January 20, 1910J 



NA TURE 



357 



at Detroit, and reproduced in a recent number of Science 

 under the title " Tlie Rehabilitation of the American 

 College and the Place, of Chemistry in It," is of more 

 than local interest and importance. The author is strongly 

 impressed with the difficulty of teaching his subject 

 effectively to classes of students of widely varying mental 

 capacities, and especially of teaching it in such a way 

 as to be of service to those who do not expect to become 

 professional chemists. He is a profound disbeliever in the 

 method of imparting instruction which relies mainly upon 

 lectures, and urges that the essential feature of all teach- 

 ing should be " problem-solving " in some form or other. 

 This method, he suggests, is fully developed in the teaching 

 of languages, in which " the grammar furnishes the laws 

 and general principles, together with all the known excep- 

 tions," "the dictionary supplies the isolated facts," and 

 " the text provides the subject of study in constant and 

 definite form." In the case of chemistry, he urges a 

 closely interwoven scheme of laboratory work and class- 

 room discussion, supplemented (if lectures are used) by 

 briefly written answers to set questions and home study 

 in varying amounts to suit the necessities of the individual 

 student. 



The annual general meeting of the Association of Head- 

 masters was held in London on January 12 and 13. Mr. 

 Philip Wood, headmaster of Darlington Grammar School, 

 the president for the year, in his presidential address re- 

 ferred to the question of the provision of free places in 

 secondary schools receiving grants from the I3oard of 

 Education. He said there are many grammar schools in 

 towns with a population of less than 20,000 which educate 

 the sons of the professional people and better-class trades- 

 men, but depend largely for their existence on being able 

 to attract boarders. The position of such a school at the 

 present time is very precarious. It has had always some- 

 thing of a struggle, and the grants of local education 

 authorities and of the Board of Education are just what it 

 requires to give it new life ; but the grants are conditioned, 

 and the conditions, at least of the Board of Education, 

 would seem to contemplate a large day school in a large 

 town rather than the kind of school in question. In a 

 small market town, for instance, it is ridiculous that a 

 school of, perhaps, seventy-five boys should be increased 

 to 100 in order to provide for the education of twenty-five 

 boys from the two or three elementary schools in the 

 town. Boys capable of taking advantage of these oppor- 

 tunities are not to be found ; and what is also a matter 

 of common experience, their admission, whether they are 

 capable or incapable, generally means the displacement of 

 an equal number of boys whose parents do not like the 

 new situation. Thus the 25 per cent, rule, which does not 

 greatly embarrass a large day school, will, if rigorously 

 applied, almost ruin many schools which we can ill afford 

 to lose. 



The Department of Agriculture and Technical Instruc- 

 tion for Ireland has issued a pamphlet giving an account, 

 by Mr. George Fletcher, assistant secretary for technical 

 instruction, of the summer courses of instruction for 

 teachers instituted by the Department in 1901. The courses 

 are held in July and August, and extend over a period of 

 about a month. They are held in Dublin and elsewhere. 

 In selecting teachers to attend the courses, regard is had 

 to the qualifications of the teachers and the needs of the 

 school or district from which they come. After each year's 

 course, teachers who pass the examinations are provision- 

 ally recognised as qualified to teach the subjects in which 

 they have passed. Courses are held in experimental 

 science, drawing, manual work in wood, and domestic 

 economy. Besides preparing teachers to conduct classes 

 in the Department's " Programme for Day Secondary 

 Schools," the summer courses are year by year coming to 

 serve a further purpose. Side by side with the develop- 

 ment of the Department's scheme in day secondary schools 

 there has grown up a system of specialised technical educa- 

 tion all over Ireland. The rate of growth has been rapid, 

 and a large and increasing number of Irish teachers are 

 engaged in the schools and classes organised through 

 urban and county councils. While it was necessary in the 

 initial stages of such a system to employ teachers having 

 experience of similar work, from whatever source they 

 NO. 2090. VOL. 82] 



might be obtained, special efforts have since been made 

 to train Irishmen when and where possible. Hence it is 

 that year by year an increasing number of summer courses 

 are organised to deal with subjects purely technical _ in 

 character and having for their object the further education 

 and training of teachers already engaged in Irish technical 

 schools. It would be difficult to over-estimate the value 

 of these courses as an element of educational progress. 

