the apparent diminution in the number of stars (which is an observed fact) indicated a continuous diminution, leading at some unknown distance to entire absence of luminous--that is, of active, energy-emitting aggregations of matter.[1] As to whether there are such other material universes or not I offer no opinion, and have no belief one way or the other. I consider all speculations as to what may or may not exist in infinite space to be utterly valueless. I have limited my inquiries strictly to the evidence accumulated by modern astronomers, and to direct inferences and logical deductions from that evidence. Yet, to my great surprise, my chief critic declares that 'Dr. Wallace's underlying error is, indeed, that he has reasoned from the area which we can embrace with our limited perceptions to the infinite beyond our mental or intellectual grasp.' I have distinctly _not_ done this, but many astronomers have done so. The late Richard Proctor not only continually discussed the question of infinite matter as well as infinite space, but also argued, from the supposed attributes of the Deity, for the necessity of holding this material universe to be infinite, and the last chapter of his _Other Worlds than Ours_ is mainly devoted to such speculations. In a later work, _Our Place among Infinities_, he says that 'the teachings of science bring us into the presence of the unquestionable infinities of time and of space, and the presumable infinities of matter and of operation--hence therefore into the presence of infinity of energy. But science teaches us nothing about these infinities as such. They remain none the less inconceivable, however clearly we may be taught to recognise their reality.' All this is very reasonable, and the last sentence is particularly important. Nevertheless, many writers allow their reasonings from facts to be influenced by these ideas of infinity. In Proctor's posthumous work, _Old and New Astronomy_, the late Mr. Ranyard, who edited it, writes: 'If we reject as abhorrent to our minds the supposition that the universe is not infinite, we are thrown back on one of two alternatives--either the ether which transmits the light of the stars to us is not perfectly elastic, or a large proportion of the light of the stars is obliterated by dark bodies.' Here we have a well-informed astronomer allowing his abhorrence of the idea of a finite universe to affect his reasoning on the actual phenomena we can observe--doing in fact exactly what my critic erroneously accuses me of doing. But setting aside all ideas and prepossessions of the kind here indicated, let us see what are the actual facts revealed by the best instruments of modern astronomy, and what are the natural and logical inferences from those facts. ARE THE STARS INFINITE IN NUMBER?