Abstract
It being generally agreed that the present very luminous stars have existed as such for only a small fraction of the past life of the Galaxy, it becomes important to decide whether they are produced from previously existing stars by the accretion of interstellar matter, in accordance with the views of Hoyle and others, or are the result of some continuing process of star formation. It is emphasized that accretion on the scale required need be only a rarely occurring phenomenon. Even so, the quantitative requirements as usually discussed do present difficulties. It is here found, however, that accretion on this scale would take place, if at all, only after a star has been reduced almost to rest relative to surrounding interstellar matter as a result of the retardation produced by such matter. This and other effects that have to be considered in a full discussion of the problem reduce the requirements to ones that seem likely to be found realized in actuality. The main purpose of the present work is to vestimate these requirements; the frequency of their realization will be discussed elsewhere. The accretion theory has naturally to account not only for the mass-increment but also for its production at a rate sufficient to compensate the transmutation of hydrogen in the stars concerned. It is shown that no additional difficulty is likely to arise in this way.

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