572 



NA TURE 



[August i8, 1904 



■arrangfements wiiich condition reason in its endeavours to 

 turn experience to account. 



Considerations like these, unless I have compressed them 

 beyond the limits of intelligibility, do undoubtedly suggest 

 a certain inevitable incoherence in any general scheme of 

 thought which is built out of materials provided by natural 

 ■science alone. Extend the boundaries of knowledge as you 

 may ; draw how you will the picture of the universe ; reduce 

 Its infinite variety to the modes of a single space filling 

 ether ; retrace its history to the birth of existing atoms ; 

 show how under the pressure of gravitation they became 

 concentrated into nebula, into suns, and all the ho^t of 

 heaven ; how, at least in one small planet, they combined 

 to form organic compounds ; how organic compounds be- 

 came living things ; how living things, developing along 

 many different lines, gave birth at last to one superior race ; 

 how from this race arose, after many ages, a learned 

 handful, who looked round on the world which thus blindly 

 brought them into being, and judged it, and knew it for 

 what it was : — perform, 1 say, all this, and, though you mav 

 indeed have attained to science, in nowise will you have 

 attained to a self-sufficing system of beliefs. One thing at 

 least will remain, of which this long-drawn sequence of 

 causes and effects gives no satisfying explanation ; and that 

 is knowledge itself. Natural science must ever regard 

 knowledge as the product of irrational conditions, for in the 

 last resort it knows no others. It must always regard know- 

 ledge as rational, or else science itself disappears. In 

 addition, therefore, to the difficulty of extracting from ex- 

 perience beliefs which experience contradicts, we are con- 

 fronted with the difficulty of harmonising the pedigree of 

 •our beliefs with their title to authority. The more successful 

 we are in explaining their origin, the more doubt we cast 

 on their validity. The more imposing seems the scheme of 

 what we know, the more difficult it is to discover by what 

 ^ultimate criteria we claim to know it. 



Here, however, we touch the frontier beyond which 

 physical science possesses no jurisdiction. If 'the obscure 

 ^nd difificult region which lies beyond is to be surveyed and 

 made accessible, philosophy, not science, must undertake 

 the task. It is no business of this Societv. We meet here 

 to promote the cause of knowledge in one of its great 

 ■divisions ; we shall not help it by confusing the limits which 

 usefully separate one division from another. It may 

 perhaps be thought that I have disregarded mv own precept 

 —that I have wilfully overstepped the ample bounds within 

 which the searchers into Nature carrv on their labours. If 

 It be so, I can only beg your forgiveness. My first desire 

 has been to rouse in those who, like mvself, are no specialists 

 in physics, the same absorbing interes't which I feel in what 

 IS surely the most far-reaching speculation about the phvsical 

 universe which has ever claimed experimental support'; and 

 if in so doing I have been tempted to hint mv own personal 

 opinion that as natural science grows it leans more, not 

 less, upon an idealistic interpretation of the universe, even 

 those who least agree may perhaps be prepared to pardon. 



SECTION A. 



m.'lthematics and physics. 

 •Opening Address by Prof. Horace L.^mb, LL.D., D.Sc, 



F.R.S., President of the Section. 

 The losses sustained by mathematical science in the past 

 ■twelvemonth have perhaps not been so numerous as in some 

 years, but they include at least one name of world-wide 

 import. Those of us who were students of Mathematics 

 thirty or forty years ago will recall the delight which we 

 felt in reading the geometrical treatises of George Salmon, 

 and the brilliant contrast which thev exhibited with most 

 of the current text-books of that time. It was from him 

 that many of us first learned that a great mathematical 

 theory does not consist of a series of detached propositions 

 carefully labelled and arranged like specimens on the 

 shelves of a museum, but that it forms an organic whole, 

 instinct with life, and with unlimited possibilities of future 

 <ievelopment. As systematic expositions of the actual state 

 ■of the science, in which enthusiasm for what is new is 

 tempered by a due respect for what is old, and in which 

 new and old are brought into harmonious relation with 

 •each other, these treatises stand almost unrivalled. 



