March I, 1881] 



NATURE 



415 



was most pressing, that of the teaching of geometry. 

 But it can hardly be denied, I thinlc, that there are other 

 branches of mathematics whose teaching might also be 

 greatly improved by an association of teachers, conferring 

 together as to the defects of existing bobks or methods, 

 and intrusting to sub-committees the task of suggesting 

 means of remedying such acknowledged defects. If this 

 be granted it appears to me that it is our ne.xt duty to 

 bring the strength of our existing organisation to bear on 

 other branches of mathematics besides pure geometry. 

 To do this would, I believe, assist rather than injure the 

 work which we have still to do for geometry. 



" I cannot doubt but that we have to some extent 

 suffered from the restriction of the field within which we 

 have hitherto worked. Elementary geo.netry is essentially 

 a school subject, that is, one in which a student of mathe- 

 matics ought to be fairly proficient before he enters on 

 his university course, and which therefore is not a subject 

 of n-ir/ /twcy//;/^' in our universities or higher colleges at 

 all. To this, and not to any ingrained spirit of oppo- 

 sition to improvement, which in the face of the changes 

 going on in our universities it seems to me it would 

 be absurd to charge upon any body of active workers 

 therein, I am inclined to attribute the small amount of 

 interest and attention which we have hitherto been able 

 to obtain for our work, and our failure as yet to procure 

 any recognition of our syllabus in any university of the 

 United Kingdom. Where a subject is not taught, but is 

 only a subject, and rather a subordinate subject, of ex- 

 amination, there can hardly be any very lively and active 

 interest in the improvement of its teaching. It is reason- 

 able to expect, therefore, that, by extending the scope of 

 our work to other subjects, of which only the elements 

 can in general be taught in schools, and which will after- 

 wards be more fully studied at the universities, we shall 

 enlist the sympathies of a wider circle of mathematical 

 teachers, extend the list of our members, and connect 

 ourselves more intimately with the living mathematical 

 teaching of our universities, and then we shall, I believe, 

 greatly promote the recognition of the work which we 



have already done .•\lgebra and trigonometry are 



perhaps less in need of our attention than other subjects, 

 though even as regards these I believe valuable sugges- 

 tions as to improved methods and range of teaching would 

 arise in the discussion of a committee specially interested 

 in them. But it is only necessary to mention the subjects 

 of analytical geometry, higher geometry, higher algebra, 

 elementary kinematics and dynamics (or mechanics), to 

 bring before the minds of those whom I am addressing a 

 number of questions as to their teaching, from the discus- 

 sion of which great advantages might arise. Further, I 

 think no one can have followed the more recent exposi- 

 tions of mathematical physics, more especially in the 

 ' Matter an 1 IVIotion ' of Maxwell, and the ' Elements 

 of Dynamic ' (alas, only a fragment) of Clifford — to 

 mention only the names of two of the most penetrative 

 geniuses and profound thinkers of our age, whom we 

 have loved and admired while living, and whose premature 

 deaths we, in common with the whole world of mathe- 

 matical and physical science, deplore as an irreparable 

 loss — without feeling convinced that the time is not far 

 distant when the notion of a vector or step, as Clifford 

 happily names it, and the simpler consequences of that 

 notion forming a vector or step-gtomeiry (the basis 

 of the calculus of quaternions), must be made a part 

 of the elementary studies of every student of mathe- 

 matics, more especially for the purposes of mathematical 

 physics, but perhaps not less for its application to pure 

 geometry. And if this be so I cannot help thinking that 

 our ."Xssociation, extended as I have suggested, might be 

 the means of bringing together the right men to organise 

 the method and bring it into a suitable stage for ele- 

 mentary instruction ... I refer to the improvement of 

 the teaching of arithmetic. I suppose there are none of 



us here who have had any experience in the teaching of 

 arithmetic, who have not often wished that they could 

 make a tabula rasa of their pupils' minds, as regards this 

 subject, so fatally destructive of all appeals to reason have 

 early unintelligent teaching and bad traditional methods 

 shown themselves to be. In an effort to reform in many 

 points the teaching of arithmetic, we might naturally 

 expect to associate with us the best teachers in prepara- 

 tory and even in primary schools ; and perhaps also mem- 

 bers of that very important body of men, the Government 

 Inspectors of Schools ; and thus our organisation might 

 become the means of linking together all grades of 

 mathematical teachers, from the humblest to the highest, 

 in an association which could not fail, if heartily sup- 

 ported, to become a powerful influence for good on the 

 whole education of the country." 



As the President's proposal took many of the members 

 present by surprise, it was ultimately resolved, as we read, 

 that a special meeting of the Association should be held 

 about Easter next, to consider the desirability or the 

 contrary of thus extending the scope of the Association. 



In connection with this matter we have also received 

 a letter addressed to non-members to ascertain, if such 

 an extension of the aims of the Association were adopted, 

 whether they would allow themselves to be proposed as 

 members of the new .-Xssociation. A draft of rules ac- 

 companies the Report, from which we extract the follow- 

 ing proposel rules : — " That the Association be called 

 'The Association for the Improvement of Mathematical 

 Teaching'; that its object shall be to effect improvements 

 in the teaching of the various branches of elementary 

 mathematics and mathematical physics by such means 

 as may appear most suitable in each particular case. 

 This object to be carried out by the reading of papers or 

 raising discussions at meetings of the Association, by the 

 appointment of committees to report on existing defects in 

 the usual methods, order, range, &c. , in teaching special 

 subjects, and the expediency of drawing up syllabuses 

 or text-books of such subjects ; by the employment of 

 suitable means for bringing the work done by the Asso- 

 ciation before the universities and other educational or 

 examining bodies, and using its influence to obtain recog- 

 nition ofjsuch work from those bodies." 



Another action on the part of the meeting was the 

 passing a resolution "that a sub-committee be appointed 

 to draw up proofs of the propositions of the syllabus of 

 plane geometry." It was shown that many teachers had 

 adopted the syllabus, and that it was meeting with a 

 growing acceptance was evidenced by the steadily im- 

 proving annual sale, 2033 copies having been already 

 sold. 



ILLUSTRA TIONS OF NEW OR RARE ANIMALS 

 IN THE ZOOLOGICAL SOCIETY'S LIVING 

 COLLECTION^ 



II. 



NORTH-EASTERN ASIA has of late years disclosed 

 to its explorers a number of very curious novelties 

 in the class of Mammals. Amongst them are several 

 species of great interest, examples of which have reached 

 the Gardens of the Zoological Society alive. 



4. The Tcheli Monkey (Macaa/s Tcheliensis) was so 

 named by the distinguished zoologist, M. Alphonse Milne- 

 Edwards of Paris, from the Chinese province of Tcheli 

 (or Petclieli), in which it is found. The existence of a 

 monkey in a latitude so far north — on nearly the same 

 isothermal line as the city of Paris ■ is a very remarkable 

 fact, and quite new to zoological distribution. 



The occurrence of this monkey in the mountains of the 

 north-eastern district of the province of Petcheli seems to 

 have been first ascertained by M. Fontanier, who was for 

 some years French Consul at Pekin, and who transmitted 



^ Conlinvied from p. 38. 



