308 POPULAR SCIENCE MONTHLY. 



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 proposi- 

 tions 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, a 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 