NO. 1816, VOL. 70] 



Whether in the originals, or in the guise of translations, 

 they are accounted as classics in every university of the 

 world. So far as British universities are concerned, they 

 have formed the starting-point of a whole series of work? 

 conceived in a similar spirit, though naturally not always 

 crowned by the same success. The necessity for this kind 

 of work grows, indeed, continually ; the modern frag- 

 mentary fashion of original publication and the numerous 

 channels through which it takes place make it difficult for 

 anyone to become initiated into a new scientific theory 

 unless he takes it up at the very beginning and follows 

 it diligently throughout its course, backwards and forwards, 

 over rough ground and smooth. The classical style of 

 memoir, after the manner of Lagrange, or Poisson, or 

 Gauss, complete in itself and deliberately composed like a 

 work of art, is continually becoming rarer. It is, there- 

 fore, more and more essential that from time to time some 

 one should come forward to sort out and arrange the 

 accumulated material, rejecting what has proved unim- 

 portant, and welding the rest into a connected system. 

 There is perhaps a tendencv to assume that such work is 

 of secondary importance, and can be safely left to sub- 

 ordinate hands. But in reality it makes severe demands 

 I on even the highest powers ; and when these have been 

 available the result has often done more for the progress 

 of science than the composition of a dozen monographs on 

 isolated points. For proof one need only point to the 

 treatises of Salmon himself, or recall (in another field) the 

 debt which we owe to such books as the " Treatise on 

 Natural Philosophv " and the " Theory of Sound," whose 

 authors are happily represented amongst us. 



A modest but most valuable worker has passed away in 

 the person of Prof. Allman. His treatise on the history 

 of Greek Geometry, full of learning and sound mathe- 

 matical perception, is written with great simplicity, and an 

 entire absence of pedantry or dog.natism. It ranks, I 

 believe, with the best that has been done in the subject. 

 It is to be regretted that, as an historian, he leaves so few 

 successors among British mathematicians. We have 

 amongst us, as a result of our system of university 

 education, many men of trained mathematical faculty and 

 of a scholarly turn of mind, with much of the necessary 

 linguistic equipment, who feel, however, no special vocation 

 for the details of recent mathematical research. Might not 

 some of this ability be turned to a field, by no means 

 exhausted, where the severity of mathematical truth is 

 tempered by the human interest attaching to the lives, the 

 vicissitudes, and even the passions and the strife of its 

 devotees, who through many errors and perplexities have 

 contrived to keep alive and trim the sacred flame, and to 

 hand it on burning ever clearer and brighter? 



In another province we have to record the loss of Dr. 

 Isaac Roberts, a distinguished example of the class of 

 non-professional investigators who have left so deep a mark 

 on British science and on .Astronomy in particular. Few 

 of us can be unaware of his long and enthusiastic devotion 

 to celestial photography, of the beauty and delicacy of 

 the results which he achieved, or of the wealth of un- 

 suspected detail which they brought to light. 



Finally, we have to lament the death, within the last 

 few days, of Prof. Everett, whose name will always be 

 associated with one of the most successful tasks which 

 the British Association has taken in hand, viz., the pro- 

 motion of a uniform system of dynamical and electrical 

 units. He acted as Reporter to the Committee entrusted 

 with the question, and by his handbook on " Units and 

 Physical Constants," he has done more, perhaps, than 

 anyone else to popularise and establish its recommenda- 

 tions. He was well known to most of us as a bright and 

 genial presence at these meetings, and contributed 

 numerous interesting papers on optical and other subjects. 

 He was happy in retaining his scientific faculties undimmed 

 to the last, and was engaged at the time of his death on 

 some problems of a mathematical kind, on point- 

 assemblages, suggested by a study of the recent specula- 

 tions of Prof. Osborne Reynolds. 



Of the various subjects which fall within the scope of 

 this Section there is no difficulty in naming that which at 

 the present time excites the widest interest. The 

 phenomena of Radio-activity, lonisation of Gases, and so on, 

 are not onlv startling and sensational in themselves, thev 



