84 Proceedings of the British Association. 



on the part of Mr. Graves, Mr. Cayley, and others. Conceptions of 

 a novel and refined kind have thus been introduced into analysis — 

 new forms of imaginary expression rendered familiar — and a vein 

 opened which I cannot but believe will terminate in some first-rate 

 discovery in abstract science. 



Neither are inquiries into the logic of symbolic analysis, con- 

 ducted as these have been, devoid of a bearing on the progress even 

 of physical science. Every inquiry, indeed, has such a bearing 

 which teaches us that terms which we use in a narrow sphere of 

 experience, as if we fully understood them, may, as our knowledge of 

 nature increases, come to have superadded to them a new set of 

 meanings and a wider range of interpretation. It is thus that modes 

 of action and communication, which we hardly yet feel prepared 

 to regard as strictly of a material character, may, ere many years 

 have passed, come to be familiarly included in our notions of light, 

 heat, electricity and other agents of this class ; and that the trans- 

 ference of physical causation from point to point in space-— nay, even 

 the generation or developement of attractive, repulsive or directive 

 forces at their points of arrival may come to be enumerated among 

 their properties. The late marvellous discoveries in actino-chemistry 

 and the phenomena of muscular contraction as dependent on the 

 will, are, perhaps, even now preparing us for the reception of ideas of 

 this kind. 



Another instance of the efficacy of the course of study in this 

 university, in producing not merely expert algebraists, but sound and 

 original mathematical thinkers — (and, perhaps, a more striking one, 

 from the generality of its contributors being men of comparatively 

 junior standing,) is to be found in the publication of The Cambridge 

 Mathematical Journal, of which already four volumes, full of very 

 original communications, are before the public. It was set on foot 

 in 1837, by the late Mr. Gregory, Fellow of Trinity College, whose 

 premature death has bereft Science of one who, beyond a doubt, had 

 he lived, would have proved one of its chief ornaments, and the 

 worthy representative of a family already so distinguished in the 

 annals of mathematical and optical science. His papers on the 

 ' Calculus of Operations/ which appeared in that collection, fully 

 justifies this impression, while they afford an excellent illustration 



