1. St. John's College, Cambridge.

Abstract

IN the system of cosmology I have advocated, and also in the parallel theory of Bondi and Gold, the nebulæ are not all of infinite age as Prof. R. O. Kapp seems to imagine. In a sufficiently large volume V cm.³ of space, the number of nebulæ with ages greater than T (T being measured in units of Hubble's constant, namely, 1.8 10⁹ years) is about 10^-72 V e^-3T, the average spacing between nebulæ older than T being about 10²⁴ e^T cm. By taking V large enough, it is true that a nebula of arbitrarily large T can be found. But this has little interest when related to astronomical observation, for the effect of the red shift of light, arising from the expansion of the universe, is to make the observation of events occurring at distances greater than about 1.7 10²⁷ cm. inherently impossible (even for an observer equipped with a perfect telescope). It follows, therefore, that tle oldest nebulæ within the observable portion of the universe have ages T given, so far as order of magnitude is concerned, by 10²⁴ exp T = 1.7 10²⁷, that is, T = 7.44 Hubble units = 1.34 10¹⁰ years. These nebulæ have been identified tentatively with the nebulæ in the great clusters. It may be noted in passing that a specially chosen observer can detect one condensation having an age T appreciably greater than the value given by the above equation. But the probability of this occurring for an observer taken at random decreases with increasing T according to the factor exp — 3T.