TRANSACTIONS OF THE SECTIONS. 3 



my ovm researches have chiefly, though by no means exclusively lain*) that I have 

 been placed in this Chair, I hope the Section will patiently bear with me in the 

 observations I shall venture to make on the natm'e of that province of the human 

 reason and its title to the esteem and veneration with which through countless 

 ages it has been and, so long as Man respects the intellectual part of his nature, 

 must ever continue to be regarded!. 



It is said of a great party leader and orator in the House of Lords that, when 

 lately requested to make a speech at some religious or charitable (at all events a 

 non-political) meeting, lie declined to do so on the ground that he could not speak 

 unless he saw an adversary' before him — somebody to attack or reply to. In 

 obedience to a somewhat similar combative instinct, I set to myself the task of 

 considering certain recent utterances of a most distinguished member of this Asso- 

 ciation, one whom I no less respect for his honesty and public spirit than I admire 

 for his genius and eloquence J, but from whose opinions on a subject which he has 

 not studied I feel constrained to differ. Gcithe has said — 

 " Verstiindige Leute kannst dti irren seliii 

 In Saclien niimlich, die sie uicht verstehn." 



ZTnderstanding people you may see erring — in those tilings, to wit, which they do not 

 understand. 



I have no doubt that had my distinguished friend, the probable President-elect 

 of the next Meeting of the Association, applied his uncommon powers of reasoning, 

 induction, comparison, observation, and invention to the study of mathematical 

 science, he would have become as great a mathematician as he is now a biologist ; 

 indeed he has given public evidence of his ability to grapple with the practical side 

 of certain mathematical questions ; but he has not made a study of mathematical 

 science as such, and the eminence of his position and the weight justly attaching 

 to his name render it only the more imperative that any assertions proceeding from 

 such a quarter, wliich may appear to me erroneous, or so expressed as to be con- 

 ducive to error, should not remain unchallenged or be passed over in silence §. 



He says " mathematical training is almost purely deductive. The mathematician 

 starts with a few simple propositions, the proof of which is so obvious that they 

 are called self-evident, and the rest of his work consists of subtle deductions from 

 them. The teaching of languages, at any rate as ordinarily practised, is of the 

 same general nature — authority and tradition furnish the data, and the mental 

 operations are deductive." It would seem from the above somewhat singularly 



* My first printed paper was on Fresnel's Optical Theory, published in the ' Philo- 

 sophical Magazine ; ' my latest contritution to the ' Philosophical Transactions ' is a 

 memoir on the " Rotation of a Free Rigid Body." There is an old adage, " pm-us mathe- 

 maticus, purus asiniis." On the other hand, I once heard the great Richard Owen say, 

 when we were opposite neighbours in Lincoln's-Inn Fields (doves nestling among hawks), 

 that he would like to see Homo Mathcmaficus constituted into a distinct subclass, thereby 

 suggesting to my mind sensation, perception, reflection, abstraction, as the successive stages 

 or phases of protoplasm on its way to being made perfect in Mathematicised Man. Would 

 it sound too presumptuous to speak of perception as a quintessence of sensation, language 

 ii. e. communicable thought) of perception mathematic of language ?. We should then 

 have four terms differentiating from inorganic matter and from each other the Vegetable, 

 Animal, Rational, and supersensual modes of existence. 



t Mr. Spottiswoode favoured the Section, in hi.s opening address, with a combined 

 history of the progress of Mathematics and Physics ; Dr. Tyndall's address \vas virtually 

 on the Umits of Physical Philosophy ; the one here in print is an attempted faint adumbra- 

 tion of the nature of Mathematical Science in the abstract. What is wanting (like a fourth 

 sphere resting on three others in contact) to build up tlie Ideal Pyramid is a discourse on 

 the Relation of the two branches (Mathematic and Physics) to, their action and reaction 

 upon, one another, a magnificent theme with which it is to be hoped some future President 

 of Section A will crown the edifice and make the Tetralogy (symbolizable by A-fA', A, A', 

 A.A') complete. 



X Although no great lecture-goer, I have heard three lectures in my life which have left 

 a lasting imin-ession as masterpieces on my memory — Clifford on Mind, Huxley on Chalk, 

 Dumas on Faraday. 



§ In his clogc of Daubenton, Cuvier remarks, " Les savants jugent toujours conime 

 vulgaire les ouvrages qui ne sout pas de leva- genre.'' 



1* 



