3 i8 THE POPULAR SCIENCE MONTHLY. 



by organs which communicate to the mind all the sensuous impressions 

 which are received at the surface of our bodies. These impressions 

 are a reality to us, and their sphere is two-dimensional, acting not in 

 our body, but only on its surface. We have only attained the con- 

 ception of a world of objects with three dimensions by an intellectual 

 pi-oeess. What circumstances, we may ask, have compelled our intel- 

 lect to come to this result ? If a child contemplate its hand, it is con- 

 scious of its existence in a double manner in the first place, by its 

 tangibility; in the second, by its image on the retina of the eye. By 

 repeated groping about and touching, the child knows by experience 

 that his hand retains the same form and extension through all the 

 variations of distance and positions under which it is observed, not- 

 withstanding that the form and extension of the image on the retina 

 constantly change with the different position and distance of the hand 

 in respect to the eye. The problem is thus set to the child's under- 

 standing : How to reconcile to its comprehension the apparently con- 

 tradictory facts of the invarlableness of the object, together with the 

 variableness of its appearance. This is only possible within space of 

 three dimensions, in which, owing to perspective distortions and 

 changes, these variations of projection can be reconciled with the con- 

 stancy of the form of a body." The italics in this extract, as in the 

 preceding one, are the author's. 



Professor Zollner describes the problem which he conceives to be 

 set before a child. The problem which the professor seems to have 

 set before himself may be described thus : Given a tatter of Kant ism, 

 a scrap from the received doctrine of our acquired perceptions, and the 

 rickety figment of a fourth dimension, to evolve a theory which shall 

 save the fourth dimension at all hazards. And Ave have here the out- 

 come. His theory is, that our idea of space is not, what Kant declared 

 it to be, a pure intuition, constituting one of the necessary conditions 

 of experience, but a conception gradually arising from experience, 

 modified by the " causal principle," or, more precisely, modifying the 

 " causal principle," which last the professor apparently regards as a 

 kind of store-house of potential dimensions, projecting into space a 

 new dimension whenever hard pressed by the contradictions of things, 

 very much, one may suppose, as M. Faure's secondary battery gives 

 out its store of energy at the touch of the operator. In short, Pro- 

 fessor Zollner holds that our idea of space is not intuitive, but ratioci- 

 native, limited only by the diversity of contradictions that present 

 themselves to thought, each of which, if otherwise irreconcilable, is 

 pregnant with a new dimension. A child, for instance, because sen- 

 suous impressions are received at the surface of its body (and partly, 

 we may presume, because it takes logical contradictions easy, and is 

 not particularly strong in ratiocination anyway), perceives only two 

 dimensions, we are told, until such time, indeed, as, grown impatient 

 of contradictions, and withal a mighty cause-hunter, it seeks to recon- 



