414 



NATURE 



[January 24, 19 18 



years to sixteen years eight months. The second 

 examination will be designed for those who have con- 

 tinued their studies for about two years after the stage 

 of the first examination. The first examination is in- 

 tended to test the pupil's general education before he 

 begins his school specialisation. It should, under cer- 

 tain conditions, serve the purposes of a matriculation 

 examination, and it is hoped that eventually it will 

 replace the numerous entrance and preliminary exam- 

 inations to which pupils leaving the secondary school 

 have had to submit themselves. The second examina- 

 tion will be based on the view that older pupils should 

 have enjoyed a more concentrated study of a connected 

 group of subjects, and the courses suggested in the 

 Circular are (a) classics and modern history, (b) modern 

 "humanistic" studies, and (c) science and mathematics. 

 The Board's scheme naturally involves increased ex- 

 penditure by the schools, and in Circular 849 the Board 

 promised further financial aid, but in a later circular 

 of December, 1915, it was announced that proposals 

 involving increased financial aid were to be considered 

 in abeyance. Circular 996, issued on May 25, 1917, 

 however, announced the Board's ability to take up its 

 examination scheme again, and the appointment of the 

 " Secondary-School Examinations Council " to assist 

 the Board to undertake its functions as the co-ordinat- 

 ing authority for secondary-school examinations. This 

 council is at work, and the schools are awaiting its first 

 report. 



Closely connected with the two examinations which 

 are being instituted by the Board of Education for 

 pupils in grant-earning secondary schools is the scheme 

 for the provision of advanced courses in such schools 

 outlined in the "Regulations for Secondary Schools" 

 issued by the Board last year. The Board states that 

 the secondary schools are not sending forward to insti- 

 tutions of higher education and research a number of 

 properly qualified students adequate to the national 

 need. The Board regards this deficiency as due partly 

 to an insufficient provision for advanced work in 

 secondary schools, and to meet this need the new ad- 

 vanced courses have been planned. They are intended 

 for pupils of about sixteen who have reached the 

 standard of the Board's first school examination, and 

 are to last for two years. The advanced course must 

 be in one or other of three groups of subjects, the 

 Regulations state : — (i) Science and mathematics, in 

 which preponderance may be given to either ; (ii) 

 classics, i.e. the Latin and Greek languages, together 

 with the literature, history, and civilisation of Rome 

 and Greece ; (iii) modern studies, which must include 

 the study of (a) two languages other than English, 

 with their literature, (b) modern history on broad lines, 

 and including the history of England and of Greater 

 Britain, but also bearing special relation to the two 

 languages chosen. Two, or even three, of these ad- 

 vanced courses may be organised in a large school, 

 where pupils enough normally remain until about 

 eighteen, but probably the number of advanced pupils 

 in the school will not allow of more than one course. 

 An additional grant for each of these courses is pro- 

 mised ; it will not be calculated on the number of pupils 

 and will in no case exceed 400L Up to the middle of 

 November last between 270 and 280 applications for 

 recognition of advanced courses were received by the 

 Board. About half of the applications were in respect 

 of courses in science and mathematics ; of the remain- 

 ing half, those for courses in classics were little more 

 than one-third of those for courses in modern studies. 

 I'p to the same date sixty-three courses in science, 

 thirteen in classics, and nineteen in modern studies 

 have been recognised. Nearly fifty were still undeter- 

 mined. In the remainder (about 130) recognition was 



withheld, because the syllabus of instruction submitted 

 was unsatisfactory, or because it was not shown that 

 it could be satisfactorily carried out, or because a 

 reasonable number of pupils qualified to enter on the 

 course was not fortl-coming. 



GERMAN ECONOMICS AND 

 TECHNOLOGY. 

 n|'"'HE first meeting was recently held of the German 

 ■*■ Union of Technical Scientific Societies, formed 

 by a combination of thirteen associations and unions, 

 when problems involving economics and technology 

 during and after the war we're discussed. Prof. Dr. 

 Wiedenfeld, of Halle, spoke on the subject, and showed 

 that whilst, during recent pre-war years, Germany had 

 become more and more dependent upon foreign coun- 

 tries for many articles of prime necessity, the bloclcade 

 had thrown her back upon her own resources, and 

 technical science had been called upon to furnish her 

 requirements out of these, under conditions which were 

 so far novel in that the question of cost of produc- 

 tion became one of secondary importance. The 

 problem had been met in three different ways : — 



(i) By re-establishing industries that had been ren- 

 dered unremunerative by foreign competition, such as 

 the production of manganese, the increased production 

 of iron, the production of sulphur, and the intensifica- 

 tion of agriculture. 



(2) By the increased utilisation of what had been 

 waste products so much that the term " non-utilisable 

 substance" had been eliminated by the war, examples 

 being the production of lubricants from coal-tar and 

 of clothing materials from various waste products. 



(3) By the production of substitutes and of various 

 substances by synthetic processes, as of nitro-com- 

 pounds from atmospheric nitrogen, and of cattle feed 

 from stravv. 



It is interesting to note that this speaker objected to 

 the multiplicity of Government authorities controlling 

 production, and holds that the production of materials 

 in large quantities can be assured after the war only 

 by means of monopolies, though not necessarily State 

 monopolies. Finally, he insisted upon the immense 

 importance of close co-operation between technical 

 science and industry, neither of which can exist with- 

 out the other. It need scarcely be added that many of 

 these observations apply quite as forcibly to conditions 

 in this country as to those in Germany. 



THE NEW INTEGRAL CALCULUS. 

 'X'HE ancient Greeks determined various areas and 

 •*■ volumes by a method known as that of exhaus- 

 tion ; but they had no integral calculus prop>erly so 

 called, any more than (pace Prof. Burnet) they had a 

 differential calculus, although they were familiar enough 

 with the idea of a locus described by the motion (or 

 flow) of a point. Even Fermat missed the analytical 

 method devised by Barrow, Newton, and Leibniz. This 

 was so rapidly developed as to assume a form which 

 (except in notation) remained practically unaltered for 

 a century and a half. The reason of this quiescence — 

 a sort of dormant vitality — was the neglect of function- 

 theory, or, rather, its non-existence. The appearance 

 of Fourier's work on the theory of heat compelled 

 mathematicians to study the properties of trigono- 

 metrical series, and the conditions under which they 

 could be used for the representation of so-called arbi- 

 trary functions. Dirichlet and Riemann shed a flood of 

 light upon the matter ; and Riemann gave a definition 

 of a definite integral which could be applied to func- 

 tions more general than those that could be integrated 



NO. 2517, VOL. 100] 



