3 i6 THE POPULAR SCIENCE MONTHLY. 



included the development of a fourth dimension, and we know he ex- 

 pressed a lofty scorn for table-tippings and other things of the sort, to 

 which the new dimension, it would seem, has thus far lent itself exclu- 

 sively. Kant, it is true, admitted the possibility of other dimensions, 

 but derived it from the impossibility of knowing what exists outside 

 of the limits of our faculties, and consequently of legitimately affirm- 

 ing or denying anything about it. He suggested the possibility of 

 other dimensions of space, and, for that matter, the possibility of no 

 space, but not the possibility of the discovery and comprehension of 

 either by the human mind. So far from this, he distinctly suggested 

 the reverse, actually citing, as an example of truths " always united 

 with the consciousness of necessity," the proposition, " Space has only 

 three dimensions " ; and, since a necessary truth is one of which 

 the contrary is inconceivable, he could not have suggested, without 

 self-contradiction, that space may have more than three dimensions. 

 If other dimensions exist, they exist, according to Kant, not for man, 

 but for other orders of beings, endowed with corresponding forms of 

 perception exist as parts of the original furniture of the intelli- 

 gences of other spheres hypothetical properties of hypothetical creat- 

 ures in hypothetical worlds, one and all of which transcend our facul- 

 ties. This, however, is by no means the theory of Professor Zollner. 



" In my first treatise, ' On Action at a Distance,' " says that distin- 

 guished physicist, "I have discussed in detail the truth, first discovered 

 by Kant, later by Gauss and the representatives of the anti-Euclidian 

 geometry, viz., that our present conception of space, familiar to us by 

 habit, has been derived from experience, i. e., from empirical facts, by 

 means of the causal principle existing a priori in our intellect. This 

 in particular is to be said of the three dimensions of our present con- 

 ception of space. If from our childhood phenomena had been of daily 

 occurrence, requiring a space of four dimensions for an explanation 

 which should be free from contradiction, i. e., conformable to reason, 

 we should be able to form a conception of space of four or more dimen- 

 sions. It follows that the real existence of a four-dimensional, space 

 can only be decided by experience, i. e., by observation of facts. A 

 great step has been made by acknowledging that the possibility of a 

 four-dimensional development of space can be understood by our intel- 

 lect, although, on account of reasons previously given, no correspond- 

 ing image of it can be conceived by the mind." Probably the first 

 thought which will occur to the intelligent reader of this passage is that 

 Professor Zollner mistakes Kant ; and perhaps the second thought 

 will be that the professor mistakes himself. If these impressions prove 

 just, he may find one day that his theory of a fourth dimension has 

 suddenly passed away more completely, if less mysteriously, than the 

 book from the slate at Vienna, or the round-table from the sitting- 

 room at Leipsic. Let us inquire whether or net they are just. 



Professor Zollner thinks " our present conception of space " has been 



