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unreasonable hypothesis that there is a quasi-cometary increase in brightness as the falling particles approach the central star.
It would seem that some force or forces, other than gravitation, must be acting conjointly with it to permit the stable existence of such shells. Radiation pressure would seem a most probable contributing force. A great deal of work has been done on the manifestations of this effect, principally as a cause of the phenomena observed in the tails of comets, by Schwarzschild,6 Nicholson,6 Poynting,7 and others. The pressure exerted by light falling on small particles (under the conditions existing in our solar system) varies with the diameter of the particle and its density, reflecting power, etc., to the effect that light pressure and gravitation are equal for a particle of specific weight 1, and of the diameter of 1.5/*. For still smaller particles radiation pressure will exceed gravitation, reaching a maximum of about eighteen times gravitation for a particle of diameter 0.18/*. For particles of smaller size than this the radiation pressure rapidly diminishes, becoming equal to gravitation again for particles 0.07/i in diameter. Of special interest in its bearing on the possibility of the existence of shells of nebular matter is Poynting's discussion of the mutual repulsion of small particles under the action of radiation pressure. Two contiguous small spheres of density 5.5, situated at the Earth's distance from the Sun, and exposed to solar radiation, will suffer no mutual attraction or repulsion when their diameter is 6.8 centimeters-; at the distance of Neptune their diameter would be, to secure the same effect, but 2 millimeters.
The relative radii, for which such a balance between gravitational attraction and light pressure repulsion will occur, are inversely proportional to the distance from the central body; i.e., for a body of the mass and radiative power of the Sun, a ring or shell of small particles 0.02 mm. in diameter at a mean distance equal to on^hundred times that of Neptune would be in equilibrium, suffering no tendency toward mutual aggregation or diffusion. It would appear that, under such conditions, particles of atomic dimensions would tend to diffuse, unless the central body were of considerably smaller radiating power than the Sun.
As a conclusion to the discussion of planetary forms which has preceded, it may be of interest to make an approximate and admittedly somewhat tentative summary of the material, assigning each planetary to that hypothetical form which it most closely resembles.
I. Ellipsoids or spheres (i.e., not shell structures). Many of these are so minute that no structure can be distinguished, and are not impossibly shells of considerable thickness, or shells like Figure 82 with the equatorial plane making an angle of approximately 90° with the line of sight. The stellar planetaries are included in this class.
II 2149 (13) 6537 (35) 6644 (43) 6807 (56) 6886 (64)
II 3568 (25) 6572 (38) II 4732 (44) 6826 (58) 6891 (65)
II 4593 (27) 6567 (39) . II 4776 (45) 6833 (59) II 4997 (67)
6210 (28) 6578 (40) II 4846 (50) 6879 (61) II 5117 (73)
II 4634 (29) 6620 (41) 6790 (53) 6881 (62) II 5217 (75)
6439 (32) 6629 (42) 6803 (54) 6884 (63)
II. Ring forms. These may be either true rings, or wide ring-shells (Figure 83), seen at angles of 90° to 70° with the equatorial plane.
2438 (18) 2610 (21) 6369 (31) 6720 (46) 6894 (66)
s Sitz. Ber. Miin. Akad., 31, 293, 1901.
Kig. .u4—Hypothetical spectral line forms at various inclinations of the equatorial plane to the line of sight for matter falling in from the polar zones of a spheroidal ring.
V. Ellipsoidal shells, apparently with thinner equatorial zones (Figure 82). At angles of about 45° to the equatorial plane, such forms may be attributed equally well to wide ring-shells (Figure 83), and some are counted in both classifications.
II 1747 (4) 6058 (26) 6751 (48) 6818 (57)
1514 (7) 6563 (36) 6772 (49) 7139 (74)
II 2165 (14) 6741 (47) 6781 (52)
VI. Forms apparently helical.
6543 (34) 7293 (76)
VII. Anomalous forms, impossible to classify.
1952 (11) 2440 (19) 7008 (69) J 900 (15) 4361 (24) 7027 (72)
It will be seen that there are twenty-one objects in classes II and III, which apparently, so far as we may judge from the appearance of the projected image, agree best with the hypothesis of a wide ring-shell (Figure 83). Classes IV and V, nearly uniform ellipsoidal shells (Figure 80), or ellipsoidal shells with thinner equatorial zones (Figure 82), include twenty-four objects. It is probable that a majority of the twenty-nine objects in Class I are spheroidal or ellipsoidal masses of gas, .and not shells, but these are in general so small that no structural details are discernible; a number of shell forms may possibly be concealed in this class.
