PROCEEDINGS 



OF THE 



€Kmhx&Qt |j{)il0sap{jkal Sbrkijr, 



January 27, 1890. 

 Mr J. W. Clark, President, in the Chair. 

 The following were elected Fellows of the Society : 



J. G. Adami, M.A., M.B., Christ's College. 

 T. Roberts, M.A., St John's College. 

 K. H. Solly, M.A., Downing College. 

 E. H. Hankin, B.A., St John's College. 



The President called attention to the proposed International 

 Memorial to Dr Joule, late Honorary Fellow of the Society, and 

 announced that subscriptions might be sent to the Honorary 

 Secretary, Joule Memorial, Royal Society of London, or that they 

 would be received by Mr R. T. Glazebrook, Treasurer of the Cam- 

 bridge Philosophical Society. 



The following Communications were made to the Society : 



(1) Non- Euclidian Geometry. By Prof. Cayley. 



{Abstract.) 



The chief object of the Memoir is the development of the 

 analytical theory : and as the form assumed for the equation of 

 the Absolute is x 2 + y 2 + z 2 + w 2 = 0, the formula? obtained may be 

 regarded as belonging to Elliptic Space. But this is not the point 

 of view of the Memoir ; the space considered is ordinary space, it 

 is only the notion of distance (linear, angular, and dihedral) which 

 is modified. Thus for instance, lines perpendicular to each other, 



VOL. VII. PT. II. 4 



