J/' 



NA TURE 



[August 17, 1905 



amination. But Euclid is on the verge of being dis- 

 established ; my own University of Cambridge, wfiich has 

 had its full share in maintaining the restriction to Euclid's 

 methods, and which was not uninfluenced by the report 

 of a Committee of this Association upon the subject, will, 

 some six or seven weeks hence, hold its last examination 

 in which those methods are prescriptively required. The 

 disestablishment of Euclid from tyranny over the youthful 

 student on the continent of Europe was effected before the 

 end of the eighteenth century. 



But it is time for me to pass on to the third of the 

 centenaries, with which the present year can be associated. 

 Not so fundamental for the initiation of modern science 

 as was the year in which the " Advancement of Learning " 



■ was published, not so romantic in the progress of modern 

 science as was the year in which Halley gave his pre- 

 diction to the world, the year 1805 (turbulent as it was 

 with the strife of European politics) is marked by the 

 silent voices of a couple of scientific records. In that year 

 Laplace published the last progressive instalment of his 

 great treatise on Celestial Mechanics, the portion that 

 still remained for the future being solely of an historical 



■ character ; the great number of astronomical phenomena 

 which he had been able to explain by his mathematical 

 presentation of the consequences of the Newtonian theory 

 would, by themselves, have been sufficient to give con- 

 fidence in the validity of that theory. In that year also 

 Monge published his treatise, classical and still to be read 

 by all students of the subject, " The Application of Algebra 

 to Geometry " ; it is the starting point of modern synthetic 

 geometry, which has marched in ample development since 

 his day. These are but landmarks in the history of 

 mathematical science, one of them indicating the com- 

 pleted attainment of a tremendous task, the other of them 

 initiating a new departure ; both of them have their signifi- 

 cance in the progress of their respective sciences. 



When we contemplate the activitv and the achievements 

 of the century that has elapsed since the stages which 

 have just been mentioned were attained in inathematical 

 science, the amount, the variety, the progressive diligence, 

 are little less than bewildering. It is not merely the vast 

 development of all the sciences that calls for remark ; no 

 less striking is their detailed development. Each branch 

 of science liow has an enormous array of workers, a 

 development rendered more easily possible by the growing 

 increase in the number of professional posts ; and through 



■ the influence of these workers and their labours there is 



■ an ever-increasing body of scientific facts. Yet an aggre- 

 gate of facts is not an explanatory theory any more neces- 

 sarily than a pile of carefully fashioned stones is a 

 cathedral ; and the genius of a Kepler and a Newton is 

 just as absolutely needed to evolve the comprehending 

 theory as the genius of great architects was needed for 

 the Gothic cathedrals of France and of England. Not in- 

 frequently it is difficult to make out what is the main 

 line of progress in any one subject, let alone in a group 

 of subjects ; and though illumination comes from striking 

 results that appeal, not merely to the professional workers, 

 but also to unprofessional observers, this illumination is 

 the exception rather than the rule. We can allow, and we 

 should continue to allow, freedom of initiative in all direc- 

 tions. That freedom sometimes means isolation, and its 

 undue exercise can lead to narrowness of view. In spite 

 of the complex ramification of the sciences which it has 

 fostered, it is a safer and a wiser spirit than that of un- 

 congenial compulsion, which can be as dogmatic in matters 

 scientific as it can be in matters theological. Owing to 

 the varieties of mind, whether in individuals or in races, 

 the progress of thought and the growth of knowledge are 

 not ultimately governed by the wishes of any individual 

 or the prejudices of any section of individuals. Here, a 

 school of growing thought may be ignored ; there, it may 

 be denounced as of no importance ; somewhere else, it may 

 be politely persecuted out of possible existence. But the 

 here, and the there, and the somewhere else do not make 

 up the universe of human activity ; and that school, like 

 Galileo's earth in defiance of all dogmatic authority, still 

 will move. 



