central portion of this remarkable region is reproduced in figure 3. Twenty-six other regions were counted as well; these are plates of sufficient exposure taken on some of the Kapteyn regions, and other special regions of the sky, which do not contain any object warranting a separate entry in the list accompanying this paper. These regions, with the number of small nebulae counted, are given below: In all, 439 regions were counted, giving a total of 5698 small, uncatalogued nebulae. To this must be added the 513 spirals described in this list, making the total number of nebulae found in all regions 6211. In the belief that practically all these very small nebulae are spirals I have designedly omitted the diffuse nebulosities and the planetaries. The exposed area of a Crossley plate is about nine-tenths of a square degree; the edges and corners of this area are, however, so poorly defined, owing to the distance from the optical axis, that only the brighter small nebulae can be picked up in these portions of the plate; the majority of the small nebulae are found in the more central portions having an area of about six-tenths of a square degree, or less. I have assumed 0.75 of a square degree as the average effective area on which the counts were made; this is certainly somewhat in excess, but is an error on the conservative side. We shall first assume that these 439 regions are uniformly distributed over the sky, and that they may be taken as a fair representation of the whole sky. Their area is 329.25 square degrees. If the proportion shown by these regions holds over the entire sky, we should expect the number of spiral nebulae to be 778,000. Because of the fact that the faintest and smallest members of the class are, in general, discernible only in the central regions of the plate, I consider the figure given an under-estimate, and believe that the total number accessible with the Crossley Reflector with rapid plates and exposures of from two to three hours may well exceed 1,000,000. It may be argued that a preponderance of plates taken in the regions near the galactic poles would have the effect of unduly increasing the estimated number of the small spirals. This objection was urged by Fath (loc. cit.) in explanation of the difference between his estimate of 162,000 and that of 500,000 by Perrine; on plotting the regions used by Perrine he found that approximately 33% of the regions counted by Perrine were located within 45° of the north galactic pole, while less than 20% of the "Selected Areas" were found in the same region. In order to test this objection, as far as it may be applied to the present counts, I have plotted in Fig. 1. Distribution of Regions on which Small Nebulae were Counted. Plane is shown by dotted lines. The Position of the Galactic figure 1 the 439 regions in which counts were made. It will be seen from this figure that the distribution of the regions may well be regarded as an approximately uniform one. There is, it is true, a marked concentration of regions between 12 and 13 hours R. A., in the vicinity of the north galactic pole, but this would seem to be balanced by the similar preponderance of regions in the Milky Way from 17 to 20 hours R. A. If we divide the celestial sphere into two equal areas, one consisting of a zone 60° wide extending 30° on each side of the galactic plane, and the other comprising the two zones of 60° radius about the two galactic poles, we shall find that 49.4% of the regions are located in the first, or galactic, area, and 50.6% in the polar areas (217 regions in the galactic area, and 222 in the polar areas). The balance in the distribution of the regions in the galactic and extra-galactic zones may then be regarded as a nearly perfect one. On the other hand, bearing in mind the well-known concentration of the spiral nebulae in the vicinity of the north galactic pole, and the fact that this programme deals primarily with the regions containing the spirals, it is necessary to investigate further any possible effect which this concentration might have upon the resulting estimate. I find that 36% of the regions used are within 45° of the galactic poles; as these zones comprise 29% of the sky, there is seen to be a slight preponderance. But a large part of the zone about the south galactic pole is not represented by any observed regions, so that the disproportion is greater than is apparent from the percentage just given. Taking only the zone 45° in radius about the north galactic pole, amount ing to 14.6% of the sky, there are 117 regions, or 26% of the regions used, which are situated in this area, and these 117 regions contain 2997 spirals, or about 48% of the whole. To avoid the effect of this concentration in the galactic north polar area, it will be advisable to consider this area separately. Assuming that the 117 regions in this area, amounting to 87.75 square degrees, are sufficiently uniform in their distribution to represent adequately the occurrence of nebulae in the galactic north polar zone, this zone would contain 205,000 nebulae to correspond with the 2997 found in the 117 regions. Assuming likewise, in the remaining 0.854 of the sky, that the proportion of nebulae is adequately represented by the 3214 nebulae found in 322 regions, or 241.5 square degrees, these would correspond to 469,000 nebulae, a total for the entire sky of 674,000. Any objection depending upon the effects of a marked concentration of the small nebulae in the north galactic area may be further met by considering separately the north galactic and south galactic polar zones, the two zones 15° wide extending from - 30° to - 45° and from +30° to +45° galactic latitude, and a zone 60° wide, 30° on each side of the galactic plane. Such a subdivision gives the following results: The concentration of small nebulae is seen from the above tabulation to be greatest in the area about the north galactic pole, just as is the case with