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Forms indicating a ring or shell structure are very common. Before discussing such forms it will be an advantage to give a classified summary of the various forms observed. The various rings and shell structures merge so into one another that it is frequently necessary to include a single object in two or more of the classification groups adopted. These groups, and the nebulae included in each, are as follows:

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Group B. Annular forms; main feature a circular or elliptical ring. Type forms: 1535 (8) and 6720 (46).

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Group C. Disks showing brighter edges; elliptical rings less perfect than those under (B), fading out at the extremities of the major axis, and giving the impression of ellipsoidal shells. This class includes such appearances in the outer and fainter disks of objects in the other classes. Type forms: 1501 (6) and 6818 (57).

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Group D. Forms like those under (C), but with a more pronounced truncated effect, as though the ends of the major axis of the ellipsoidal shell were cut off; faint ansae are generally seen at these extremities. Type form: 40 (1).

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Group E. Objects considerably fainter along and at the ends of the major axis, including some nebulae from all the first four classes.

Type form: 6818 (57).

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Group F. Circular or elliptical disks, fading out slightly at the edges, and without discernible structure. Most of these are small and the lack of structural details may be only apparent. Type form: II 3568 (25).

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Group H. Stellar planetaries. These are indistinguishable from a star on the scale of the Crossley negatives, but have been shown by visual observations to have a minute disk. In all probability they differ from the objects in Group F solely in size.

6644 (43)

II 4732 (44)

II 4846 (50)
6790 (53)

6807 (56)
6833 (59)

II 4997 (67)
II 5117 (73)

That all the ring forms observed are true rings of relatively small thickness appears highly improbable. Were these in all cases actual rings of nebulous matter, we should expect to find a considerable proportion making small angles with the line of sight so as to show in projection as

greatly elongated ellipses; 3242 (22) and 7009 (70) are the only examples showing a considerable ellipticity. There should also be a few cases of "linear" planetaries, as a result of rings seen almost exactly edgewise; no such form has been observed, unless 650-1 (3) be regarded as an example of this type.

It is true that in a number of cases ansae are observed, which may be regarded as possibly indicating an edgewise ring formation, as in the following nebulae:

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The ansae noted above, however, are exceedingly faint appendages, and are not at all convincing as possible edgewise forms of the many planetaries where a circular or only slightly elliptical ring formation is by far the brightest feature visible. The difficulty in explaining the great preponderance of circular or only slightly elliptical rings as true ring structures leads naturally to the hypothesis of spherical or ellipsoidal shells, which would always give a ring effect when seen in projection from any angle in space. When the thickness of such a shell is a considerable fraction of the outer diameter we should expect a nearly homogeneous disk of nebular matter, fading out somewhat toward the edges, as observed in the objects in group (F). There are numerous objects, however, where the theory of a spherical or ellipsoidal shell fails in one important respect. A homogeneous, transparent, luminous, spherical shell of uniform thickness should appear in projection as a disk with a brighter peripheral ring. If d be the thickness of the shell expressed as a fraction of the outer radius, the intensity at the brightest part of the ring will exceed that at the center of the projected luminous disk by the factor,

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With shells of various relative thickness we shall then have the following maximum brightness of the rings as compared with the brightness at the center of the disk:

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In such ring forms as 6720 (46), 6894 (66), 6369 (31), and 2610 (21), the brightness of the matter within the ring seems certainly less than one-tenth of that observed in the rings. We should then expect in these cases shells of a thickness of the order of one-fiftieth of the outer radius of the nebulosity, giving rise to a very narrow projected ring, sharp and clear-cut on its outer edge. As a matter of fact the width of the ring in 6720 (the Ring Nebula in Lyra) is about four-tenths of the outer radius, and we should accordingly expect that the brightness of the ring formation should be not more than twice that of the matter near the center of the ring. In the other cases noted the maximum brightness of the ring should not be more than three times that at the center. For a shell of elliptical cross-section the maximum brightness of the ring will be

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times the brightness of the matter at the center, where a and b are the semi-axes of the outer

elliptical shell, and d the thickness of the shell expressed as a fraction of the minor axis. This will increase the values given in the table above by a factor depending upon the ratio of the major and minor semi-axes. This increase can never be more than twofold, to judge from the observed ratios of major and minor axes in these objects, and will generally be less. A uniform spherical or ellipsoidal shell would then appear to be inadequate as an explanation of the numerous ring forms where the matter inside the ring is but a small fraction of the brightness of that in the ring.

