August 17, 1905J 



NA TURE 



Z7: 



by a freedom from formality that even the least tolerant 

 audience could find admirable. The lapse of time, perhaps 

 assisted by presidential ambitions which have been veiled 

 under an almost periodic apology for personal short- 

 comings, has deprived these addresses of their ancient 

 brevitv, and has invested them with an air of oracular 

 gravity. The topics vary from year to year, but this 

 variation is due to the predilection of the individual Presi- 

 dents ; the types of address are but few in number. Some- 

 times, indeed, we have had addresses that cannot be ranged 

 under any comprehensive type. Thus one year we had an 

 account of a particular school of long-sustained consecutive 

 research ; another year the President made a constructive 

 (and perhaps defiant) defence of the merits of a group of 

 subjects that were of special interest to himself. But 

 there is one type of address which recurs with iterated 

 frequency ; it is constituted by a general account of recent 

 progress in discovery, or by a survey of modern advances 

 in some one or other of the branches of science to which 

 the multiple activities of our Section are devoted. No 

 mc dern President has attempted a general survey of recent 

 progress in all the branches of our group of sciences ; such 

 an attempt will probably be deferred until the Council dis- 

 covers a President who, endowed with the omniscience of a 

 Whewell, and graced with the tongue of men and of angels, 

 shall once again unify our discussions. 



On the basis of this practice, it would have been not 

 unreasonable on my part to have selected some topic from 

 the vast range of pure mathematics, and to have e.Kpounded 

 some body of recent investigations. There certainly is no 

 lack of topics : our own day is peculiarly active in many 

 directions. Thus, even if we leave on one side the general 

 progress that has been made in many of the large branches 

 of mathematics during recent years, it is easv to hint at 

 numerous subjects which could occupy the address of a 

 mathematical President. He might, for instance, devote 

 his attention to modern views of continuity, whether of 

 quantity or of space; he might be heterodo.x or orthodox 

 :is to the so-called laws of motion ; he might e.xpound his 

 notions as to the nature and properties of analytic 

 functionality ; a discussion of the hypotheses upon which 

 a consistent system of geometry can be framed could be 

 made as monumental as his ambition might choose ; he 

 could revel in an account of the most recent philosophical 

 analysis of the foundations of mathematics, even of logic 

 Itself, in which all axioms must either be proved or be 

 compounded of notions that defy resolution by the human 

 intellect at the present day. Such discussions are bound 

 to be excessively technical unless they are expressed in 

 unmathematical phraseology ; when they are so expressed, 

 and in so far as such expression is possible, they become 

 very long and they can be very thin. Moreover, had I 

 chosen any topic of this character, it would have been 

 the merest natural justice to have given early utterance 

 of the sibyllic warning to the uninitiated ; I must also 

 have bidden the initiated that, as they come, thev should 

 summon all the courage of their souls. So I abstain from 

 making such an experiment upon an unwarned audience ; 

 yet it is with reluctance that I have avoided subjects in 

 the range which to me is of peculiar interest. 



On the other hand, I must ask your indulgence for not 

 conforming to average practice and expectation. My desire 

 is to mark the present occasion by an address of un- 

 specialised type which, while it is bound to be mainly 

 mathematical in tenor, and while it will contain no new 

 information, may do little more than recall some facts 

 that are known, and will comment briefly upon obvious 

 tendencies. Let me beg you to believe that it is no strain- 

 ing after novelty which has dictated my choice ; such an 

 ambition has a hateful facility of being fatal both to the 

 performer and to the purpose. It is the strangeness of our 

 circumstances, both in place and time, that has suggested 

 my subject. With an adventurous audacitv that quite 

 overcrows the spirit of any of its past enterprises, the 

 British .Association for the .Advancement of Science has 

 travelled south of the Equator and, in accepting your 

 hospitality, proposes to traverse much of South Africa. 

