INAUGURAL ADDRESS BEFORE THE BRITISH ASSOCIATION. 499 



matter and in mode of treatment each has exer- 

 cised his undoubted right of taking an indepen- 

 dent 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 discourses 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 misapprehension 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 Association cannot 

 fairly be considered as in any way committed to 

 its tenor or conclusions. Whether this immunity 

 from comment and reply be really on the whole 

 so advantageous to the president 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 else- 

 where, and in the parallel case it is not always 

 considered that the result is altogether either ad- 

 vantageous to the speaker or conducive to excel- 

 lence in the discourse. 



But, apart from this, the question of a limita- 

 tion of range in the subject-matter for the presi- 

 dential 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 expanding, 

 and the boundaries of the known and the un- 

 known 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 igno- 

 rance 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 sci- 

 ence 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 precise 

 set of questions placed before him ; he must first 



himself act the part of the examiner, and select 

 questions from the repertory 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 sympa- 

 thetic trust to the intricate whisperings of Nature 

 — the goddess, as she has been called, of a hun- 

 dred voices — until here and there he can pick out 

 a few simple notes to which his own powers can 

 resound. 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 possibilities which seem open- 

 ing 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 alike 

 ours if we refused to listen calmly, and temper- 

 ately to form our 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 contained in such 

 a discourse, and assumed that they had all been 

 put on the same footing. 



But to whatever decision we may each come 

 on these controverted 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 

 therefrom, 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 your present representative, 

 like his predecessors, feels himself this moment 

 J n a similar predicament. The reason which he 

 now offers is that the branch of science which be 

 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 ex- 

 periences 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 in- 

 telligible. 



Now, if this esoteric view bad been the only 



