ADDRESS. 1 3 



paraphernalia may after all be little more than that of a theatrical trans- 

 formation scene. The process of reducing to formula? is really one of 

 abstraction, the restilts 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 

 abstraction is completely attained, and even in cases where it is never 

 attained at all, a subject may to all intents and purposes become mathe- 

 matical. It is not so much elaborate calculations or abstruse processes 

 which characterise this phase as the principles of precision, of exactness, 

 and of proportion. But these are principles with which no true know- 

 ledge 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 otherwise have 

 ever remained mere dry bones of fact, which reunites the scattered limbs 

 and re-creates from them a new and organic whole. 



And as a matter of fact, in the words used by Professor Jellett at our 

 meeting at Belfast, viz., " Not only are we applying our methods to many 

 sciences already recognised 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 

 Nature modifications of that one phenomenon (namely, 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 prin- 

 ciples." 



If, turning from this aspect of the subject, it were my purpose to 

 enumerate how the same tendency has evinced itself in the Arts, un- 

 consciously it may be to the artists themselves, I might call as witnesses 

 each one in turn with full reliance on the testimony wbich they would 

 bear. And, having more special reference to mathematics, I might con- 

 fidently 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 mathematical principles ; but I might 

 cite also the literary as well as the artistic remains of the great artists of 

 Cinqueceuto, both painters and sculptors, in evidence of the geometry 

 and the mechanics which, having been laid at the foundation, appear to 

 have found their way upwards through the superstructure of their works. 

 And in a less ambitious sphere, but nearer to ourselves in both time and 

 place, I might point with satisfaction to the great school of English con- 

 structors of the 18th century in the domestic arts ; and remind you^that 

 not only the engineer and the architect, but even the cabinetmakers, 

 devoted half the space of their books to perspective and to the principles 



