September 29, 19 10] 



NATURE 



599 



of the English — of the Government as of the exhibitors 

 — who, in reconstructing in the space of a few 

 weeks a section as beautiful and interesting as any- 

 one could possibly wish for, have once more shown of 

 what that unconquerable tenacity, the characteristic 

 of the British Empire, is capable. I find no words 

 to express to Your Excellency my admiration and my 

 gratitude." 



One of the most interesting exhibits is that of 

 the Thermal .Syndicate. The articles are manufac- 

 tured at the high temperature of the electric arc, and 

 it is of particular interest to notice that even the 

 intense heat of the conflagration had no effect upon 

 the silica ware. In the new section, tubes and pipes 

 which had been through the fire are exhibited along- 

 side of articles freshly manufactured. These tubes 

 have glass fused to them, but, except for slight dis- 

 coloration, are absolutely uninjured by the ordeal 

 through which they have passed. 



-Although Messrs. Johnson and Matthey have not 

 been able to exhibit again, it should be mentioned 

 that the transparent silica shown by them in the 

 oriijinal section was also in no w-ise injured by the 

 heat, although much of it was broken by the falling 

 debris. The writer found pieces of platinum exhibited 

 by the same firm absolutely embedded in fused glass, 

 which gives a good idea of the intense heat to which 

 everything in the burning building was subjected. 



.\s showing the resource of energy of some of the 

 exhibitors, mention should be made of the pottery 

 exhibit of Mr. Bernard Moore. A large vase is shown 

 which has been designed and manufactured since the 

 tire and bears a commemorative design — a phoenix 

 rising from the flames with the motto Quod ignis 

 debit inccndium abstiilit. The Pilkington Tile and 

 Pottery Co. also shows a commemorative v-ase. This 

 is of particular interest, because it shows a new lustre 

 which has not been discovered more than three 

 months. 



The International Salt Co., Ltd., shows salt purified 

 by a new process. The salt is fused and air blown 

 Ihroui^h it, the impurities separate out, and the pure 

 salt is run off. Whether this process will be able 

 to compete against the older process remains to be 

 seen, but at least it is interesting. 



Owing to the exigencies of time and of space, it 

 has not been found possible to instal again completely 

 the very fine display of scientific instruments and of 

 chemical products which was shown in the original 

 section, but the chemical court makes quite a good 

 display. The section, as a whole, is a splendid ex- 

 ample of what can be done by organisation and the 

 courage which knows no defeat. 



It should be mentioned in closing that the advances 

 due to recent science have been found to be of the 

 utmost value in the cutting and removal of the tangled 

 mass of iron-work which is all that remains of the 

 burnt-out parts of the exhibition. The cutting of even 

 thick girders is done entirely by burning' with the 

 oxyhydrogen flame, and it is extremely interesting to 

 notice how rapidly it is possible to work by means 

 of this method. 



F. MoLLWo Perkin. 



MATHEMATICS IN AUSTRIA. 

 A S the result of an educational conference, con- 

 -^~*- vened at Vienna in 1908, changes of consider- 

 able importance have been made in the curriculum of 

 the secondary schools of .Austria. At the instance of 

 the Board of Education, the mathematical syllabus 

 issued in iqoq for the .Austrian Gymnasien has been 

 translated into English, and it deserves the thoughtful 

 NO. 2135. VOL. 84] 



consideration of all those who are interested in the 

 efficiency of our own educational system. It comes at 

 an opportune moment and forms a useful contribution 

 to all the discussions and e.xperimental investigations 

 of the last few years, which should provide a sound 

 foundation for the work of the International Commis- 

 sion on Mathematical Teaching, which will report to 

 the congress at Cambridge in 1912. We do not pro- 

 pose to examine this pamphlet in detail, but it may be 

 useful to note some of its salient features. 



.Although in recent years the theoretical has been 

 replaced by the practical in our secondary schools to 

 a degree which many have considered dangerous, it is 

 clear that far more drastic measures have been adopted 

 by the .Austrian authorities. The course of arithmetic 

 is limited to multiplication and division of decimals, 

 contracted methods, proportion and interest. There 

 are few who will not admit that the time spent on 

 mixtures, discount, stocks, and the various other 

 specialised arithmetical problems, which occupy so 

 large a space in our text-books, might be employed to 

 far greater advantage. .At present only a small pro- 

 portion of boys ever obtain a working knowledge of the 

 elements of trigonometry and the calculus. Reform 

 in this direction is badly needed, but it is almost impos- 

 sible for changes to be made in the school curriculum 

 so long as the various examining bodies, and in par- 

 ticular the Oxford and Cambridge joint board and the 

 Civil Service Commissioners, continue to require a 

 standard in arithmetic, which can only be attained bv 

 a large expenditure of time. There is much to be said 

 for omitting altogether the arithmetic paper 

 from these examinations, but, if this should 

 be regarded as too extreme a measure, we are 

 profoundly convinced of the desirability of re- 

 stricting it to simple questions on the laws of the sub- 

 ject ; the time thus saved would be devoted to numerical 

 triijonometry, and consequently it would be reasonable 

 to expect from candidates for such examinations as the 

 leaving certificate or army qualifying an elementary 

 practical knowledge of trigonometry. It would be 

 difficult to exaggerate the benefits which would result 

 from such a change as this, and we do not doubt that 

 it will come, although not in the near future. 



The next feature of interest is the importance which 

 is attached to the idea of functionality. 



"The notion of Function is recognised as the idea 

 which differentiates higher from elementary mathe- 

 matics, and a full s^rasp of it is held to be the 

 proper aim of school teaching ... the habit -of look- 

 ing at variable quantities as varying continuously 

 and in obedience to law is to be fostered from the 

 beginning." 



Experience shows how slow is the fjrowth of appre- 

 ciation of this conception, but the sphere of its opera- 

 tion is so extensive and its application so stimulating 

 that it well repays the effort required. If the arraphical 

 work in algebra is not designed to illustrate this prin- 

 ciple, it is reduced to a valueless mechanical operation. 



The last noteworthy variation is the combination of 

 plane and solid geometry throughout. The cultivation 

 of the power of thinking in three dimensions receives 

 far more attention on the Continent than in England. 

 Many even of those w-ho win mathematical scholar- 

 ships at our universities have no knowledge of the 

 rudiments of practical solid geometry. There are 

 signs, however, of change in this direction, and the 

 value of an elementary course on plan and elevation 

 of sintple solids is being gradually realised. 



Enough has been said to show that the guiding 

 principles of this syllabus are progressive and eminently 

 practical, and the Board of Education have done well 

 to render it accessible. 



