September 12, 1901] 



NATURE 



477 



in a somewhat difl'erent direction. At present he is checked in 

 his theories by the necessity of making them agree with a com- 

 paratively small number of fundamental hypotheses. If this 

 check were removed, his fancy might run riot in the wildest 

 speculations, which would be held to be legitimate if only they 

 led to formulse in harmony with facts. But the very habit of 

 regarding the end as everything, and the means by which it 

 was attained as unimportant, would prevent the discovery of those 

 fragments of truth which can only be uncovered by the painful 

 process of trying to make inconsistent theories agree, and using 

 all facts, however remote, as the tests of our central generaUsa- 

 tion. 



" Science," said Helmholtz, " Science, whose very object it 

 it is to comprehend Nature, must start with the assumption that 

 Nature is comprehensible." And again, " The first principle 

 of the investigator of Nature is to assume that Nature is 

 intelligible to us, since otherwise it would be foolish to attempt 

 the investigation at all." These axioms do not assume 

 that all the secrets of the universe will ultimately be laid 

 bare, but that a search for them is hopeless if we under- 

 take the quest with the conviction that it will be in 

 vain. As applied to life, they do not deny that in living 

 matter something may be hidden which neither physics nor 

 chemistry can explain, but they assert that theaction of physical 

 and chemical forces in living bodies can never be understood, if 

 at every difficulty and at every check in our investigations we 

 desist frorii further attempts in the belief that the laws of physics 

 and chemistry have been interfered with by an incomprehensible 

 vital force. As applied to physics and chemistry, they do not 

 mean that all the phenomena of life and death will ultimately be 

 included in some simple and self-sufficing mechanical theory : 

 they do mean that we are not to sit down contented with para- 

 doxes such as that the same thing can fill both a large space and 

 a little one ; that matter can act where it is not, and the like, 

 if by some reasonable hypothesis, capable of being tested by 

 experiment, we can avoid the acceptance of these absurdities. 

 Something will have been gained if the more obvious difficulties 

 are removed, even if we have to admit that in the background 

 there is much that we cannot grasp. 



The Limits of Physical Theories. 



And this brings me to my last point. It is a mistake to treat 

 physical theories in general, and the atomic theory in particular, 

 as though they were parts of a scheme which has failed if it 

 leaves anything unexplained, which must be carried on indefi- 

 nitely on exactly the same principles, whether the ultimate 

 results are, or are not, repugnant to common-sense. 



Physical theories begin at the surface with phenomena which 

 directly affect our senses. When they are used in the attempt to 

 penetrate deeper into the secrets of Nature, it is more than probable 

 that they will meet with insuperable barriers, but this fact does 

 not demonstrate that the fundamental assumptions are false, 

 and the question as to whether any particular obstacle will be 

 for ever insuperable can rarely be answered with certainty. 



Those who belittle the ideas which have of late governed the 

 advance of scientific theory too often assume that there is no 

 alternative between the opposing assertions that atoms and the 

 ether are mere figments of the scientific imagination, or that, on 

 the other hand, a mechanical theory of the atoms and of the 

 ether, which is now confessedly imperfect, would, if it could be 

 perfected, give us a full and adequate representation of the 

 underlying realities. 



For my own part I believe that there is a via media. 



A man peering into a darkened room, and describing what he 

 thinks he sees, may be right as to the general outline of the 

 objects he discerns, wrong as to their nature and their precise 

 forms. In his description fact and fancy may be blended, and 

 it may be difficult to say where the one ends and the other 

 begins ; but even the fancies will not be worthless if they are 

 based on a fragment of truth, which will prevent the explorer 

 from walking into a looking-glass or stumbling over the furniture. 

 He who saw " men as trees walking " had at least a perception 

 of the fundamental fact that something was in motion around 

 him. 



And so, at the beginning of the twentieth century, we are 

 neither forced to abandon the claim to have penetrated below 

 the .surface of Nature, nor have we, with all our searching, torn 

 the veil of mystery from the world around us. 



