June 13, 1913] 



SCIENCE 



887 



sensible space and geometric space, it would 

 indeed be indispensable to draw it sharply 

 and to keep it always in mind, if we were 

 undertaking to ascertain what the subject 

 (or the object) of geometry is, or, what is 

 tantamount, if we were seeking to get 

 clearly aware of what it is that geometry is 

 about. But in discvissing the subject be- 

 fore us it is unnecessary to be always 

 guarding that distinction; for, whilst it is 

 the space of geometry, and not sensible 

 space, that we shall be talking about, yet 

 it would be a hindrance rather than a help 

 if we did not allow, as we habitually do 

 allow, the two varieties of space — the 

 imagery of the one, the conceptual charac- 

 ters of the other — to mingle freely in our 

 thinking. There will be finesse enough for 

 the keenest arrows of our thought without 

 our going out of the way to find it. A pro- 

 cedure less sophisticated will suffice. It 

 will be sufficient to regard space as being 

 what, to the layman and to the student of 

 natural science, it has always seemed to be : 

 a vast region or room round about us, an 

 immense exteriority, locus of all suspended 

 and floating objects of outer sense, the 

 whence, where and whither of motion, 

 theater, in a word, of the ageless drama of 

 the physical universe. In naturally so con- 

 struing the term we do not commit ourselves 

 to the philosophy, so-called, of common 

 sense; we thus merely save our discourse 

 from the encumbrance of needless refine- 

 ments; for it is obvious that, if space be 

 not indeed what we have said it seems to 

 be, the seeming is yet a fact, and our ques- 

 tions would remain without essential 

 change : what, then, we should ask, are the 

 dimensions and what is the figure of that 

 seeming ? 



Though all the things contained within 

 that triply extended spread or expanse 

 which we call space are subject to the law 



of ceaseless change, the expanse itself, the 

 container of all, appears to suffer no varia- 

 tion whatever, but to be, unlike time, a 

 genuine constant, the same yesterday, to- 

 day and forever, sole absolute invariant 

 under the infinite host of transformations 

 that constitute the cosmic flux. Whether it 

 be so in fact, of course we do not know. 

 We only know that no good reason has ever 

 been advanced for holding the contrary as 

 an hypothesis. 



And yet there is a sense, which we ought 

 I think to notice, an interesting sense, in 

 which space seems to be, not a constant, 

 but, like time, a variable. There is a sense, 

 deeper and juster perhaps than at first we 

 suspect, in which the space of our universe 

 has in the course of time alternately 

 shrunken and grown. During the last cen- 

 tury, for example, it has, so it seems, 

 greatly grown, in response, it may be, to an 

 increasing need of the human mind. By 

 grown I do not mean grown in the usual 

 sense, I do not mean the biological sense, I 

 do not mean the sense that was present to 

 the mind of that great man, Leonardo da 

 Vinci, when he wrote in effect as follows: 

 if you wish to know that the earth has been 

 growing, you have only to observe "how, 

 among the high mountains, the walls of an- 

 cient and ruined cities are being covered 

 over and concealed by the earth's in- 

 crease ' ' ; and, if you would learn how fast 

 the earth is growing, you have only to set 

 a vase, filled with pure earth, upon a roof; 

 to note how green herbs will immediately 

 begin to shoot up ; to note that these, when 

 mature, will cast their seeds; to allow the 

 process to continue through repetition; 

 then, after the lapse of a decade, to meas- 

 ure the soil 's increase ; and, finally, to multi- 

 ply, in order to have thus determined ' ' how 

 much the earth has grown in the course of 

 a thousand years." In this matter, Leo- 



