XXVl REPORT—1845. 
in which their moral influence, if I may so term it, was more needed, as a 
corrective to that propensity which is beginning to prevail widely, and, I fear, 
balefully, over large departments of our philosophy, the propensity to crude 
and over-hasty generalization. To all such propensities the steady concentra- 
tion of 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 as- 
sembled, 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 col- 
lection, 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 under-valuing any part of this collection, I may be allowed to par- 
ticularize, as adding largely to our stock of knowledge of their respective 
subjects, the Hydro-dynamical 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 conjunc- 
tion with the prior researches of the Dean of Ely and Mr. Warren on the © 
geometrical interpretation of imaginary symbols in that science, have effectu- 
ally dissipated every obscurity which heretofore prevailed on this subject. 
The elucidation of the metaphysical difficulties in question, by this remark- 
able 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 himself, as well as to a variety of interesting inquiries of a similar 
nature 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 can- 
not but believe will terminate in some first-rate discovery in abstract science. 
Neither are inquiries into the logic of symbolic analysis, conducted as these 
have been, devoid of a bearing ov 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 transference of physical causation 
from point to point in space—nay, even the generation or development of 
attractive, repulsive or directive forces at their points of arrival may come to 
be enumerated among their properties. The late marvellous discoveries in 
