406 



SCIENCE. 



[N. S. Vol. XVll. No. 428. 



character, 'Anwendung der Differential 

 und Integral-Rechmtng auf Geometi'ie: 

 Eine Revision der Prineipien' (Gottingen, 

 summer semester, 1901, Teubner, 1902). 

 This course of lectures is designed to 

 present particular applications of the gen- 

 eral notions of Klein, and, furthermore, it 

 is in continuation of the discussion between 

 Pringsheim and Klein and others, as to 

 the desirable character of lectures on 

 mathematics in the universities of Ger- 

 many. 



Elementary Mathematics.— Ihis separa- 

 tion between pure mathematics and applied 

 mathematics is grievous even in the domain 

 of elementary mathematics. In witness, 

 in the first place: The workers in physics, 

 chemistry and engineering need more prac- 

 tical mathematics; and numerous text- 

 books, in particular, on calculus, have re- 

 cently been written from the point of view 

 of these allied subjects. I refer to the 

 works by Nernst and Schoenflies,* Lo^ 

 rentzf Perry J and Mellor,§ and to a book 

 on the very elements of mathematics now 

 in preparation by Oliver Lodge. 



In the second place, I dare say you are 

 all familiar with the surprisingly vigorous 

 and effective agitation with respect to the 

 teaching of elementary mathematics which 

 is at present in progress in England, 

 largely under the direction of John Perjy, 

 professor of mechanics and mathematics of 



* Nernst und Schoenflies, ' Einfuhrung in die 

 mathematische Behandlung der Naturwissen- 

 schaften (Munich and Leipsic, 1895) ; the basis of 

 Young and Linebarger's ' Elements of Differential 

 and Integral Calculus,' New York, 1900. 



t Lorentz, ' Lehrbuch der Differential- und In- 

 tegralrechnung,' Leipsic, 1900. 



t Perry, ' Calculus for Engineers ' ( second edi- 

 tion, London, E. Arnold, 1897 ) ; German transla- 

 tion by Prioke (Teubner, 1902). Cf. also the 

 citations given later on. 



§ Mellor, • Higher Mathematics for Students of 

 Chemistry and Physics, with special reference to 

 Practical Work,' Longmans, G-reen & Co., 1902, 

 pp. xxi -|- 543. 



the Royal College of Science, London, and 

 chairman of the Board of Examiners of 

 the Board of Education in the subjects of 

 engineering, including practical plane and 

 solid geometry, applied mechanics, prac- 

 tical mathematics, in addition to more 

 technical subjects, and in this capacity in 

 charge of the education of some hundred 

 thousand apprentices in English night 

 schools. The section on Education of the 

 British Association had its first session at 

 the Glasgow meeting, 1901, and the session 

 was devoted to the consideration, in con- 

 nection with the section on Mathematics 

 and Physics, of the question of the peda- 

 gogy of mathematics, and Perry opened 

 the discussion by a paper on 'The Teach- 

 ing of Mathematics.' A strong committee 

 under the chairmanship of Professor For- 

 syth, of Cambridge, was appointed 'to 

 report upon improvements that might be 

 effected in the teaching of mathematics, 

 in the first instance, in the teaching of 

 elementary mathematics, and upon such 

 means as they think likely to effect such 

 improvements.' The paper of Perry, with 

 the discussion of the subject at Glasgow, 

 and additions including the report of the 

 committee as presented to the British As- 

 sociation at its Belfast meeting, September, 

 1902, are collected in a small volume, 'Dis- 

 cussion on the Teaching of Mathematics,' 

 edited by Professor Perry (Macmillan, 

 second edition, 1902).* 



One should consult the books of Perry, 

 'Practical Mathematics, ' f 'Applied Me- 

 chanics,']: 'Calculus for Engineers '§ and 

 'England's Neglect of Science, '|| and his 



* Cf . also ' Report on the Teaching of Elemen- 

 tary Mathematics issued by the Mathematical 

 Association,' G. Bell & Sons, London, 1902. 



t Published for the Board of Education by Eyre 

 and Spottiswoode, London, 1899. 



t D. Van Nostrand Co., New York, 1898. 



§ Second edition, London, E. Arnold, 1897. 



II T. Fisher Unwin, London, 1900. 



