PROCEEDINGS 



OF THE 



Cambritrgc IHjibsopbixal Scrrictn, 



Monday, May 2, 1898. 



Mr F. Darwin, President, in the Chair. 



At a Meeting of the Society held at the Cavendish Laboratory 

 the following were elected Fellows : 



J. Stanley Gardiner, M.A., Gonville and Cams College. 

 W. F. Sedgwick, M.A., Trinity College. 



The following Communications were made to the Society : 



(1) On the theory of Order. By E. T. Dixon, M.A., Trinity 

 College. 



All the theorems of non-metrical (projective) geometry depend 

 solely on the conception of " order " so defined as to be independent 

 of the idea of " before and after," which belongs only to Time. It 

 follows from this definition that no " order " can be ascribed to less 

 than four units in any uniform group ; and this is why less than 

 four points have no " projective relation " or anharmonic ratio. The 

 paper further discusses the way in which numbers (or coordinates) 

 may be assigned to the units of a group for purposes of analysis, 

 with or without a system of " unique " lines having already been 

 determined. 



(2) On a certain system of differential equations defining 

 periodic functions*. By H. F. Baker, M.A., St John's College. 



(1) Suppose we have a consistent system of differential 

 equations 



d 4 w „ / dhu \ 



duidujdukdui lJ \?u r duj ' 



* [21 September. The contents and the title of this note have been modified 

 since it was presented to the Society.] 



VOL. IX. PT. viii. 41 



