OCTOBKR. 1912. 



KNOWLEDGE. 



405 



this magnificent series are like pictures painted with a full 

 brush. The boldness and mastery which they show sprang 

 from long discipline and wide experience. 



Finally, the chief results of the phyto-geographical work of 

 himself and of others were summed up in the great address 

 on "Geographical Distribution" at York. The Jubilee of 

 the Kritish .Association was held there in KSSl. It had been 

 decided that each section should be presided over by a past 

 President of the Association, and he had occupied that position 

 at Norwich in 186S. Accordingly, at York Hooker was 

 appointed President of the Geographical Section, and he 

 chose as the subject of his address " The Geographical Dis- 

 tribution of Organic Beings." To him it illustrated " the 

 interdependence of those Sciences which the Geographer 

 should study." It is not enough merely to observe the topo- 

 graphy of organisms, but their hypsometrical distributibn 

 nmst also be noted. Further, the changes of area and of 

 altitude is exposed land-surfaces of which geology gives evi- 

 dence, are essential features in the problem, together with the 

 changes of climate, such as have determined the advance and 

 retrocession of glacial conditions. Having noted these factors, 

 he continued thus : " With the establishment of the doctrine 



of orderly evolution of species under known laws I close this 

 list of those recognised principles of the science of geographical 

 distribution, which must guide all who enter upon its pursuit. 

 .■\s Humboldt was its founder, and Forbes its reformer, so we 

 must regard Darwin as its latest and greatest law-giver." 

 Now, after thirty years, may we not add these words of his, 

 that Hooker was himself its greatest exponent ? 



.And so we have followed, however inadequately, this famous 

 man into the various lines of scientific activity which he 

 pursued. We have seen him to excel in them all. The cumu- 

 lative result is that he is universally held to have been, during 

 several decades, the most distinguished botanist of his time. 



He was before all a philosopher. In him we see the 

 foremost student of the broader aspects of plant-life at the 

 time when evolutionary belief was nascent. His influence at 

 that stirring period, though quiet, was far-reaching and deep. 

 His work was both critical and constructive. His wide 

 knowledge, his keen insight, his fearless judgment were 

 invaluable in advancing that intellectual revolution which 

 found its pivot in the mutability of species. The share he 

 took in promoting it was second only to that of his life-long 

 friend. Charles Darwin. 



THE romancp: of mathematics. 



Bv F. T. DEL .M.VK.\U)L, B.Sc. (Paris), C.E. (Madrid). 



C.WIBRIDGE, w-ith its glorious scientific history, has had under 

 the hospitable roof of its University the fifth international 

 congress of mathematics, presided over by Sir George Darwiii, 

 and attended by many eminent mathematicians of the world. 

 The most interesting of all the speeches has been the 

 presidential address, the culminating point of which was the 

 distinction established by Sir George between pure and applied 

 mathematics, showing clearly the superiority of the former, 

 which never err in their results, while deductions made from 

 their applications to other sciences must depend upon the 

 greater or lesser exactness of the hypotheses on which the 

 applications are based. .As an example the chairman quoted 

 the marvellous and complex calculations of Lord Kelvin, who 

 conceded a superior limit of less than one hundred million 

 years as the age of the solid mass of our globe, while geologists, 

 after observing the different terrestrial strata, insisted, and 

 still do so. on a minimum of eight hundred million years. At 

 the present time the conclusions of Kelvin have been generally 

 rejected. Professor Strutt has demonstrated conclusively, 

 from a study of the properties of radioactive bodies, that this 

 limit must be at least seven hundred and eleven million years, 

 a figure which agrees fairly well with that put forward by the 

 geologists. The error of the great mathematician may be 

 easily explained : firstly, he was dealing with a problematic 

 ground sown thickly with hypotheses and more or less con- 

 tradictory facts ; secondly, when Lord Kelvin made his 

 calculations, the extremely modern theories of radio-activity 

 were unknown. But it would be unjust to put the blame on 

 the science of mathematics for this or for similarly unsatis- 

 factory results. The calculations of that great man, whom 

 many called the second Newton, were always marvellous. 

 But as in this particular case he had to work out the problem 

 with incomplete data, the results were necessarily defective. 



Many similar cases might be cited. There have been few- 

 mathematicians worthy of being compared with Laplace and 

 Lagrange, who imagined they had proved the absolute 

 stability of the solar system, when there is no such stability. 

 The calculations of the two great Frenchmen remain a model 

 of elegance and rigorous, precision. Unfortunately, they 

 started from false premises : they supposed that all the bodies 

 of the system possess an absolute rigidity, whereas there is no 

 star absolutely rigid. If they were so, then Lagrange's 

 famous prophecy regarding the eternal duration of the solar 

 system would be true. Rightly did the chairman of the 



Congress point out that pure mathematics must not be con- 

 fused with applied, since, although both aim at truth, the 

 former seeks absolute truth, while the latter essays, often 

 without success, to discover truths about the universe I Sir 

 George Darwin himself has presented astronomers with a 

 most fascinating mathematical theory of the Moon as born 

 from the Earth, and notwithstanding the rigorous reasoning 

 and the severely accurate mathematics of this illustrious 

 astronomer, it is obvious that his theory can only be true if 

 our planet possessed once the stupendous rotational velocity 

 that Sir George supposes it to have possessed at a certain 

 epoch. 



A Frenchman over whose recent death Science mourns 

 to-day, Henri Poincare, who was the world's first mathe- 

 matician — with the exception, I believe, of Sir George Darwin, 

 and to whose last works many eulogistic references were made 

 at the congress of Cambridge, succeeded, before his death, in 

 crowning his already gigantic labour by the publication of a 

 powerful work, "' Les Hypotheses Cosmogoniques," in which 

 he submits transcendental problems on the constitution and 

 origin of the universe to the test of the infinitesimal calculus. 

 His judgment in most cases is severe, excessively so at' times; 

 for we notice that in certain questions wliere the difficulty rather 

 consists in picking out the true theory amongst several that 

 explain the facts satisfactorily, the author declares that none 

 of the solutions are to his liking. This happens, for instance, 

 in the mathematical study of the problem of the conservation 

 of solar heat, which is accounted for b\- at least three theories : 

 that of the radioactivity of some elements of the Sun ; that 

 of the gravitational pressure of the ether, which is proportional 

 to the quotient of the solar mass by the square of the diameter, 

 and that of the fall of meteorites upon the solar surface, and 

 perhaps also a combination of the three causes. But it must 

 be pointed out that Poincare, like several other men of genius, 

 belonged to the metaphysical school of eternal pessimists 

 who distrust the power of the sciences, including that of 

 mathematics, and go so far as to deny these their faculty 

 of representing absolute truth. Poincare's tendency at 

 arriving at negative results, makes him sometimes look 

 at problems from so arbitrary a point of view that his 

 conclusions lose a great deal of their value. Thus, in 

 the chapter of the problem of the solar heat, on reaching 

 the mathematical analysis of the theory of the meteoric 

 shower, he resolves his equations by eliminating the factor 



