5oo 



NATURE 



{Sept. 20, 1883 



to the student, give him really useful knowledge, and would be 

 at the same time of true educational value. 



The chief progress in geometrical teaching has to be sought in 

 the introduction of modern ideas and methods into the very 

 elements, and modern teaching ought to take full account of 

 this. 



In favour of this view I might bring forward the opinions of 

 many teachers and mathematicians from England as well as 

 from abroad, but I will confine myself to one quotation. Prof. 

 Sylvester gives his opinion thus: — "I should rejoice to see 

 mathematics taught with that life ami animation which the 

 presence and example of her young and buoyant sister (viz. 

 natural and experimental science) c iuld not fail to impart, short 

 roads preferrtd to long ones, Euclid honourably shelved or 

 buried ' deeper than did ever plummet sound ' out of the 

 schoolboy's reach, morphology introduced into the elements of 

 algebra — projection, correlation, motion accepted as aids to geo- 

 metry — the mind of the student quickened and elevated and his 

 faith aw akened by early initiation into the ruling ideas of polarity, 

 continuity, infinity, and familiarisation with the doctrine of the 

 imaginary and inconceivable. It is this living interest in the 

 subject which is so wanting in our traditional and mediaeval 

 modes of teaching." 



If from this point of view we now look towards the work of 

 the Association for the Improvement of Geometrical Teaching, 

 the result is not as satisfactory as might have been wished. 

 There is very little of the influence of modern ideas to be found 

 in the different syllabuses which have been published. Even in 

 the one headed "Modern Geometry" there is nothing of the 

 genius of modern thought. The subject-matter is partly taken 

 from modern geometry, but for modern methods one looks in 

 vain. In the geometrical conies, too, one would like to see 

 Steiner's generation of conies, but of these there is no trace. 



Nevertheless it is satisfactory to see that the use of the syl- 

 labus on plane geometry lias spread pretty widely, and it is to be 

 hoped that it will continue to do so. A thorough reform in the 

 direction indicated will be a difficult task, and it will perhaps be 

 a long time before it is possible. At present it has not even 

 been settled which series of axioms will ultimately be adopted. 

 Of the various systems which have been proposed since the in- 

 vestigations of Kiemann and Helmholtz, I may mention here 

 Clifford's suggestion to replace Euclid's axiom about parallels by 

 the new one, which maintains that in a plane similar figures 

 exist, or, more completely, that at any part in a plane a figure is 

 possible which is similar to any given figure in that plane. This 

 axiom is somewhat startling as long as we have the usual theory 

 of similar figures in our mind, but the notion of similar figures 

 is truly axiomatic, and it has lately become my conviction that 

 this axiom may be extremely fruitful, and the working out of a 

 syllabus of plane geometry based on it would be very desirable. 



Possibly many such attempts have still to be made before a 

 new Euclid finds the materials sufficiently prepared for him to 

 raise the hoped-for edifice. 



SECTION B 



CHEMICAL SCIENCE 



Opening Address by J. H. Gladstone, Ph.D., F.R.S., 



V.P.C.S., PRkSlDENT OF THE SECTION. 



A sectional address usually consists either of a review of the 

 work done in the particular sc.ence during the past year, or of 

 an exposition of some branch of that science to which the speaker 

 has given more especial attention. I propose to follow the latter 

 of these practices, and shall ask the indulgence of my brother 

 chemists while I endeavour to place before them some thoughts 

 on the subject of Elements. 



Though theoretical and practical chemistry are now inter- 

 twined, with manifest advantage to each, they appear to have 

 been far apart in their origin. Practical chemistry arose from 

 the arts of life, the knowledge empirically and laboriously ac- 

 quired by the miner and metallurgist, the potter and the glass- 

 worker, the cook and the perfumer. Theoretical chemistry 

 derived its origin from cosmogony. In the childhood of the 

 human race the question was eagerly put, "By what process 

 were all things made?" and some of the answers given started 

 the doctrine of elements. The earliest documentary evidence of 

 the idea is probably contained in the Shoo King, the most 

 esteemed of the Chinese classics for its antiquity. It is an 

 historical work, and comprises a document of still more vener- 

 able age, called "The Great Plan, with its Nine Divisions," 



