All this goes to suggest that the central stars of the planetary nebulae must, in all probability, be regarded as “white dwarfs” of enormous weight. It seems possible that they are exactly the type of star needed by our theory. The 52 planetary nebulae already mentioned have the same average distance from the sun, and the same distribution with respect to the galaxy, as the _O_-type stars, so that it is possible that _O_-type stars and planetary nebulae are forms assumed either successively or alternatively in the course of evolution of similar bodies. It should be mentioned that the planetary nebulae exhibit spectral displacements which, if interpreted in the ordinary way, would indicate that they are moving with very high speeds, in some cases reaching hundreds of miles a second. Such speeds would be entirely inappropriate to stars of large weight. Yet this objection rather defeats itself, for if the spectral shifts really arose from high speeds of motion, the highest of the observed speeds would suffice to carry the planetary nebulae possessing them clear of the galactic system altogether; they would be random travellers through our system of stars, whereas their orderly arrangement and concentration near the galactic plane suggests very forcibly that they are permanent members of it. Thus the observed large shifts of the spectral lines can hardly indicate large speeds in space; some other interpretation must be found. Professor Perrine considers that they arise in the main from internal motions, contraction, expansion and rotation of the nebulae. If so, the motions in space cannot be determined, but at least they no longer present any difficulty. If these stars are, as our hypothesis requires, white dwarfs of very great weight and small radius, their spectra ought to exhibit a relativity displacement to the red of the same type as that actually observed in Sirius _B_. It is possible that this may be found to present a more serious difficulty, although it is also possible that it again may prove to be merged in the large observed displacements. In view of all this, it seems quite possible that both the planetary nebulae, and also other _O_- or _B_-type stars of feeble luminosity, may be very massive stars in the dormant condition contemplated by the hypothesis we have just been discussing. In brief, we imagine that a massive star may have its weight conserved through existing as a planetary nebula or a dwarf _O_-type star for millions of millions of years, and then burst out as a highly luminous star with all the appearance of extreme youth. But there is at present insufficient observational evidence either for or against such a hypothesis. Some pieces of the puzzle are missing, and we can only wait until they turn up.