3o6 



NA TURE 



\yan. 28, 1886 



as enduring as language itself. We study tongues that we may 

 know the men of other climes and other days ; we study literature 

 to enjoy it. .\s an aid to intercourse with people of other 

 nations and for the purpose of keeping up with the record of 

 modern science, nobody doubts that the modern languages are 

 to be encouraged ; but if we really would own the inheritance 

 which is our birthright, if we wish to appreciate the master- 

 pieces of literature, if it is well to put ourselves in sympathy 

 with mankind, to 1 mgh with those who have laughed, and weep 

 with those who have wept, we must not be restricted to tlie 

 writings of to-day. In science, it has been said, read the newest 

 and latest ; riot so in literature — but the best. Isaiah and John, 

 Homer and -Eschylus, Cicero and Virgil, the "Nibehmgen Lied" 

 and Chaucer, Dante and Petrarch, are as full of life, beauty, 

 instruction, and entertainment to us as to former generations. 

 But from the classical standard of excellence this busy worUl 

 would soon depart, were it not that in every university there are 

 scholars keeping bright the altar fires, and warming us with 

 the glow of their enthusiasm, whenever we come under their 

 influence — sharpening too our wits by their critical acumen. 



It is not uncommon, nowadays, to hear objections to classical 

 education, usually from those wiho have never had it, and decla- 

 mations against dead languages, usually from those who have 

 never learned them. But the Humanists may unquestionably 

 leave it to the Geologists to fight the battle for antiquity. Tlie 

 latter assure us that the older the fossils the more instructive 

 their lessons ; indeed, so much importance is attached to ancient 

 animal life that the national government, with great liberality, 

 encourages its study by promoting explorations, museums, and 

 costly publications. Be it so ; but let not the nation which does 

 this forget that men are of "more value th.in many sparrows" ; 

 that the oldest literature is not old or dead, but fresh and living 

 in comparison with the bones of the cave-dwellers ; and that 

 though a Megatherium is wonderfully instructive, an ancient epic 

 or a drama is not unuorthy of attention. 



Jebb, in his life of Bentley, asserts that probably " the study 

 of classical antiquity, in the largest sense, has never been more 

 really vigorous than it i-; at the present d.ay." We might add 

 that classical poetry has never been so popular — else why these 

 innumerable editions and translations ? Why, after VVorsley, 

 Butcher, Bryant, and their predecessors, are we reading aloud 

 and smiling over the immortal Odyssey as it is given to us in the 

 rhythmical prose of Palmer? This is a good sign ; only it is well 

 to remember that reading translations is not reading Greek, and, 

 as Jebb goes on to say, we must not forget the difference 

 between " the knowledge at second hand," which the intelligent 

 public can possess, and " the knowledge at first hand " which it 

 is the business of the libraries and professorships of a university 

 to perpetuate. 



If the defenders of classical study would confine their argu- 

 ment to the line which was lately followed by Butcher, they 

 would silence their opponents. " To Greece," he says, "we owe 

 the love of science, the love of art, the love of freedom — not science 

 alone, art alone, or freedom alone, but these vitally correlated with 

 one another and brought into organic union. . . . The Greek 

 genius is the European genius in its first and brightest bloom. 

 From a vivifying contact with the Greek spirit, Europe deriveil 

 that new and mighty impulse which we call progress." 



But I must not pass from the subject without a word upm 

 the study of language in general, that faculty of the human race 

 which was never half understood until the universities of Germany 

 entered upon the study of comparative philology, by the intro- 

 duction of Sanscrit study. With this new torch they have 

 thrown a flood of light upon the nature of speech, the history of 

 our race, the brotherhood of nations, and the development of 

 ideas which lie at the basis of all Indo-European civilisation. 



The Shemitic tongues have long been subjects of university 

 study, especially Hebrew and Ar.ibic — the former so much 

 esteemed as the Language of the Old Testament that it used to 

 be spoken of as the language of Paradise, and the latter being 

 regarded as a key to the ideas and religion, the ancient literature 

 and science, of one of the largest families of men. Of late years 

 the domain of Shemitic study has been widened ; libraries long 

 hidden have been exhumed on the sites of ancient Babylon and 

 Nineveh ; records, the very existence of which was unknown at 

 the beginning of this century, written in characters to which 

 there was then but the slightest clue, are now read and printed 

 and studied as a part of the history of mankind. Assyrian 

 becomes a language of university study — not, indeed, for many 

 scholars, but for a few, and the bearing of their discoveries is so 



important upon the language and history of the Hebrews that 

 one of tlie most learned of English theologians h.as recently said 

 that, in respect to certain of the obscurer passages of the Old 

 Testament, the world must wait for the light which would come 

 from Assyriology. 



