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 conception of a world of objects with three dimensions by an intellectual process. What circumstances, we may ask, have compelled our intellect to come to this result? If a child contemplate its hand, it is conscious 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, notwithstanding 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 understanding: How to reconcile to its comprehension the apparently contradictory facts of the invariableness 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 constancy of the form of a body." The italics in this extract, as in the preceding one, are the author's.
Professor Zöllner 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 Kantism, 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 we have here the outcome. 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, Professor Zöllner holds that our idea of space is not intuitive, but ratiocinative, 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 sensuous 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-