In order to ascertain the degree in which the observed rings and shells agree or fail to agree with theory in this respect, I have made estimates of the ratio of the brightness of such rings or shell effects to the brightness of the matter near the central star. Such estimates are not difficult to make with a fair degree of approximation from series of graduated short exposures, when the matter near the center of the projected disk is reasonably uniform in its distribution. When, however, the object is very small, or when the matter within the ring is irregular and patchy, the estimates are difficult and uncertain. Inasmuch as the density of the photographic image is not a linear function of the exposure time, the use of the term "brightness" is not strictly accurate here, though probably sufficiently so for the short exposures, from which most of the estimates were made. In the two short tables which follow, the first column contains the number of the planetary and the second column gives my estimate of the relative brightness of the projected ring or shell, assuming the brightness of the matter near the nucleus as unity. In the third column will be found the estimated thickness of the shell, expressed in tenths of the semi-minor axis; as these rings or shells are seen in projection, there is manifestly some degree of uncertainty in any estimate of the actual thickness. The first table gives those planetaries which apparently agree with theory, showing a ratio of brightness of the projected shell to that of the matter near the center which accords approximately with that to be expected from a shell of the thickness given; in the second table are given those planetaries which show marked divergence from the theoretical ratio.

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While the planetaries tabulated in the first group agree fairly well with the relative intensities of ring and disk to be expected from the projection of an ellipsoidal shell, it should be noted that many show such a marked diminution in brightness at the ends of the major axis, that it would seem impossible to postulate a complete shell of this character; the hypothesis of a truncated shell will be discussed later. The divergencies of the second group are so marked that the ellipsoidal shell hypothesis would seem untenable in these cases.

In figure 80 are shown the cross-sections, intensity curves, and the hypothetical projected images of three homogeneous, uniform, oblate, spheroidal shells whose thickness are respectively 0.11, 0.22, and 0.33 of the outer semi-axis major. The arguments for and against the postulate of uniform ellipsoidal shells may be summed up as follows:

(a) Such shells, seen in projection, will show ring formations from any angle in space. (b) Relatively thick shells will approximate in appearance to the disk forms enumerated under (F).

(c) The rings shown in projection for such ellipsoidal shells will be slightly fainter at the ends of the major axis, and many such objects are given under (E). The brightness at the ends of the axes of the projected ellipse will, however, be only in the ratio of the major and minor axes of the elliptical cross-section, and the ellipticities observed are inadequate to explain thus the differences in brightness in many of the forms under (E).

(d) Numerous ring forms show intensities of the matter near the center far less than would be expected to exist from a consideration of the observed width of the ring, if of shell structure. A still more puzzling phenomenon is that presented by the twenty-six planetaries tabulated in group (E) above, all of which show to a greater or less degree a marked diminution in brightness along and at the ends of the major axis of the projected ellipse. In the planetaries which indicate a peripheral ring structure it appears to be the invariable rule that the maximum brightness is found at the ends of the minor axis, and never at the ends of the major axis; it seems also to be without an exception that any darkening or diminution in brightness takes place along the major axis.

At first thought, the most natural and evident explanation for this very common darkening along the major axis would be the assumption that this effect was caused by a peripheral equatorial band or ring of absorbing or occulting matter, which would partially or completely obliterate the luminous matter in the equatorial zone. Messrs. Campbell and Moore have tentatively suggested absorption effects as a possible cause of the curiously doubled lines observed by them in the spectra of several planetary nebulae, and to this extent such an absorption theory has the support of observation. The writer has shown that rings of occulting matter are a very frequent phenomenon in the outer portions of the spiral nebulae.