which purports to have been given by Heaven to the Great Yu, 

 to teach him his royal duty and "the proper virtues of the various 

 relations." Of course there are wide differences of opinion as to 

 its date, but we can scarcely be wrong in considering it as older 

 than Solomon's writings. The First Division of the Great Plan 

 relates to the Five Elements. "The first is named Water ; the 

 second, Fire ; the third, Wood ; the fourth, Metal ; the fifth, 

 Earth. The nature of water is to soak and descend ; of fire, to 

 blaze and ascend ; of wood, to be crooked and to be straight ; ot 

 metal, to obey and to change ; while the virtue of the earth is 

 seen in seed-sowing and ingathering. That which soaks and 

 descends becomes salt ; that which blazes and ascends becomes 

 bitter; that which is crooked and straight becomes sour; that 

 which obeys and changes becomes acrid ; and from seed sowiDg 

 and ingathering comes sweetness." 1 



A similar idea of five elements was also common among the 

 Indian rao s, and is stated by Professor Rodwell to have been in 

 exi-tence before the fifteenth century B.C., but, though the num- 

 ber is the same, the elements themselves are not identical with 

 those of the ancient Chinese classic ; thus, in the Institutes of 

 Menu, the " subtle ether " is spoken of as being the first created, 

 from which, by transmutation, springs air, whence, by the 

 operation of a change, rises light or fire ; from this comes water, 

 and from water is deposited earth. These five are curiously 

 correlated with the five senses, nnd it is very evident that they 

 are not looked upon as five independent material existences, but 

 as derived from one another. This philosophy was accepted 

 alike by Hindoos and Buddhists-. It was largely extended over 

 Asia, and found its way into Europe. It is best known to us in 

 the writings of the Greeks. Among these people, however, the 

 elements were reduced to four — fire, air, earth, and water — 

 though Aristotle endeavoured to restore the "blue ether" to its 

 position as the mo-t subtle and divine of them all. It is true that 

 the fifth element, or " quinta essentia," was frequently spoken of 

 by the early chemist--, though the idea attaching to it was some- 

 what changed, and the four elements continued to retain their 

 place in popular apprehension, and still retain it even among 

 many of the scholars who take degrees at our universities. The 

 claim of wood to be considered an element seems never to have 

 been recognised in the West, unless, indeed, we are to seek this 

 origin for the choice of the wcrd 6Atj to signify that original 

 chaotic material out of which, according to Plato and his schoo', 

 all things were created.- The idea also of a primal element, 

 from which the others, and everything else, were originated, was 

 common in Greece, the difficulty being to decide which of the 

 four had the greatest claim to this honour. Thales, as is well 

 known, in the sixth century B.C. affirmed that water was the first 

 principle of things ; but Anaxamenes afterwards looked upon air, 

 Heraclytus upon fire, and Theracleides on earth, as the primal 

 element. This notion of element*, however, was essentially 

 distinct from our own. It was always associated with the idea 

 of the genesis of matter rather than with its ultimate analysis, 

 and the idea of simple as contrasted with compound bodies 

 probably never entered into the thoughts of the contending 

 philosophers. 



The modern idea appears to have had a totally different origin, 

 and we must again travel back to China. There, also in the 

 <ixth century B.C., the great philosopher Lao-tse was meditating 

 on the mysteries of the world and the soul, and his disciples 

 funded the religion of Taou. They were materialists; never- 

 theless they believed in a "finer essence," or spirit, that rises 

 from matter, and may become a star ; thus they held that the 

 souls of the five elements, water, metal, fire, wood, and earth, 

 arose and became the five planets. These speculations naturally 

 led to a search after the sublimated essences of things, and the 

 means by which this immortality might be secured. It seems 

 that at the time of Tsin she-hwang, the builder of the Great 

 Wall, about two centuries before Christ, many romantic stories 

 were current of immortal men inhabiting islands in the Pacific 

 Ocean. It was supposed that in these magical islands was found 

 the "herb of immortality" growing, and that it gave them 



1 Quoted from the translation by the Rev. Dr. I.egge. In that most 

 obscure classic, the '* Yi-King." fire and water wind and thunder, the ocean 

 and the mountains, appear m be recognised as the elements. 



2 Students of the Apocrypha will remember the expression in the Book of 

 Wisdom, xi. \j. ' 7} TravToSvvapos cov X*V Ka ^ K T ' l(ra(Ta T & v xitrfioy e| 

 a/xi'p'pou uAtjs-' ('Thy Almighty hand, that made the world of matter 

 without form ') The same book contains two allusions to the ordinary 

 elements, vii. 17, and xix. 18 to 20. The word aTOtx^"" is used in the 

 New Testament only in a general sense (2 Pet. tii. to), or in its more 

 popular meaning of the first steps in knowledge. 



