INAUGURAL ADDRESS BEFORE THE BRITISH ASSOCIATION. 501 



taken its direction from the philosopher. Every 

 manufacture is in reality but a chemical process, 

 and the machinery requisite for carrying it on 

 but the right application of certain propositions 

 in rational mechanics." So far your academician. 

 Every subject, therefore, whether in its usual 

 acceptation scientific or otherwise, may have a 

 mathematical aspect ; as soon, in fact, as it be- 

 comes a matter of strict measurement, or of nu- 

 merical statement, so soon does it enter upon a 

 mathematical phase. This phase may, or it may 

 not, be a prelude to another in which the laws of 

 the subject are expressed in algebraical formulae 

 or represented by geometrical figures. But the 

 real gist of the business does not always lie in 

 the mode of expression ; and the fascination of 

 the formulae or other mathematical paraphernalia 

 may after all be little more than that of a the- 

 atrical transformation-scene. The process of re- 

 ducing to formulae is really one of abstraction, the 

 results of which are not always wholly on the side 

 of gain ; in fact, through the process itself the 

 subject may lose in one respect even more than 

 it gains in another. But long before such ab- 

 straction is completely attained, and even in cases 

 where it is never attained at all, a subject may to 

 all intents and purposes become mathematical. 

 It is not so much elaborate calculations or abstruse 

 processes which characterize this phase, as the 

 principles of precision, of exactness, and of pro- 

 portion. But these are principles with which no 

 true knowledge can entirely dispense. If it be 

 the general scientific spirit which at the outset 

 moves upon the face of the waters, and out of the 

 unknown depth brings forth light and living 

 forms, it is no less the mathematical spirit which 

 breathes the breath of life into what would other- 

 wise have ever remained mere dry bones of fact, 

 which reunites the scattered limbs and recreates 

 from them a new and organic whole. 



And as a matter of fact, in the words used by 

 Prof. Jellett at our meeting at Belfast, viz., "Not 

 only are we applying our methods to many sci- 

 ences already recognized as belonging to the 

 legitimate province of mathematics, but we are 

 learning to apply the same instrument to sciences 

 hitherto wholly or partially independent of its 

 authority. Physical science is learning more and 

 more every day to see in the phenomena of Na- 

 ture modifications of that one phenomenon (name- 

 ly, motion) which is peculiarly under the power 

 of mathematics." Echoes are these, far off and 

 faint perhaps, but still true echoes, in answer to 

 Newton's wish that all these phenomena may some 

 day " be deduced from mechanical principles." 



If, turning from this aspect of the subject, it 

 were my purpose to enumerate how the same 

 tendency has evinced itself in the arts, uncon- 

 sciously it may be to the artists themselves, I 

 might call as witnesses each one in turn, with 

 full reliance on the testimony which they would 

 bear. And, having more special reference to 

 mathematics, I might confidently point to the 

 accuracy of measurement, to the truth of curve, 

 which, according to modern investigation, is the 

 key to the perfection of classic art. I might 

 triumphantly cite not only the architects of all 

 ages, whose art so manifestly rests upon mathe- 

 matical principles, but I might cite also the liter- 

 ary as well as the artistic remains of the great 

 artists of the Cinque-cento, both painters and 

 sculptors, in evidence of the geometry and the 

 mechanics which, having been laid at the founda- 

 tion, appear to have found their way upward 

 through the superstructure of their works. 1 .And 

 in a less ambitious sphere, but nearer to our- 

 selves in both time and place, I might point with 

 satisfaction to the great school of English con- 

 structors of the eighteenth century in the do- 

 mestic arts, and remind you that not only the 

 engineer and the architect, but even the cabinet- 

 makers, devoted half the space of their books to 

 perspective and to the principles whereby solid 

 figures may be delineated on paper, or what is 

 now termed descriptive geometry. 2 



Nor perhaps would the sciences which con- 

 cern themselves with reasoning and speech, nor 

 the kindred art of music, nor even literature it- 

 self, if thoroughly probed, offer fewer points of 

 dependence upon the science of which I am speak- 

 ing. What, in fact, is logic but that part of uni- 

 versal reasoning ; grammar but that part of uni- 

 versal speech ; harmony and counterpoint but 

 that part of universal music, " which accurately 

 lays down " and demonstrates (so far as demon- 

 stration is possible) precise methods appertaining 

 to each of these arts ? And I might even appeal 

 to the common consent which speaks of the 

 mathematical as the pattern form of reasoning 

 and model of a precise style. 



Taking, then, precision and exactness as the 

 characteristics which distinguish the mathemati- 

 cal phase of a subject, we are naturally led to 

 expect that the approach to such a phase will be 



1 See "Trattato della Pittura," by Leonardo da 

 Vinci ; also the "Memoir on tue MSS. of L. d. V.," by 

 Venturi, 1797. 



2 " The Gentleman and Cabinet-Maker's Director," 

 by Thomas Chippendale. London, 1754. " The Cabi- 

 net -Maker and Upholsterer's Drawing- Book," by 

 Thomas Sheraton. Londoa, 1793. 