This complete freedom in the development of scientific 

 thought, when the thought is applied to natural pheno- 

 mena, is all the more necessarv because of the wavs of 



NO. 1868, VOL. 72] 



Nature. Physical nature cares nothing for theories, nothing 

 for calculations, nothing for difficulties, whatever their 

 source ; she will only give facts in answer to our questions, 

 without reasons and without explanations ; we may explain 

 as we please and evolve laws as we like, without her help 

 or her hindrance. If from our explanations and our laws 

 we proceed to prediction, and if the event justifies the 

 prediction through agreement with recorded fact, well and 

 good ; so far we have a working hypothesis. The signifi- 

 cance of working hypotheses, in respect of their validity 

 and their relation to causes, is a well known battle-ground 

 of dispute between different schools of philosophers ; it 

 need not detain us here and now. On the other hand, 

 when we proceed from our explanations and our laws to 

 a prediction, and the prediction in the end does not agree 

 with the fact to be recorded, it is the prediction that has 

 to give way. But the old facts remain and the new fact 

 is added to them ; and so facts grow until some working 

 law can be extracted from them. This accumulation of 

 facts is only one process in the solution of the universe ; 

 when the compelling genius is not at hand to transform, 

 knowledge into wisdom, useful work can still be done 

 upon them by the construction of organised accounts 

 which shall give a systematic exposition of the results, 

 and shall place them as far as may be in relative 

 significance. 



Let me pass from these generalities, which have been 

 suggested to my mind by the consideration of some of 

 the scientific changes that have taken place during the 

 last hundred years, and let me refer briefly to some of 

 the changes and advances which appear to me to be most 

 characteristic of that period. It is not that I am con- 

 cerned with a selection of the most important researches 

 of the period. Estimates of relative importance are often 

 little more than half-concealed expressions of individual 

 preferences or personal enthusiasms ; and though each 

 enthusiastic worker, if quite frank in expressing his 

 opinion, would de?lare his own subject to be of supreme 

 importance, he would agree to a compromise that the 

 divergence between the different subjects is now so wide 

 as to have destroyed any common measure of comparison. 

 My concern is rather with changes, and with tendencies 

 where these can be discerned. 



The growth of astronomy has already occupied so large 

 a share of my remarks that few more words can be spared 

 here. Not less, but more, remarkable than the preceding 

 centuries in the actual exploration of the heavens, which 

 has been facilitated so much by the improvements in 

 instruments and is reinforced to such effect by the co- 

 operation of an ever-growing band of American astro- 

 nomers, it has seen a new astronomy occupy regions 

 undreamt of in the older days. New methods have supple- 

 mented the old ; spectroscopy has developed a science of 

 physics within astronomy ; and the unastronomical brain 

 reels at the contents of the photographic chart of the 

 heavens which is now being constructed by international 

 cooperation and will, when completed, attempt to map 

 ten million stars (more or less) for the human eye. 



Nor has the progress of physics, alike on the mathe- 

 matical side and the experimental side, been less remark- 

 able or more restricted than that of astronomy. The 

 elaborate and occasionally fantastic theories of the 

 eighteenth century, in such subjects as light, heat, even 

 as to matter itself, were rejected in favour of simpler and 

 more comprehensive theories. There was one stage when 

 it seemed as if the mathematical physicists were gradually 

 overtaking the experimental physicists; but the discoveries 

 in electricity begun by Faraday left the mathematicians 

 far behind. Much has been done towards the old duty, 

 ever insistent, of explaining new phenomena ; and the 

 names of Maxwell, ^^'eber, Neumann, and Hertz need only 

 to be mentioned in order to suggest the progress that has 

 been made in one subject alone. We need not hesitate 

 to let our thoughts couple, with the great physicists of 

 the century, the leaders of that brilliant band of workers 

 upon the properties of matter who carrv us on from wonder 

 to wonder with the passage of each successive year. 



Further, it has been an age when technical applications 

 have marched at a marvellous pace. So great has been 

 their growth that we are apt to forget their comparative 

 youth ; yet it was only the middle of the century which 



