The views of those astronomers who have paid attention to this subject are, on the whole, in favour of the view that the stellar universe is limited in extent and the stars therefore limited in number. A few quotations will best exhibit their opinions on this question, with some of the facts and observations on which they are founded. Miss A.M. Clerke, in her admirable volume, _The System of the Stars_, says: 'The sidereal world presents us, to all appearance, with a finite system.... The probability amounts almost to certainty that star-strewn space is of measurable dimensions. For from innumerable stars a limitless sum-total of radiations should be derived, by which darkness would be banished from our skies; and the "intense inane," glowing with the mingled beams of suns individually indistinguishable, would bewilder our feeble senses with its monotonous splendour.... Unless, that is to say, light suffer some degree of enfeeblement in space.... But there is not a particle of evidence that any such toll is exacted; contrary indications are strong; and the assertion that its payment is inevitable depends upon analogies which may be wholly visionary. We are then, for the present, entitled to disregard the problematical effect of a more than dubious cause.' Professor Simon Newcomb, one of the first of American mathematicians and astronomers, arrives at a similar conclusion in his most recent volume, _The Stars_ (1902). He says, in his conclusions at the end of the work: 'That collection of stars which we call the universe is limited in extent. The smallest stars that we see with the most powerful telescopes are not, for the most part, more distant than those a grade brighter, but are mostly stars of less luminosity situate in the same regions' (p. 319). And on page 229 of the same work he gives reasons for this conclusion, as follows: 'There is a law of optics which throws some light on the question. Suppose the stars to be scattered through infinite space so that every great portion of space is, in the general average, equally rich in stars. Then at some great distance we describe a sphere having its centre in our sun. Outside this sphere describe another one of a greater radius, and beyond this other spheres at equal distances apart indefinitely. Thus we shall have an endless succession of spherical shells, each of the same thickness. The volume of each of these shells will be nearly proportional to the squares of the diameters of the spheres which bound it. Hence each of the regions will contain a number of stars increasing as the square of the radius of the region. Since the amount of light we receive from each star is as the inverse square of its distance, it follows that the sum total of the light received from each of these spherical shells will be equal. Thus as we add sphere after sphere we add equal amounts of light without limit. The result would be that if the system of stars extended out indefinitely