Nov. 23, 1876] 



NATURE 



79 



how it is related to the entity called matter, is no less mysterious 

 than how subjectivity may be a pioperty of matter. Energy 

 moreover may be divided, Why may not subjectivity? Energy 

 exists in isolated as well as in grouped and combined forms. 

 Why may it not be so with subjectivity ? Energy exists in a 

 potential form when opposing forces neutralise each other — that 

 condition of matter we call rest. May not subjectivity exist in a 

 potential form when opposite kinds of subjective states tend to 

 establish themselves in the same material mass — so constituting 

 that condition of matter which we call unconsciousness ? Energy 

 is only kinetic or active, that is, only shows itself in the form 

 best realised by us when one force has of all the others the 

 ascendency, or is the expression of their united tendencies. May 

 it not be so of subjectivity that it only develops into its active 

 md best recognised form when one kind of subjective state has 

 the ascendency, or is the expr-'sion of the united subjective 

 states? Thu=, as energy potential is rest, so subjectivity potential 

 is unconsciousness. As kinetic energy is motion, so active sub- 

 jectivity is consciousness. 



In this way while all matter is subjective or susceptible of 

 consciousness, this subjectivity seems to exist in the potential 

 form only in all but organisms possessed of a nervous system. 

 In the active nerve fibre the subjectivity of matter appears alone 

 to be active or conscious, while the complex organisation of the 

 nervous systems of the hightrr animals alone permits of matter 

 rising to the powers of mind by harmoniously combining many 

 subjective states so as to build them up into perception, under- 

 standing, memory, imagination, reason, invention, and judg- 

 ment. Wm. S. Duncan 



Stafford, November 9 



Meteor 



I OBSERVED from a high point overlooking the Weald, on the 

 night of November 6, about the time Mr. Nostro mentions, a 

 large meteor fall from a point a little below the zenith in the 

 northern sky. It burst twice, emitting bluish sparks in doing 

 so, once shortly before it disappeared, and the second time on 

 its disappeiring. Could it have been the same meteor seen 

 from different positions ? 



I could not l3e positive to a point or two as to its exact mag- 

 netic bearing, but I do not think I am far wrong in saying it 

 fell almost due north from where I observed it, 



Cecil H. Sp. Perceval 



Pulborough, November 18 



\THE PRESENT STATE OF MATHEMATICAL 

 SCIENCE 



AT the meeting of the Mathematical Society on 

 November 9, Prof. H. J. S. Smith gave an ad- 

 dress on this subject, in which he excluded all reference 

 jto applied mathematics. "I shall regard it," he said, "as 

 a fortunate circumstance if my successor when he, in his 

 turn, is looking round for a subject for his own presidential 

 address, should be attracted by a domain on which I must 

 myself decline to enter, but of which he, better perhaps than 

 anyone among us, is fitted to give us a clear and compre- 

 hensive view." He professed to ofTer only fragmentary 

 remarks, " hoping that even such fragmentary remarks 

 may not be without their use if they serve to remind us 

 of the vastness of our science, and yet of its unity ; of its 

 unceasing development, rapid at the present time, pro- 

 mising to be still more rapid in the immediate future, and 

 yet deriving strength and vitality from roots which strike 

 far back into the past, so that the organic continuity of 

 its gigantic growth has been preserved throughout. In 

 every science there is a time and place for general con- 

 templations, as well as time for minute investigations. 

 And it is a rule of sound philosophy that neither of these 

 shall be neglected in its proper season (' itaque alter- 

 nandse sunt istae contemplationes,' says Lord Bacon, * et 

 vicissim sumendae ut intellectus reddatur simul penetrans 

 et capax ')." 



Touching upon a charge brought against the Proceed- 

 ings of the Society that its memoirs " have shown and 



still continue to show a certain partiality in favour of one 

 or two great branches of mathematical science to the com- 

 parative neglect and possible disparagement of others," it 

 might be rejoined " with great plausibility that ours is not 

 a blamable partiality but a well-grounded preference. 

 So great (we might contend) have been the triumphs 

 achieved in recent times by that combination of the 

 newer algebra with the direct contemplation of space 

 which constitutes the modern geometry — so large has 

 been the portion of these triumphs, which is due to the 

 genius of a few great English mathematicians — so vast 

 and so inviting has been the field thus thrown open to 

 research, that we do well to press along towards a coimtry 

 which has, we might say, been 'prospected' for us, and 

 in which we know beforehand we cannot fail to find 

 something that will repay our trouble, rather than adven- 

 ture ourselves into regions where, soon after the first step, 

 we should have no beaten tracks to guide us to the lucky 

 spots, and in which (at the best) the daily earnings of the 

 treasure-seeker are but small, and do not always make a 

 great show, even after long years of work. Such regions, 

 however, there are in the realm of pure mathematics, and it 

 cannot be for the interest of science that they should be 

 altogether neglected by the rising generation of English 

 mathematicians. I propose, therefore, in the first in- 

 stance, to direct your attention to some few of these com- 

 paratively neglected spots." 



The foremost place is assigned, by Prof. Smith, to the 

 Theory of Numbers. " Of all branches of mathematical 

 knowledge this is the most remote from all practical 

 application, and yet, perhaps more than any other, it has 

 kindled an extraordinary enthusiasm in the minds of the 

 greatest mathematicians. We have the examples of 

 Fermat, of Euler, of Lagrange, Legendre, of Gauss, 

 Cauchy, Jacobi, Lejeune Dirichlet, Eisenstein, without 

 mentiorang the names of others who have passed away, 

 and of some who are still living. But, somehow, the 

 practical genius of the English mathematician has in 

 general given a different direction to his pursuits ; and it 

 would sometimes seem as if we measured the importance 

 of the subject by what we find of it in our best treatises 

 of algebra, or as if we accepted the denunciations of 

 Auguste Comte, and regarded the votaries of the higher 

 arithmetic as reprobate of positive science, as moving in 

 a vicious circle of metaphysical ideas, and as guilty of a 

 great crime against humanity in the pursuit of knowledge 

 beyond the limits of the useful. ... I would rather ask 

 you to listen to what is recorded of the great master of 

 this branch of science." 



Gauss (we are told by his biographer) held mathe- 

 matics to be the queen of the sciences, and arithmetic to 

 be the queen of mathematics—" She sometimes con- 

 descends to render services to astronomy and other 

 natural sciences (so spoke the great astronomer and 

 physicist) ; but under all circumstances the first place is 

 her due." A citation was also made from Jacobi's Life of 

 Gopel : " Many of those who have natural vocation for 

 pure mathematical contemplation find themselves in the 

 first instance attracted by the higher parts of the theory 

 of numbers." 



Three great departments of arithmetic were instanced : 

 The arithmetical theory of homogeneous forms (or quan- 

 tics) — " It is a memorable fact that some of the greatest 

 conceptions of modern algebra had their origin in con- 

 nection with arithmetic, and not with geometry or even 

 with the theory of equations." In the " Disquisitiones 

 Arithmeticae " are given for the first time the charac- 

 teristic properties of an invariant and a contravariant (for 

 ternary quadratic forms). " But the progress of modern 

 algebra and of modern geometry has far outstripped the 

 progress of arithmetic ; and one great problem which 

 arithmeticians have now before them is to endeavour to 

 turn to account for their own science the great results 

 which have been obtained in the sister sciences. How 



