THE KANSAS UNIVERSITY 

 SCIENCE BULLETIN. 



Vol. VII, No. 14] JANUARY, 1913. [v^rxv.rNru. 



COLLINEA IONS IN SPACE OF FOUR 

 DIMENSIONS.* 



BY R. S. POND. 



THE object of this paper is to outline the theory of 

 collineations in space Rj, of four dimensions ; in 

 particular, to derive what Professor Newson has called 

 the "normal forms," and to deduce the twenty-seven 

 types of collineations which exist in the Rj, . 



The subject is introduced by a brief discussion of the 

 ordinary analytic form of a collineation in point coordi- 

 nates with regard to its geometrical interpretation, and 

 of the dependent transformations which line, plane and 

 space coordinates undergo. The geometrical termi- 

 nology followed is that of M. Jouffert, in his Traite de 

 Geometrie a Qiiatre Dimensions. 



* Received for publication September 23. 1912. 



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