August 15, 1878] 



NATURE 



407 



for the value of their subject-matter. Some of our presidents, 

 and especially those who officiated in the earlier days of our 

 existence, have passed in review the various branches of science, 

 and have noted the progress made in each during the current 

 year. But, as the various sciences have demanded more and 

 more special treatment on the part of those who seriously pursue 

 them, so have the cases of individuals who can of their own 

 knowledge give anything approaching to a general review 

 become more and more rare. To this may be added the fact 

 that although no year is so barren as to fail in affording sufficient 

 crop for a strictly scientific budget, or for a detailed report of 

 progress in research, yet one year is more fertile than another 

 in growths of sufficient prominence to arrest the attention of the 

 general public, and to supply topics suitable for the address. 

 On these accounts, apparently, such a presidential survey has 

 ceased to be annual, and has dropped into an intermittence of 

 longer period. Some presidents have made a scientific principle, 

 such as the time-element in natural phenomena, or continuity, or 

 natural selection, the theme of their discourse, and have 

 gathered illustrat'ons from various branches of knowledge. 

 Others again, taking their own special subject as a fundamental 

 note, and thence modulating into other kindred keys, have 

 borne testimony to the fact that no subject is so special as to be 

 devoid of bearing or of influence on many others. Some have 

 described the successive stages of even a single but important 

 investigation ; and while tracing the growth of that particular 

 item, and of the ideas involved in it, have incidentally shown to 

 the outer world what manner of business a serious investigation 

 is. But there is happily no pattern or precedent which the 

 president is bound to follow ; both in range of subject-matter and 

 in mode of treatment each has exercised his undoubted right of 

 taking an independent line. And it can hardly be doubted that 

 a judicious exercise of this freedom has contributed more than 

 anything else to sustain the interest of a series of annual dis- 

 courses extending now over nearly half a century. 



The nature of the subjects which may fairly come within the 

 scope of such a discourse has of late been much discussed ; and 

 the question is one upon which every one is of course entitled to 

 form his own judgment ; but lest there should be any misappre- 

 hension as to how far it concerns us in our corporate capacity, it 

 will be well to remind my hearers that as, on the one hand, there 

 is no discussion on the presidential address, and the members as 

 a body express no opinion upon it, so, on the other, the Associa- 

 tion cannot fairly be considered as in any way committed to its 

 tenoiur or conclusions. Whether this immunity from "comment 

 and reply be really on the whole so advantageous to the pre- 

 sident as might be supposed need not here be discussed, but 

 suffice it to say that the case of an audience assembled to listen 

 without discussion finds a parallel elsewhere, and in the parallel 

 case it is not always considered that the result is altogether either 

 advantageous to the speaker or conducive to excellence in the 

 discourse. 



Their Rajtge of Subjects. 



But, apart from this, the question of a limitation of range in 

 the subject-matter for the presidential address is not quite so 

 simple as may at first sight appear. It must, in fact, be borne 

 in mind that, while on the one hand knowledge is distinct from 

 opinion, from feeling, and from all other modes of subjective 

 impression, still the limits of knowledge are at all times expand- 

 ing, and the boundaries of the known and the unknown are 

 never rigid or permanently fixed. That which in time past or 

 present has belonged to one category, may in time future belong 

 to the other. Our ignorance consists partly in ignorance of 

 actual facts, and partly also in ignorance of the possible range 

 of ascertainable fact. If we could lay down beforehand precise 

 limits of possible knowledge, the problem of physical science 

 would be already half solved. But the question to which the 

 scientific explorer has often to address himself is, not merely 

 whether he is able to solve this or that problem, but whether he 

 can so far unravel the tangled threads of the matter with which 

 he has had to deal as to weave them into a definite problem at 

 all. He is not like a candidate at an examination with a pre- 

 cise set of questions placed before him ; he must first himself 

 act the part of the examiner and select questions from the reper- 

 tory of nature, and upon them found others, which in some 

 sense are capable of definite solution. If his eye seem dim, he 

 must look steadfastly and with hope into the misty vision, until 

 the very clouds wreath themselves into definite forms. If his 

 ear seem dull, he must-' listen patiently and with sympathetic 

 trust to the intricate whisperings of nature — the goddess, as she 



has been called, of a hundred voices — until here and there he can 

 pick out a few simple notes to which his own powers can re- 

 sound. If, then, at a moment when he finds himself placed on 

 a pinnacle from which he is called upon to take a perspective 

 survey of the range of science, and to tell us what he can see 

 from his vantage ground ; if, at such a moment, after straining 

 his gaze to the very verge of the horizon, and after describing 

 the most distant of well-defined objects, he should give utterance 

 also to some of the subjective impressions which he is conscious 

 of receiving from regions beyond ; if he should depict possi- 

 bilities which seem opening to his view ; if he should explain 

 why he thinks this a mere blind alley and that an open path ; 

 then the fault and the loss would be alil<e curs if we refused to 

 listen calmly, and temperately to form cur own judgment on 

 what we hear ; then assuredly it is we who would be committing 

 the error of confounding matters of fact and matters of opinion, 

 if we failed to discriminate between the various elements con- 

 tained in such a discourse, and assumed that they had all been 

 put on the same footing. 



« ■ - 

 Presidential Difficulties. 



But to whatever decision we may each come on these contro- 

 verted points, one thing appears clear from a retrospect of past 

 experience ; viz., that first or last, either at the outset in his 

 choice of subject or in the conclusions ultimately drawn there- 

 from, the president, according to his own account at least, finds 

 himself on every occasion in a position of " exceptional, or 

 more than usual difficulty." And ycur present representative, 

 like his predecessors, feels himself this moment in a similar pre- 

 dicament. The reason which he now offers is that the branch 

 of science which he represents is one whose lines of advance, 

 viewed from a mathematician's own point of view, offijr 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. 



View of Mathematics here taken. 



Now if this esoteric view had been the only aspect of the sub- 

 ject 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 Mohere's well-known character, been talking 

 mathematics without knowfng it. It is, moreover, a fact not to 

 be overlooked 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 w ithout 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 discomrse, it may be 

 not altogether unprofitable 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 mathe- 

 matics and the cuter world which have been frequently over- 

 looked; whether its lines do not in seme 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 utterances on the relation of mathematics to natural, 

 including also therein what are commonly called artificial, phe- 

 nomena. 



NrJi'tons Prefa:e. 



' ' The ancients divided mechanics into two parts, rational and 

 practical ; and since artisans often work inaccurately, it came to 

 pass that mechanics and geometry were distinguished in this 

 ^•ay — that everything accurate was referred to geometry, and 

 everything inaccurate to mechanics. Put the inaccuracies apper- 

 tain to the artisan and not to the art, and geometry itself has its 