Certainly, if the histoiy of mankind is worth studying, if the 

 lessons of the past are of value, language and literature, the 

 ancient, the modern, the primitive, and the cultivated, will 

 never be neglected among the studies of an enlightened 

 community. 



When we turn from Man to his environment, we soon per- 

 ceive that mathematics lies at the basis of all our knowledge of 

 this world. To count, to measure, and to weigh, are steps in 

 civilisation, and as we extend our powers in these directions, we 

 find that even the distance and mass of the planets, the form of 

 the earth, the velocity of light, the mechanical equivalent of 

 heat, and the unit of electrical resistance may be accurately 

 .ascertained, and the results, with many of the ideas which they 

 involve, may become a part of the intellectual possessions of 

 every educated person. Vet when we reflect that hardly any 

 branch of knowledge is so depreciated by the average man as 

 the modern advancement of pure mathematics, we must believe 

 th.at its influence upon civiUsation is not sufficiently considered. 



Prof. Cayley, in a recent address, alluded to the connection 

 of mathematics with comiuon life, on the one hand, and with 

 the deepest questions of philosophy, for example, the meta- 

 physical ideas of time and space, on the other. As to its utility, 

 he declared that he would defend this science as Socrates de- 

 fended justice, quite irrespective of worldly advantages, — and 

 then he proceeds to show the relations of mathematics to the 

 certainty of knowledge, and to emphasise the idea that mathe- 

 matical science is not built upon experience but upon certain 

 fundamental assumptions— wdiich are indeed found to be in con- 

 formity with experience. I wish that every student, however 

 remote his studies may be from mathematical text-books, would 

 turn to the opening passages of this discourse, and steady his 

 own mental equilibrium by the .assurance that the science which 

 is most exact, and most satisfactory in its reasonings, is 

 based upon fundamental postulates which are assumed and not 

 proved by experiment. " In the theory of numViers," he says, 

 "there are very remarkable instances of propositions observed 

 to hold good for very long series of numbers — and which are 

 nevertheless untrue." 



If you persist in taking the utilitarian view, and ask me what 

 is the good of Mr. Glaisher's determination of the least factors 

 of the missing three out of the first nine million numbers, the 

 volume containing the sixth million having lately been published ; 

 — or if you put a much more comprehensive question, what is 

 the use of the Abelian functions, I shall be forced to say, I do 

 not know ; and if you press me harder I shall be obliged to 

 express my conviction that nobody knows ; but I know, and 

 you know, and everybody may know, who will take the pains 

 to inquire, that the progress of mathematics underlies and 

 sustains all progress in exact knowledge. 



Whewell, the author of the " History of Inductive Sciences," 

 has brought out very elearly the fact that " the opening of Greek 

 civilisation was marked by the production of geometry, the idea 

 of space was brought to a scientific precision ; and likewise the 

 opening of modern European civilisation was distinguished by 

 the production of a new science. Mechanics, which soon led to 

 the mechanics of the heavens, and this step, like the former, 

 depended on men arriving at a properly distinct fundamental 

 idea, the idea of force." Henry Smith, arguing for the value of 

 his favourite study to mankind, points out the injury which 

 would come to the intellectual strength of any nation "whose 

 notions of the world and of the things in it, were not braced and 

 girt together with a strong frame-work of mathematical reasoning. 

 It is something," he conFinues, "for men to learn what proof is 

 and what it is not." The work in mathematics at Alexandria or 

 Syracuse two thousand years ago is as perfect in its kind and as 

 direct and unerring in its appeal to our intelligence, as if it had 

 been done yesterday at Berlin or Gottingen by one of our own 

 contemporaries. In kindred language, Cayley, working forward 

 as well as backward, and not unmindful, let us hope, of the 

 Sylvestrian school upon this side of the Atkantic, in which he 

 had been a master and a guest, thus concluded the address from 

 which I have already quoted : — 



"Mathematics has steadily advanced from the time of the 

 Greek geometers. Nothing is lost or wasted ; the achievements 

 of Euclid, Archimedes, and ApoUonius are as admirable now as 



