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tlie 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 com- 

 pletely 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 cal- 

 culations 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 

 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 mathe- 

 matical 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 Pro- 

 fessor 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 j 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." 

 Mathematics, If, turning from this aspect of the subject, it 

 and Ai"^^' were my purpose to enumerate how the same ten- 

 dency has evinced itself in the Arts, unconsciously 