the larger spirals. While only 43 regions are available in the area about the south galactic pole, it will be seen that they indicate a similar, but less marked, concentration of the small nebulae in the southern polar area. The results given in the third line of the table for the zones 15° wide between the galactic zone and the two polar zones are of great interest. While the number of regions is only 62 they give the valuable indication that the density of the small nebulae persists to at least 60° from the galactic poles, with only a comparatively small diminution of the frequency of distribution which obtains about the two galactic poles. I regard the estimate of 722,000 nebulae made by the foregoing subdivision of the observed data, as more reliable than the two estimates, 778,000, and 674,000, made earlier in the discussion. As this revised estimate is equal to that of Fath plus that of Perrine, with several thousand to spare, a discussion of possible reasons for the discrepancy becomes imperative. The following points may be considered: (a) It may be urged that my count has not been sufficiently conservative, and that I have possibly included many spurious objects. The detection of the faintest and smallest nebulae is very largely a matter of experience; all who have worked with photographic plates soon learn, by hard necessity, to recognize the average flaw at a glance. A very large proportion of the objects counted are unmistakably nebulae; as to the faintest nebulae, it is astonishing how faint and small are the nebulae which two "good" duplicate plates will reproduce. For a large proportion of my regions no duplicate plates exist, and I have necessarily been guided by the experience derived from regions taken in duplicate. I am unwilling at present to admit that as many as 5% of the nebulae counted by me are spurious. If 20% were spurious, we should still have to account for a total of over half a million nebulae. (b) The theory may be advanced that the small spirals occur in greatest profusion in the regions immediately contiguous to the larger members of the class, which would explain why fewer nebulae were found by Fath, inasmuch as his plates were taken at the centers of Kapteyn areas where the larger nebulae would be included only by chance, whereas, from the purpose of the Crossley nebular programme, nearly all the plates have some N. G. C. object central. This point is difficult to prove or disprove without a special investigation based upon many plates taken at random in the galactic north polar region. It is certain that the small nebulae frequently show a gregarious tendency; occasionally one-half of a plate will record many small spirals while the other half records very few; the remarkable region at 12h 55m, +28° 30' shows 304 nebulae, while the region about N. G. C. 4826, less than 7° distant, shows only 2. While the small nebulae are evidently quite irregular in their distribution, it would seem that the large number of regions included in this discussion is sufficient to afford a true representation of their average frequency. (c) I have already pointed out that sharp focus and perfect images are essential for the detection of the smallest and faintest spirals. On plates where great numbers of small nebulae are found, the majority are, as a rule, detected in the area 20′ in radius about the optical axis as center, comprising only 0.35 of a square degree. At distances of 30' from the optical axis the parabolic images are very poor, and only the brighter of the small nebulae can be detected in these regions. Almost stellar and moderately bright nebulae are easily detected at such distances from the optical axis, as they will show fan-shaped images which are as large as those of brighter stars, but much fainter, and of nebular texture, but the very faint nebulae are obliterated by the blurring and spreading of the image. These "blurring factors" and the form of the extra-axial image in optical systems have been investigated by Schwarzschild" in three papers of great power, the work of a master. For the convenience of those to whom the original papers may not be accessible the formulae are given here for the only two aberrations which affect the form of the image of an infinitely distant object in the focal plane of a single, perfect, parabolic mirror. Radial distortion from astigmatism and field curvature (Bild wölbung)=586 g2v. In the above, g is the diameter of the field, regarding a field diameter of 6° as the unit, while v is the ratio of aperture to focal length, taking the ratio 1:10 as the unit. It will be seen that the distortion due to coma increases as the square of the focal ratio, so that this quickly becomes very large for reflectors of large focal ratio, even at small angular distances from the optical axis. Dr. Fath used very large plates, 612 x 82 inches in size, in his work with the 60-inch reflector on the number of the small nebulae, and it appears that he used nearly the full area, inasmuch as he states that the area of his plates was 1.88 square degrees. As the full exposed area of the Crossley plate is 0.9 square degrees (and the outer regions of this are so poor because of the parabolic distortions that the effective area used in the counts is believed to be less than 0.75 square degrees) this would mean, if the two reflectors were of the same focal ratio, that the images on one-half of the angular area of the large plates used by Fath were worse than on the rejected edge strips of the Crossley plates. But the greater focal ratio of the 60-inch would increase this disadvantage, even allowing for certain advantages which would partially counterbalance this due to the greater linear scale of the plates. The following comparisons, computed from Schwarzschild's formulae, will illustrate this point. 6 Untersuchungen zur geometrischen Optik, Abh. Kön. Ges. d. Wiss. zu Göttingen, Math.-phys. Kl., N. F. 4, 1, 2, and 3, 1905. |