The first and third of these questions will be recognized by students of Kant as substantially those raised by the great philosopher in the form of antinomies. Kant attempted to show that both the propositions and their opposites could be proved or disproved by reasoning equally valid in either case. The doctrine that the universe is infinite in duration and that it is finite in duration are both, according to him, equally susceptible of disproof. To his reasoning on both points the scientific philosopher of to-day will object that it seeks to prove or disprove, à priori, propositions which are matters of fact, of which the truth can be therefore settled only by an appeal to observation. The more correct view is that afterward set forth by Sir William Hamilton, that it is equally impossible for us to conceive of infinite space (or time), or of space (or time) coming to an end. But this inability merely grows out of the limitations of our mental power, and gives us no clue to the actual universe. So far as the questions are concerned with the latter, no answer is valid unless based on careful observation. Our reasoning must have facts to go upon before a valid conclusion can be reached.
The first question we have to attack is that of the extent of the universe. In its immediate and practical form, it is whether the smallest stars that we see are at the boundary of a system, or whether more and more lie beyond, to an infinite extent. This question we are not yet ready to answer with any approach to certainty. Indeed, from the very nature of the case, the answer must remain somewhat indefinite. If the collection of stars which forms the Milky Way be really finite, we may not yet be able to see its limit. If we do see its limit, there may yet be, for aught we know, other systems and other galaxies, scattered through infinite space, which must forever elude our powers of vision. Quite likely the boundary of the system may be somewhat indefinite, the stars gradually thinning out as we go further and further, so that no definite limit can be assigned. If all stars are of the same average brightness as those we see, all that lie beyond a certain distance must evade observation, for the simple reason that they are too far off to be visible in our telescopes.
There is a law of optics which throws some light on the question. Suppose the stars to be scattered through infinite space in such a way that every great portion of space is, in the general average, about equally rich in stars.
Then imagine that, at some great distance, say that of the average stars of the sixth magnitude, we describe a sphere having its center in our system. Outside this sphere, describe another one, having a radius greater by a certain quantity, which we may call S. Outside that let there be another of a radius yet greater, and so on indefinitely. Thus we shall have an endless succession of concentric spherical shells, each of the same thickness, S. The volume of each of these regions will be
