ADDRESS. 



11 



science which he represents is one whose lines of advance, viewed from a 

 mathematician's own point of view, offer so few points of contact with 

 the ordinary experiences of life or modes of thought, that any account of 

 its actual progress which he might have attempted must have failed in 

 the first requisite of an address, namely, that of being intelligible. 



Now if this esoteric view had been the only aspect of the subject 

 which he could present to his hearers, he might well have given up the 

 attempt in despair. But although in its technical character Mathematical 

 Science suffers the inconveniences, while it enjoys the dignity, of its 

 Olympian position, still in a less formal garb, or in disguise, if you are 

 pleased so to call it, it is found present at many an unexpected turn ; 

 and although some of us may never have learnt its special language, not 

 a few have, all through our scientific life, and even in almost every 

 accurate utterance, like Moliere's well known character, been talking 

 mathematics without knowing it. It is, moreover, a fact not to be over- 

 looked that the appearance of isolation, so conspicuous in mathematics, 

 appertains in a greater or less degree to all other sciences, and perhaps 

 also to all pursuits in life. In its highest flight each soars to a distance 

 from its fellows. Each is pursued alone for its own sake, and without 

 reference to its connection with, or its application to, any other subject. 

 The pioneer and the advanced guard are of necessity separated from the 

 main body, and in this respect mathematics does not materially differ 

 from its neighbours. And, therefore, as the solitariness of mathematics 

 has been a frequent theme of discourse, it may be not altogether unpro- 

 fitable to dwell for a short time upon the other side of the question, and 

 to inquire whether there be not points of contact in method or in subject- 

 matter between mathematics and the outer world which have been 

 frequently overlooked ; whether its lines do not in some cases run parallel 

 to those of other occupations and purposes of life ; and lastly, whether we 

 may not hope for some change in the attitude too often assumed towards 

 it by the representatives of other branches of knowledge and of mental 

 activity. 



In his Preface to the ' Principia ' Newton gives expression to some 

 general ideas which may well serve as the key-note for all future utter- 

 ances on the relation of mathematics to natural, including also therein 

 what are commonly called artificial, phenomena. 



" The ancients divided mechanics into two parts, rational and prac- 

 tical ; and since artizans often work inaccurately, it came to pass that 

 mechanics and geometry were distinguished in this way, that everything 

 accurate was referred to geometry, and everything inaccurate to 

 mechanics. But the inaccuracies appertain to the artizan and not to the 

 art, and geometry itself has its foundation in mechanical practice, and is 

 in fact nothing else than that part of universal mechanics which accu- 

 rately lays down and demonstrates the art of measuring." He next 

 explains that rational mechanics is the science of motion resulting from 



