November 24, 19 10] 



NATURE 



1:25 



its refractive power. For the second liquid Mr. Ahrens 

 has succeeded in finding in the paraffin series a white oil 

 which is a suitable material in its mechanical as well as 

 in its optical properties. It has not, however, the same 

 mean refractive index as methyl salicylate, so therefore, for 

 1 direct-vision prism, the end faces cannot be square to 

 le principal axis of the transmitted light. Their obliquity, 

 iiowever, is not great — not more than 15° if the refracting 

 angle of the middle prismatic cell is from 120° to 125°. 

 The dispersion of these prisms is ver>" good, and there is 

 nuch less absorption of the blue end of the spectrum than 

 > usually found with a bisulphide or flint-glass prism. 

 The writer, in a rough comparison of one of the Ahrens 

 biliquid prisms with a Wernicke prism and a 60° bisulphide 

 prism, found the following angular dispersions between 



Ahrcns's Biliquid Direct-vision Prism. 



" le C and F hydrogen lines : — bisulphide of carbon prism, 

 .' 27 ; Wernicke prism, 3^ 6'; Ahrens prism, 3° 12'. 



If direct-vision is not desired, a prism of high dispersion 



can be made on the same biliquid plan by constructing a 



class cell with the end faces at about 30° to the line of 



ght, and with internal oblique partitions at from 20° to 



-4° to the line of sight, dividing the whole into three 



prismatic chambers, the two outer of which are filled with 



methyl salicylate and the middle one with the white oil. 



This prism has marked superiority over a flint-glass prism 



f equal size. It must not, of course, be forgotten that 



'.\ liquid prisms are unsuitable for fine definition of the 



jectral lines owing to the change of refractive index in 



le liquid when the temperature rises. 



The biliquid prism is being put on the market by Mr. 

 nilischer. 



THE REFORM OF MATHEMATICAL AND 



SCIENCE TEACHING IN GERMANY> 



TTHE revolt against formal culture which characterised 



mathematical instruction has within the last decade 



, produced a large bibliography in English, French, and 



] <Jerman, and inspired systematic inquiry into possible and 



needful reform. The movement has been assisted in 



<iermany by an extension of the privileges of the 



'iymnasium to the Realgxmnasiura and the Oberreal- 



:hule, which in time may share the prestige of the 



'Vmnasium and win for the exact sciences a place 



.enburtig with the classics. 



V\ hen the Reformschulen were founded to provide a 



• ommon foundation for all pupils in nine-class schools 



between the ages of nine and twelve, engineers were 



pronouncedly favourable, thinking that the exact sciences 



ould benefit, and that an Einheitsmiitelschule (secondarv 



hool with uniform curriculum) was in sight. But thev 



ere doubly disappointed ; the classics have benefited, and 



-.e Einheitsmittelschule is condemned for svstematic per- 



rction. 



Reform of mathematical and science teaching depends 



losely on the inexorable demands of civilisation, and for 



ie understanding of modern culture a proper grasp of 



le meaning of a function is considered indispensable. On 



as account it is proposed to include analvtical geometrv 



id the calculus in the work of the nine-class schools'. 



^s no more time can be allotted to mathematics, anv relief 



'ust come from further pruning of the svUabus. Hence 



^ementary mathematics must be relieved 'of its lumber, 



tne desire to achieve systematic perfection must be left 



unfulfilled, pedantic thoroughness must be killed bv 



ridicule, and the exclusively deductive form abandoned, 



lore value being attached to intuition than to a cunning 



-e of the syllogism. Though mathematicians attack the 



^olation of their subject, thev do not advocate Fach- 



dung (professional studies) in secondary schools. Pro- 



Sori^f^M"^"^?!"^ w'^'l meeting of the Edinburgh Matbcmatical 

 =ociety on November 11 by Mr. A. J. Prcs^land. 



NO. 2143, VOL. 85] 



! fessional bodies have always protested against it, and the 



protest has been taken to indicate the attitude of Trade 



Unions also. Nevertheless, German universities are try- 



' ing to give the teacher an acquaintance with practical 



I applications and arrange courses in applied mathematics 



or recognise attendance at technical high schools. The 



i courses include descriptive geometry, mathematical 



i methods of technical mechanics, sur\-eying, life assurance, 



; and laboratory- work. 



I The introduction of practical work in the teaching of 

 ' physics is urgently needed. It is provided in the best 

 Prussian schools and in South Germany, notably at 

 I Munich, it forms part of the primary syllabus during the 

 last two years. .\ statistical inquiry showed that 75 per 

 cent., at least, of Prussian secondary- schools desired facili- 

 ties for experimental work, whilst only about thirty 

 possessed them. 



The minimum amount of time demanded is se\-en hours 

 per week for science — physics, chemistry, biology, and 

 geography — and four for mathematics. If proposals for 

 introducing specialisation in the last three years are enter- 

 tained, further hours may fall to the lot of the exact 

 sciences. 



The reintroduction of biolog}', which disappeared in 

 1879 as a result of the writings of Darwin and Haeckel, 

 is being advocated as a training of the powers of obser%'a- 

 tion, in which the German freshman is said to be woefully 

 deficient, and as an exercise in the use of the microscope. 

 Geography comprises economic geology, Erdkunde, and 

 astronomy, as well as commercial products. To bring it 

 into organic connection with mathematics, courses of 

 lectures on the interconnection of mathematics are being 

 projected. 



Matters are still in an indefinite position, but there are 

 indications that the Cambridge Congress of 19 12 will mark 

 the beginning of a new era. It is to be hoped, for our 

 sakes. that the results of this congress can be laid before 

 the Consultative Committee of the Board of Education to 

 be recommended for adoption throughout the Empire. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



BiRMixGHAM. — Mr. John Dale has been awarded the 

 Walter Myers studentship for a further period of one 

 year, having proved himself a student of exceptional merit. 

 An award of the same studentship for the present year 

 has been made to Mr. Cranston Walker. The value of 

 the studentship is 150/. per annum, and it must be used 

 for research in pathology or clinical medicine at some 

 German university. Mr. Dale, the first holder, is working 

 at Hamburg, and Mr. Cranston Walker is at the Uni- 

 versity of Freiburg, in Baden. The holder must possess 

 a degree in science in addition to degrees in medicine and 

 surgery. 



Ca-MBRIDGE. — .An election to an Isaac Newton student- 

 ship will be held in the Lent term, 191 1. It will be the 

 duty of the student to devote himself during the tenure 

 of his studentship to study or research in some branch 

 of astronomy or of physical optics, according to a course 

 profx>sed by himself and approved by the electors. The 

 student's course of study or research must be pursued at 

 j Cambridge. The studentship will be tenable for the term 

 I of three years from .April 15, 191 1. The emolument of 

 i the student will be 200/. per annum. Candidates for the 

 i studentship are invited to send in their applications to the 

 I \'ice-Chancellor between January 16 and 26, 191 1, together 

 j with testimonials and such other evidence as to their 

 j qualifications and their proposed course of study or re- 

 search as they may think fit. 



Mr. A. E. Shipley, F.R.S., master of Christ's College, 

 ; has been nominated by the general board of studies as a 

 member of the board of electors to the professorship of 

 zoologv and comparative anatomv in succession to the 

 i late Mr. J. W. Clark; and Prof. W. J. Pope, F.R.S., 

 I has been nominated by the council of the Senate a member 

 I of the board of electors to the Allen scholarship.. 



Oxford. — On November 22 another stage was reached 



in the discussion of the changes jM-oposed by the 



I Hebdomadal Council at the instance of the Chancellor of 



