THE FOURTH DIMENSION. 



MATHEMATICAL AND SPIRITUALISTIC. 



I. 

 INTRODUCTORY. 



/r T" N HE tendency to generalise long ago led mathematicians to 

 -* extend the notion of three-dimensional space, which is the 

 space of sensible representation, and to define aggregates of points, 

 or spaces, of more than three dimensions, with the view of employ- 

 ing these definitions as useful means of investigation. They had 

 no idea of requiring people to imagine four-dirnensional things and 

 worlds, and they were even still less remote from requiring them 

 to believe in the real existence of a four-dimensioned space. In 

 the hands of mathematicians this extension of the notion of space 

 was a mere means devised for the discovery and expression, by 

 shorter and more convenient ways, of truths applicable to com- 

 mon geometry and to algebra operating with more than three un- 

 known quantities. At this stage, however, the spiritualists came in, 

 and coolly took possession of this private property of the mathema- 

 ticians. They were in great perplexity as to where they should put 

 the spirits of the dead. To give them a place in the world acces- 

 sible to our senses was not exactly practicable. They were com- 

 pelled, therefore, to look around after some terra incognita, which 

 should oppose to the spirit of research inborn in humanity an insu- 

 perable barrier. The abiding-place of the spirits had perforce to be 

 inaccessible to the senses and full of mystery to the mind. This 

 property the four-dimensioned space of the mathematicians pos- 

 sessed. With an intellectual perversity which science has no idea of, 

 these spiritualists boldly asserted, first, that the whole world was 