But the hypothesis of absorbing matter, as a general cause of the darkening observed along the major axis, meets at once with an objection, derived from the observational evidence, which appears to be insuperable. Twenty-six planetaries give indications of a darkening along their major axes. It would seem both a priori probable, and is as well confirmed by spectroscopic evidences of rotation, that the equatorial plane of the rotating planetary is indicated by the position of the major axis, and that the polar diameter corresponds to the minor axis (a relation which will be precisely indicated only when the equatorial plane includes the line of sight). On the hypothesis of a peripheral equatorial ring of absorbing matter, the equatorial planes of these twenty-six planetaries must all pass very closely through our own position in space, for all these planetaries are almost precisely symmetrical with regard to the fainter strip along their major axes. We find no instance where the lobes on either side of the major axis are perceptibly different in brightness, no case where one lobe is quite faint or entirely lacking. It has already been pointed out that the apparent major axes of the planetary nebulae are oriented at random in space; it manifestly transcends all the possibilities of the theory of probability that we should

chance to be thus placed very closely in the equatorial planes of twenty-six planetaries. There are a few nebulae which show some degree of asymmetry; among such cases are:

246 (2). This is quite irregular, and one end of the apparent major axis is considerably fainter.

1514 (7). Of very irregular structure; the dark lane is displaced to one side of the (probable) major axis. 2438 (18). A very irregular ring, nearly round.

6369 (31). Fainter at one end of the major axis.

6781 (52). Quite irregular; one end of the major axis is fainter.

6894 (66). An indistinct ring, broader at one end of the minor axis.

A careful study of these cases affords little ground for qualifying in any way the statement just made.

As bearing upon the question of absorption effects, the point may be raised whether the planetaries which are fainter along and at the ends of the major axis average fainter than other types. Excluding eight stellar planetaries, forty-four objects which apparently show no such diminution in brightness at the ends of the major axis have an average relative exposure time of about 16, while the twenty-six objects of Group E have an average relative exposure time of 50. At first sight these figures would seem to indicate a much greater degree of faintness for planetaries of the type of Group E. It is very doubtful whether any such conclusion is, in fact, justifiable. The planetaries with faint major axis and faint ends include both very bright and very faint planetaries; bright objects like II 2165 (14), J 900 (15), the Ring Nebula (46), etc., and exceedingly faint nebulae like 6772 (49), and 7139 (74). It should be noted, also, that the forty-four objects with which the comparison is made include all the very small nebulae, most of which average quite bright; the structural details in these minute objects are indistinguishable. Only the relatively large planetaries of extreme faintness stand much chance of being discovered. The argument will perhaps be clearer from a consideration of figure 81. This represents a homogeneous, uniform, oblate spheroidal shell with a peripheral equatorial ring of absorbing matter of such density as to transmit but 0.2 of the light in the equatorial plane. The intensity curves of such a structure are shown along the projected major and minor axes, and the general form of the projected image as well, for inclinations of the equatorial plane of 0°, 15°, 30°, 45°, and 60°, respectively, to the line of sight. The intensity curves for this figure and the others used to illustrate this portion of the paper were determined graphically, and the projected "nebular" images were drawn in with crayon, from a consideration of the curves along the axes, and from small semitransparent models suspended in a liquid of nearly the same refractive index, and viewed by transmitted light. It will be seen that the form assumed when the line. of sight lies in the equatorial plane is an excellent representation of the type form shown by many planetaries; the peripheral ring is brightest at the ends of the minor axis, and shows a marked diminution of brightness along and at the ends of the major axis. With the equatorial plane making an angle of 15° with the line of sight, the projection has the same general characteristics, but the dark lane is displaced to one side of the middle, and one lobe is about twice the brightness of the other. At inclinations of 30°, 45°, and 60° the asymmetry becomes much more marked; at 30° the fainter lobe has disappeared entirely; at 60° about three-quarters of a ring formation is shown, with one end of the minor axis almost invisible. This fainter portion will become brighter as the inclination increases to 90°, finally showing a circular ring of the general appearance of the central projection in Figure 80. No asymmetrical planetaries of this form have been observed. It is entirely possible that absorption effects may be present in some of the planetary nebulae, but it would seem certain that the frequent darkening along the major axis can not be attributed to this as a general cause.

Any comprehensive discussion of the mechanism of the planetary nebulae must necessarily take into account three distinct lines of evidence-first, the observed forms as shown by direct photographs; second, the remarkable spectrographic results secured by Messrs. Campbell and Moore showing doubled, inclined, and distorted lines; and third, the equally remarkable results

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