80 THE POPULAR SCIENCE MONTHLY. 



which divides two adjacent portions of space. The question, then, 

 " Has space (in general) a boundary ? " involves a contradiction in 

 terms, and is, therefore, unmeaning. But the question, "Does space 

 contain a finite number of cubic miles, or an infinite number ? " is a 

 perfectly intelligible and reasonable question which remains to be 

 answered by experiment. 1 The surface of the sea would still contain 

 a finite number of square miles, if there were no land to bound it. 

 Whether or no the space in which we live is of this nature remains to 

 be seen. If its extent is finite, we may quite possibly be able to assign 

 that extent next year ; if, on the other hand, it has no end, it is true that 

 the knowledge of that fact would be quite different from any knowledge 

 we at present possess, but we have no right to say that such knowledge 

 is impossible. Either the question will be settled once for all, or the 

 extent of space will be shown to be greater than a quantity which will 

 increase from year to year with the improvement of our sources- of 

 knowledge. Either alternative is perfectly conceivable, and there is 

 no contradiction. Observe especially that the supposed contradiction 

 arises from the assumption of theoretical exactness in the laws of 

 geometry. Now, the other case that I mentioned has a very similar 

 origin. The idea of a piece of matter the parts of which are held 

 together by forces, and are capable* of being torn asunder by greater 

 forces, is entirely derived from the large pieces of matter which we 

 have to deal with. "We do not know whether this idea applies in any 

 sense to the molecules of gases even ; still less can we apply it to the 

 atoms of which they are composed. The word " force " is used of two 

 phenomena : the pressure, which when two bodies are in contact con- 

 nects the motion of each with the position of the other ; and attraction 

 or repulsion ; that is to say, a change of velocity in one body depending 

 on the position of some other body which is not in contact with it. We 

 do not know that there is any thing corresponding to either of these 

 phenomena in the case of a molecule. A meaning can, however, be 

 given to the question of the divisibility of matter in this way. We may 

 ask if there is any piece of matter so small that its properties as matter 

 depend upon its remaining all in one piece. This question is reason- 

 able ; but we cannot answer it at present, though we are not at all sure 

 that we shall be equally ignorant next year. If there is no such piece 

 of matter, no such limit to the division which shall leave it matter, the 

 knowledge of that fact would be different from any of our present 

 knowledge ; but we have no right to say that it is impossible. If, on 

 the other hand, there is a limit, it is quite possible that we may have 

 measured it by the time the Association meets at Bradford. Again, 

 when we are told that the infinite extent of space, for example, is some- 

 thing that we cannot conceive at present, we may reply that this is 

 only natural, since our experience has never yet supplied us with the 



1 The very important distinction between unboundedncss and infinite extent is made by 

 Riemann, Joe. cit. 



