HO Transactions. — Miscellaneous. 



the circumference of a circle return into themselves. In other 

 words, the totality of space may have a finite volume, just as 

 the surface of a sphere has a finite area, and the circumference 

 of a circle a finite length. As far as pure mathematics go, we 

 cannot decide whether space is infinite or finite. Experience 

 alone can decide ; or, rather, although we cannot imagine any 

 experience sufficiently extensive to prove the infinitude of spare, 

 experience may possibly some day prove its finiteness. 



5. "The prime object" of the paper "is to spread and 

 support the views of the metaphysical school." .... 

 " This view is supported by the fact, that just recently this 

 gentleman has read before us a very able and profound paper, 

 entitled, ' Mind Stuff,' and which is evidently of a highly meta- 

 physical character " (p. 101 ). The allegation here quoted is so far 

 from being correct, that I claim for my paper on " Mind Stuff" 

 the character of complete consistency with the experiential 

 philosophy. It endeavours to show that the only things of 

 which we have any direct knowledge are the feelings we our- 

 selves experience. By a legitimate inference from experience 

 we conclude that there is a world outside us which causes these 

 feelings, and this world I infer to be composed of stuff I" mind 

 stuff," Professor Clifford called it,) remotely similar to our own 

 feelings, but not worked up into so complex a structure. If 

 by the "metaphysical school " be meant the school which holds 

 that we can discover truth otherwise than by experiment and 

 observation, then it is precisely the school which the non- 

 Euclidian geometry has done more than' anythi ig else to 

 confute. The geometry of Euclid has hitherto been their 

 stronghold: "Here, at least," they have hitherto said, "the 

 human mind can, without any appeal to experiuu nt, evolve, 

 from its own structure, truths which hold good with absolute 

 exactness, throughout immensity and eternity.'" Now, since 

 the researches of Lobatchewsky and Gauss this can no longer 

 be said. They and their successors have conclusively shown 

 that, as far as logical consistency is concerned, there are an 

 infinite number of alternative geometries, and that experience 

 alone can decide which of these is physically true. 



(i. To the expression "geometers of the Euclidian school" 

 (p. 101) I take exception, believing that none such are left in 

 the sense in which Mr. Skey uses the word. The triumph of 

 the non-Euclidian geometry, or, I will say, the " general " 

 geometry, has been complete. I can safely appeal, on this 

 point, to any distinguished member of any Mathematical Society 

 in Europe or America. 



7. "It is not this equivalent which Lobatehewbky is sup- 

 posed to use in his attempt at demonstrating the truth of his 

 assumption" (p. 102). Neither Lobatchewsky nor any one else 

 has attempted to demonstrate the truth of the assumption, but 



