200 



NA TURE 



[December 31, 1891 



■can not." I had, originally, added a sentence to the 

 effect that, if y be taken equal to /3, Van der Waals's 

 result would at once be obtained. But I struck it out as 

 irrelevant, because the discussion turned mainly upon 

 the question of the value of the free path at a volume 

 nearly equal to the critical volume. Here Van der 

 Waals expressly recognized that his b must be dimin- 

 ished in value. From my point of view, /3 (having been 

 determined once for all) is unchangeable ; while y is 

 essentially less than /3, possibly even negative. 



Prof. Korteweg takes a different view, and says that 

 the "true" formula is obtained by the process above 

 .hinted at : — i.e. by putting (with the preceding notation) 



7 = ^. 



4. Prof. Korteweg speaks of the equation written above 

 as ''quite worthless." But, in all this discussion, where 

 the rival expressions differ only by the introduction or 

 rejection of terms of the order /3-/t/" ; which, according 

 to Prof. Korteweg, make an equation "true" or " quite 

 worthless '" as the case may be : — are we not introducing 

 an error, of that order at least, in calmly writing 



A =^ + .5' 

 instead of some such expression as 



^^ ^ ^ v{v + a) 



We have, fortunately, one practical test at hand to help 

 in the decision of such questions. The introduction of the 

 form last written, certainly more likely to be approximate 

 than the first, renders the " quite worthless " equation 

 capable of at least fairly representing the results of 

 Andrews. The "true" equation, we know, does not 

 represent them. P. G. Tait. 



Edinburgh, 21/12/91. 



ON THE RELA TION OF NA TURAL SCIENCE 

 TO ART.^ 



I. 



V\/'E are assembled to-day in annual commemoration 

 *^ * of a man whose marvellous breadth of view and 

 •extraordinary variety of interests are each time a fresh 

 surprise to us. It seems incredible that the same hand 

 -could have penned the "Protogea" and the State-paper 

 adjudging the Principality of Neufchatel to the King of 

 Prussia ; or that the same mind could have conceived the 

 infinitesimal calculus and the true measure of forces, as 

 well as the pre-established harmony and the " Theodicea." 

 A closer examination, however, reveals a blank in the 

 universality of his genius. We seek in vain for any con- 

 nection with art, if we except the Latin poem composed 

 by Leibnitz in praise of Brand's discovery of phosphorus. 

 We need hardly mention that his "Ars Combinatoria " has 

 nothing to do with the fine arts. In his letters and 

 works, observations on the beautiful are few and far 

 between ; once he discusses more at length the pleasure 

 excited by music, the cause of which he attributes to an 

 equable, though invisible, order in the chordal vibrations, 

 which " raiseth a sympathetic echo in our minds." How- 

 ever, the world of the senses had little reality for Leibnitz. 

 With his bodily eye he saw the Alps and the treasures of 

 Italian art, but they, conveyed nothing to his soul. He 

 was indifferent to beauty ; in short, we never surprise 

 this Hercules at Omphale's distaff. 



The same neglect, at least of sculpture and painting, 



' An Address delivered by E. du Bois-Reymond, M.D., F.R.S., at the 

 annual meeting of the Royal Academy of Sciences of Berlin in commemora- 

 tion of Leibnitz, on July 3, 1890. Translated by his daughter. This Address 

 was first printed in the weekly reports (Sitzungsberichte) of the Berlin 

 Academy, then in Dr. Rodenberg's Deutsche Rundschau, and lastly it was 

 published as a separate pamphlet by Veit and Co., at Leipzig, 1891. 



NO. I 157, VOL. 45] 



strikes us in Voltaire, who as polyhistorian can in some 

 measure compare with Leibnitz. We are obliged to 

 descend as far as the third generation— that is, to Diderot 

 in France, to Winckelmann and Lessing in Germany — 

 before we meet with a decided interest in the fine arts, 

 and an appreciation of the part they play in the progress 

 of civilization. 



The period thus defined, though it excels in science, 

 shows with few exceptions a falling-off in the fine arts. 

 On considering the historical development of these two 

 branches of human productiveness, we find no corre- 

 spondence whatever between their individual progress. 

 When Greek sculpture was in its prime, science scarcely 

 existed. True, Lionardo's gigantic personality, which 

 combines the immortal artist with the physicist of high 

 rank, towers at the beginning of the epoch generally 

 known in the history of art as the Cinquecento. Still, he 

 was too far in advance of his age in the latter capacity to 

 be cited as an example of simultaneous development in 

 art and science ; so little that Galilei was born the day of 

 Michael Angelo's death. The mutual development of art 

 and science at the commencement of our century is, I 

 believe, merely a casual coincidence ; moreover the fine 

 arts have since been at the best stationary, whereas 

 science strides on victoriously towards a boundless future. 

 ' In fact, both branches differ too widely for the services 

 rendered to science by art, and vice versa, to be other 

 than external. " Nature," Goethe very truly observed to 

 Eckermann — little thinking how harshly this remark 

 reflects on part of his own scientific work — " Nature 

 allows no trifling ; she is always sincere, always serious, 

 always stern ; she is always in the right, and the errors 

 and mistakes are invariably ours." Fully to appreciate 

 the truth of this, one must be in the habit of trying one's 

 own hand at experiments and observations, while gazing 

 in Nature's relentless countenance, and of bearing, as it 

 were, the tremendous responsibility incurred by the state- 

 ment of the seemingly most insignificant fact. For every 

 correctly interpreted experiment means no less than this : 

 whatever occurs under the present ciixumstances, would 

 have occurred under the same conditions before an 

 infinite negative period of time, and would still occur 

 after an infinite positive period. Only the mathematician, 

 whose method of research has more in common with 

 that of the experimenter than is generally supposed, 

 experiences the same feeling of responsibility in presence 

 of Nature's eternally inviolable laws. Both are sworn 

 witnesses before the tribunal of reality, striving for know- 

 ledge of the universe as it actually is, within those limits 

 to which we are confined by the nature of our intellect. 



However, there is a compensation for the philosopher, 

 labouring under this anxious pressure, in the conscious- 

 ness that the slightest of his achievements will carry him 

 one step beyond the highest reached by his greatest 

 predecessor ; that possibly it may contain the germ of 

 vastly important theoretical revelations and practical 

 results, as Wollaston's lines contained the germ of spectral 

 analysis ; that, at any rate, such a reward is not only in 

 the reach of a born genius, but of any conscientious 

 worker ; and, finally, that science, by subduing Nature 

 to the rule of the human intellect, is the chief instrument 

 of civilization. No real civilization would exist without 

 it, and in its absence nothing could prevent our civiliza- 

 tion, including art and its master-works, from crumbling 

 away again hopelessly, as at the decline of the ancient 

 world. 



This consciousness will also make up to the philosopher 

 for the thoughtlessness of the multitude, who, while en- 

 joying the benefits thus lavished upon them, hardly know 

 to whom they owe them. The country rings with the 

 name of every fashionable musical virtuoso, and 

 cyclopaedias insure its immortality. But who repeats the 

 name of him who achieved that supreme triumph of the 

 inventive intellect— to convey through a copper wire across 



