Proceedings of the British Association, 83 



thought, and its fixation on the clear and the definite, which a long 

 and stern mathematical discipline imparts, is the best, and, indeed, 

 the only proper antagonist. That such habits of thought exist, and 

 characterize, in a pre-eminent degree, the discipline of this University, 

 with a marked influence on the subsequent career of those who have 

 been thoroughly imbued with it, is a matter of too great notoriety to 

 need proof. Yet, in illustration of this disposition, I may be allowed 

 to mention one or two features of its Scientific History, which seem 

 to me especially worthy of notice on this occasion. The first of these 

 is the institution of the Cambridge University Philosophical Society, 

 that body at whose more especial invitation we are now here assembled, 

 which has now subsisted for more than twenty years, and which has 

 been a powerful means of cherishing and continuing those habits among 

 resident members of the University, after the excitement of reading 

 for academical honours is past. From this society have emanated 

 eight or nine volumes of memoirs, full of variety and interest, and 

 such as no similar collection, originating as this has done in the bosom, 

 and, in great measure, within the walls of an academical institution, 

 can at all compare with ; the Memoirs of the Ecole Polytechnique of 

 Paris, perhaps, alone excepted. Without undervaluing any parts of this 

 collection, I may be allowed to particularize, as adding largely to our 

 stock of knowledge of their respective subjects, the Hydrodynamical 

 contributions of Prof. Challis — the Optical and Photological papers of 

 Mr. Airy — those of Mr. Murphy, on Definite Integrals — the curious 

 speculations and intricate mathematical investigations of Mr. Hopkins 

 on Geological Dynamics — and, more recently, the papers of Mr. De 

 Morgan on the foundations of Algebra, which taken in conjunction 

 with the prior researches of the Dean of Ely and Mr. Warren on 

 the geometrical interpretation of imaginary symbols in that science, 

 have effectually dissipated every obscurity which heretofore prevailed 

 on the subject. The elucidation of the metaphysical difficulties in 

 question, by this remarkable train of speculation, has in fact, been so 

 complete, that henceforward they will never be named as difficulties, 

 but only as illustrations of principle. Nor does its interest end here, 

 since it appears to have given rise to the theory of Quaternions of 

 Sir W. Hamilton, and to the Triple Algebra of Mr. De Morgan him- 

 self, as well as to a variety of interesting inquiries of a similar nature 



