5 so POPULAR SCIENCE MONTHLY 



regarded as identical, the cut C reducing to a single element would 

 have dimension, and visual space would have 2. 



And yet most often it is said that the eye gives us the sense of a 

 third dimension, and enables us in a certain measure to recognize the 

 distance of objects. When we seek to analyze this feeling, we ascer- 

 tain that it reduces either to the consciousness of the convergence of 

 the eyes, or to that of the effort of accommodation which the ciliary 

 muscle makes to focus the image. 



Two red sensations affecting the same point of the retina will 

 therefore be regarded as identical only if they are accompanied by the 

 same sensation of convergence and also by the same sensation of effort 

 of accommodation or at least by sensations of convergence and accom- 

 modation so slightly different as to be indistinguishable. 



On this account the cut C is itself a continuum and the cut C has 

 more than one dimension. 



But it happens precisely that experience teaches us that when two 

 visual sensations are accompanied by the same sensation of con- 

 vergence, they are likewise accompanied by the same sensation of 

 accommodation. If then we form a new cut C" with all those of the 

 sensations of the cut C , which are accompanied by a certain sensation 

 of convergence, in accordance with the preceding law they will all be 

 indistinguishable and may be regarded as identical. Therefore C" 

 will not be a continuum and will have dimension; and as C" divides 

 C it will thence result that C" has one, C two and the whole visual 

 space three dimensions. 



But would it be the same if experience had taught us the contrary 

 and if a certain sensation of convergence were not always accompanied 

 by the same sensation of accommodation? In this case two sensations 

 affecting the same point of the retina and accompanied by the same 

 sense of convergence, two sensations which consequently would both 

 appertain to the cut C" could nevertheless be distinguished since they 

 would be accompanied by two different sensations of accommodation. 

 Therefore C" would be in its turn a continuum and would have one 

 dimension (at least) ; then C would have two, C three and the whole 

 visual space would have four dimensions. 



Will it then be said that it is experience which teaches us that space 

 has three dimensions, since it is in setting out from an experimental 

 law that we have come to attribute three to it? But we have therein 

 performed, so to speak, only an experiment in physiology; and as also 

 it would suffice to fit over the eyes glasses of suitable construction to 

 put an end to the accord between the feelings of convergence and of 

 accommodation, are we to say that putting on spectacles is enough to 

 make space have four dimensions and that the optician who constructed 

 them has given one more dimension to space? Evidently not; all we 