 The prophet of old declared that " many shall run to and 

 fro, and knowledge shall be increased"; if the second 

 part of the prophecy is not fulfilled, it will not be for the 

 want of our efforts to fulfil the first part. .And if the place 



NO. 1868, VOL. 72] 



and the range of this peripatetic demonstration of our 

 annual corporate activity are unusual, the occasion chosen 

 for this enterprise recalls memories that are fundamental 

 in relation to our subject. It is a modern fashion to 

 observe centenaries. In this section we are in the unusiral 

 position of being able to observe three scientific centenaries 

 in one and the same year. Accordingly I propose to refer 

 to these in turn, and to indicate a few of the events filling 

 the intervals between them ; but my outline can be of only 

 the most summary character, for the scientific history is 

 a history of three hundred years, and, if searching enough, 

 it could include the tale of nearly all mathematical and 

 astronomical and physical science. 



It is exactly three hundred years since Bacon published 

 "The Advancement of Learning." His discourse, alike 

 in matter, in thought, in outlook, was in advance of its 

 time, and it exercised no great influence for the years that 

 immediately followed its appearance ; yet that appearance 

 is one of the chief events in the origins of modern natural 

 science. Taking all knowledge to be his province, he 

 surveys the whole of learning : he deals with the discredits 

 that then could attach to it ; he expounds both the dignity 

 and the influence of its pursuit ; and he analyses all 

 learning, whether of things divine or of things human, 

 into its ordered branches. He points out deficiencies and 

 gaps ; not a few of his recommendations of studies, at his 

 day remaining untouched, have since become great branches 

 of human thought and human inquiry. But what concerns 

 us most here is his attitude towards natural philosophy, 

 all the more remarkable because of the state of knowledge 

 of that subject in his day, particularly in England. It is 

 true that Gilbert had published his discovery of terrestrial 

 magnetism some five years earlier, a discovery followed 

 onlv too soon by his death ; but that was the single con- 

 siderable English achievement in modern science down to 

 Bacon's day. 



In order to estimate the significance of Bacon's range 

 of thought let me recite a few facts, as an indication of 

 the extreme tenuity of progressive science in that year 

 (1605). They belong to subsequent years, and may serve 

 to show how restricted were the attainments of the period, 

 and how limited were the means of advance. The tele- 

 scope and the microscope had not yet been invented. The 

 simple laws of planetary motion were not formulated, for 

 Kepler bad them only in the making. Logarithms were 

 vet to be discovered by Napier, and to be calculated by 

 Briggs. Descartes was a boy of nine and Fermat a boy 

 of only four, so that analytical geometry, the middle-life 

 discovery of both of them, was not yet even a dream for 

 either of them. The Italian mathematicians, of whom 

 Cavalieri is the least forgotten, were developing Greek 

 methods of quadrature by a transformed principle of in- 

 divisibles ; but the infinitesimal calculus w-as not really in 

 sight, for Newton and Leibnitz were yet unborn. Years 

 were to elapse before, by the ecclesiastical tyranny over 

 thought, Galileo was forced to make a verbal disavowal 

 of his adhesion to the Copcrnican system of astronomy, of 

 which he was still to be the protagonist in propounding 

 any reasoned proof. Some mathematics could be had, 

 cumbrous arithmetic and algebra, some geometry lumber- 

 ing after Euclid, and a little trigonometry ; but these were 

 mainly the mathematics of the Renaissance, no very great 

 advance upon the translated work of the Greeks and the 

 transmitted work of the .Arabs. Even our old friend the 

 binomial theorem, which now is supposed to be the 

 possession of nearly every able schoolboy, remained un- 

 known to professional mathematicians for more than half 

 a century yet to come. 



Nor is it merely on the negative side that the times 

 seemed unpropitious for a new departure ; the spirit of 

 the age in the positive activities of thought and deed was 

 not more sympathetic. Those were the days when the 

 applications of astronomy had become astrologv. Men 

 sought for the elixir of life and pondered over the trans- 

 mutation of baser metals into gold. Shakespeare not long 

 before had produced his play As You JJke It, where the 

 strange natural historv of the toad which, 

 ■ " Uely and venomous. 

 Bears yet a precious jewel in his head." 

 is made a metaphor to illustrate the sweetening uses of 

 adversity. The stiffened Elizabethan laws against witch- 