The range of our speculations is limited both in space and 

 time : in space, for we have no right to claim, as is sometimes 



NO. 1663, VOL. 64] 



done, a knowledge of the "infinite universe " ; in time, for 

 the cumulative effects of actions which might pass undetected in 

 the .short span of years of which we have knowledge, may, if 

 continued long enough, modify our most profound generalisa- 

 tions. If some such theory as the vortex-atom theory were 

 true, the faintest trace of viscosity in the primordial medium 

 would ultimately destroy matter of every kind. It is thus a 

 duty to state what we believe we know in the most cautious 

 terms, but it is equally a duty not to yield to mere vague doubts 

 as to whether we can know anything. 



If no other conception of matter is possible than that it 

 consists of distinct physical units — and no other conception has 

 been formulated which does not blur what are otherwise clear 

 and definite outlines— if it is certain, as it is, that vibrations 

 travel through space which cannot be propagated by matter, the 

 two foundations of physical theory are well and truly laid. It 

 may be granted that we have not yet framed a consistent image 

 either of the nature of the. atoms or of the ether in which they 

 exist ; but I have tried to show that in spite of the tentative 

 nature of some of our theories, in spite of many outstanding 

 difficulties, the atomic theory unifies so many facts, simplifies so 

 much that is complicated, that we have a right to insist — at all 

 events till an equally intelligible rival hypothesis is produced — 

 that the main structure of our theory is true ; that atoms are not 

 merely helps to puzzled mathematicians, but physical realities. 



SECTION A. 



MATHE.MATICS AND PHYSICS. 



Opening Address by Major P. A. M.\cMahon, D.Sc, 

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

 During the seventy meetings of the Association a pure 

 mathematician has been president of Section A on ten or a 

 dozen occasions. A theme taken by many has been a defence 

 of the study of pure mathematics. I take Cayley's view ex- 

 pressed before the whole .Association at Southport in 1883, that 

 no defence is necessary, but were it otherwise, I feel that 

 nothing need be added to the eloquent word, of Sylvester in 

 1869 and of Forsyth in 1S97. I intend, therefore, to make 

 some remarks on several matters which may be interesting to 

 the Section even at the risk of being considered unduly 

 desultory. 



Before commencing I must remark that during the twelve 

 months that have elapsed since the Bradford Meeting we have 

 lost several great men whose lives were devoted to the subjects 

 of this Section. Hermite, the veteran mathematician of France, 

 has left behind him a splendid record of purely scientific work. 

 His name will be always connected with the herculean achieve- 

 ment of solving the general quintic equation by means of elliptic 

 modular functions. Other work, if less striking, is equally of 

 the highest order, and his treatise " Cours d'.\nalyse " is a model 

 of style. Of Fitzgerald of Dublin it is not easy to speak in 

 this room without emotion. For many years he was the life and 

 soul of this Section. His enthusiasm in regard to all branches 

 of molecular physics, the force and profundity of his speech, the 

 vigour of his advocacy of particular theories, the acute thinking 

 which enabled him to formulate desiderata, his warm interest in 

 the work of others, and the unselfish aid he was so willing to 

 give, are fresh in our remembrance. Rowland was in the fore- 

 front of the ranks of physicists. His death at a comparatively 

 early age terminates the important series of discoveries which 

 were proclaimed from his laboratory in the Johns Hopkins 

 University at Baltimore. In Viriamu Jones we have lost an 

 assiduous worker at physics whose valuable contributions to 

 knowledge indicated his power to do much more for science. 

 In Tait, Scotland possessed a powerful and original investigator. 

 The extent and variety of his papers are alike remarkable, and 

 in his collected works there exists an imperishable monument to 

 his fame. 



It is interesting, in this the first year of the new century, to 

 take a rapid glance at the position that mathematicians of this 

 country held amongst mathematicians a hunilred years ago. 

 During the greater part of the eighteenth century the study 

 of mathematics in England, Scotland and Ireland had been 

 at a very low ebb. Whereas in 1801 on the Continent 

 there were the leaders Lagrange, Laplace and Legendre, and of 

 rising men, Fourier, Ampere, Poisson and Gauss, we 

 could only claim Thomas Young and Ivory as men who were 

 doing notable work in research, .\m0ng5t schoolboys of various 