On The Number And The Evolutionary Classification Of The Planetary Nebulae
Of the three classes into which the nebulae are ordinarily divided—the planetaries, the diffuse nebulosities, and the spiral nebulae—the two first named seem clearly, from the known facts as to their space-distribution, to be an integral part of our own galactic system. This is not the place to enter into any discussion of the position of the great class of spiral nebulae in any evolutionary scheme, further than to say that all the available evidence as to spectrum, space-distribution, and space-velocity, seems to stamp the spirals as very clearly a class apart— not only unconnected with our galaxy but perhaps individual galaxies.
The main, and perhaps the only, points of similarity between the planetary nebulae and the diffuse nebulae are, first, both classes are typically galactic in distribution, and in the second place, the planetaries and many of the diffuse nebulosities agree in showing bright-line spectra essentially identical in character. Here the relationships cease; greater differences of form and structure could scarcely exist than obtain between the small, clear-cut planetaries, and the enormous, tenuous, highly irregular and cloud-1 ike, diffuse nebulosities. Many small.masses of diffuse nebulosity are associated with stars more or less centrally placed within the nebula, but there is never, in such cases, any resemblance to the typical planetary form, nor is there ordinarily any doubt as to the group of nebulae with which such objects should be classified. The spectrum of such small diffuse nebulosities has frequently been found to be continuous, supporting the theory that the light emitted by them may be wholly or in part a reflection phenomenon, or possibly some as yet unidentified form of a resonance effect.
We have no very definite data as to the total number of the nebulosities classed as diffuse, but the number must be considerable. On the other hand, the planetaries are very few in number, and appear to be relatively very rare objects; fewer than one hundred and fifty are known in the entire sky. From the fact of their small size, and their almost invariable connection with a central stellar nucleus, the tendency is a natural one to attempt to classify the planetaries as, in some capacity or other, a sub-group of the great class of stars in general. No very accurate comparison is passible of the relative ratio of the number of the planetary nebulae to the number of the stars as a whole, because of our ignorance as to the average magnitudes of the stars to which the planetaries may be regarded as corresponding. We have planetary nebulae with central stars ranging from about the ninth to the eighteenth magnitudes, and presumably much fainter than this; neither do we know what proportion of the entire mass is represented by the central star, but it is probably considerable. However, on any reasonable and probable basis of correlation between the planetary nebulae and the stars of supposedly corresponding magnitudes, it would seem certain that the relative proportion of the planetaries to the stars must be of the order of one one-thousandth of 1 per cent, or less. This minute percentage would seem to stamp the planetary at once as an exceptional case, a sporadic manifestation of a path which has been but rarely followed in stellar evolution.
On the other hand, if we attempt to place the planetary nebulae in a definite niche in the general scheme of stellar evolution, and to assign them to a fixed position at the beginning of the gamut, of stellar types, our only alternative appears to lie in regarding the planetary stage of existence as one of relatively very brief duration, through which the great majority of stars have long since passed. Professor Wright has shown the essential identity of the nuclei of the planetary nebulae with the Wolf-Rayet stars. These stars are likewise a very rare type, fully as uncommon, relatively to the total number of the stars, as are the planetaries, and their proved connection with the planetary nebulae gives us no assistance in assigning the planetary nebula as a definite stage of stellar development. Were it possible to assume that the course of stellar evolution is a continuous, self-renewing process, the relative percentages of the various classes of stars might be taken as a rough criterion of the effective duration of the life of the stars in the stages corresponding to these spectral classes. If the average duration of the life of a star from its birth as a star to stellar old age and extinction is of the order of a thousand million years, the planetary stage would apparently average less than ten thousand years. The relatively short life which must be presumed for the planetary stage of existence in the attempt to account for the very small existing proportion of planetary nebulae does not seem inherently probable; it is, of course, as yet unsupported by any direct evidence.
Perhaps of even greater weight as a support to the thesis that the planetary nebula is an exceptional and sporadic case in stellar evolution is the fact that these bodies likewise stand apart from the stars in the very important criterion of average space-velocity. The following short table will serve to show the main data of the space-velocity factor.
The Diffuse Nebulosities; velocities low; almost at rest relatively to the Galaxy.
Class B Stars; average velocities 12 km. (8 miles) per second.
Class A Stars; average velocities 21 km. (13 miles) per second.
Class F Stars; average velocities 29 km. (18 miles) per second.
Class G Stars; average velocities 32 km. (20 miles) per second.
Class K Stars; average velocities 34 km. (21 miles) per second.
Class M Stars; average velocities 34 km. (21 miles) per second.
Planetary Nebulae; average velocities 77 km. (48 miles) per second.
Spiral Nebulae; average velocities 770 km. (480 miles) per second.