 The typical courses described in the pamphlet by means 

 of syllabuses, descriptions, and illustrations indicate what 

 great pains have been taken by the authorities to make 

 the lectures and practical work meet the needs of the 

 teachers exactly. 



SOCIETIES AND ACADEMIES. 



London. 

 Royal Society, January 13.— Sir Archibald Geikie, 

 K.C.B., president, in the chair.— Sir Edward Thorpe and 

 A. G. Francis : The atomic weight of strontium.— L. F. 

 Richardson : The approximate arithmetical solution by 

 finite differences of physical problems involving differ- 

 ential equations, with an application to the stresses in a 

 masonry dam. In order to deal with irregular boundaries, 

 analysis is replaced by arithmetic, continuous functions are 

 represented by tables of numbers, differentials by central 

 differences. Then problems fall into two classes. (A) The 

 relation between the equation obtaining throughout the 

 body and the boundary condition is such that the integral 

 can' be stepped out from a boundary. This class includes 

 equations of all orders and degrees. It has been treated 

 by arithmetical differences by Runge, W. F. Sheppard, 

 Karl Heun, W. Kutta, and Richard Ganz. Examples of a 

 specially simple method are given. (B) The integral must 

 be determined with reference to the boundary as a whole, 

 as in Dirichlet's problem. The method given has only 

 been worked out for a limited group of linear equations, 

 namely, for those in connection with which a function 

 analogous to potential energy exists, which is a complete 

 minimum when and only when the difl'erence equations 

 are satisfied. Under this condition the difference between 

 the integral «„ and a function *, of the independents, 'having 

 the correct boundary conditions but otherwise arbitrary, can be 

 expanded in the form <p^ - (t>„ = 2A,P,- where the .\,s . . ■ A" 

 are constants and P, . . . P„ are "principal modes of oscilb- 

 tion" defined by D'P, = ;i,-Pi where D>„ = o is the difference 

 equation to be integrated and A- is a constant. Now we start 

 with the table of numbers .}>, and calculate D>,. Then as 

 D>„ = o we have D'*, = D'((p, - 4>„1 = 2A,.\,-Pj. Multiplying 

 both sides bv some number Oi"' and subtracting from ip,, and 

 altering the boundary numbers so that the boundary condition 

 is still satisfied, we have a new table which may be called ((>, : 

 and>j-(J)„ = 2A,(l-a,-'''t-)Pj- Repeating the process with 

 a„ . . . a„ v/e get : • _, n t> 



f<P,„+,-*.. = 2Ai.(l-o.3-iA,.2)(l-05-'Ai^) . . . (l-a,„ 1Aj-)Pa. 



Now a function I exists such that SIP,2=I, SIP,P,=o where 

 S denotes a summation throughout the region. Therefore : 

 SI(<(>,„ + ,-*„)= = 2[A,.(l-a,-'AA-) . • • (l-Om"'''*-)]-- 

 Now by a sufficient number of suitably chosen as the 

 polynomial in A= on the right can be made small through- 

 out the range from X,^ to A,,'. Therefore the error of 

 <f,„4., can be made small ; for, since I is one signed it is 

 measured by the L.H.S. The process is arithmetical. The 

 error due to finite central differences is of the form 



eji- + eji* + eji'+ &c., 

 where h is the coordinate difference and the es are func- 

 tions of position independent of h. If the integral has 

 been found for two or more sizes of h, more exact values 

 of it can be extrapolated by this formula. These methods 

 have been applied in the paper to calculate the stress- 

 function in a masonry dam. — A. O. nankine : A method 

 of determining the vis'cositv of gases, especially those avail- 

 able only in small quantities. — Dr. P. Phillips : Re- 

 combination of ions at different temperatures. — Dr. G. C. 

 Simpson : The electricity of rain and snow. This paper 

 relates to measurements of the electricity of rain made in 

 continuation of those described at the beginning of last 



