NATURE 



[September 5, 1912 



meriting: on this report, Profs. Hobson, Love, and 

 Sir J. Larmor were of opinion that to limit the 

 mathematics of science students to those portions 

 which might be considered of direct utility would 

 destroy that logical unity which is the essential 

 feature of the subject, and relegate it to a sub- 

 servient position little in keeping with its import- 

 ance. Sir A. G. Greenhill uttered a warning 

 against the excessive attention engineering pupils 

 are apt to give to descriptive geometry, to the 

 detriment of their studies in the calculus. Sir 

 J. J. Thomson was in favour of physicists learning 

 mathematics from pure mathematicians, if the 

 latter would reserve some of their latest refine- 

 ments for special lectures. 



Prof. D. E. Smith (New York) presented a 

 report on intuition and experiment in mathe- 

 matical teaching in secondary schools. The 

 object of the inquiry was to ascertain to what 

 extent intuitional methods are at present employed. 

 A general spirit of unrest is apparent. In geo- 

 metry it may be said that it is the plan of the 

 Teutonic countries to mix the intuitional and 

 deductive work from the outset, while in France, 

 and now in England, the plan is to let an inductive 

 cycle precede a deductive one. The United States 

 is only beginning to talk about the question, what- 

 ever tendency there is being towards the Anglo- 

 French plan. The second important movement 

 is the elaboration of the function concept ; starting 

 in France within the last twenty years, and 

 vigorously advocated in Germany within the last 

 decade, the movement is, as a whole, too recent 

 to judge of its permanence. A practical form of 

 outdoor mensuration seems to be developing, 

 especially in Austria, Germany, and Switzerland. 

 Geometric drawing and the graphic representation 

 of solids are passing from the hands of the art 

 teacher to the mathematician. Graphic methods 

 of representing functions have become universal 

 in the last generation. The contracted methods 

 of computation that were prominently advocated 

 fifty years ago do not seem to have advanced 

 materially, owing to the feeling that they are not 

 really practical; on the other hand, logarithms 

 have come into general use, and the slide rule is 

 in great favour in technical schools. In general, 

 it may be said that intuitional and experimental 

 methods have made more progress in Austria, 

 Germany, and Switzerland than in England, 

 France, and the United States. 



At the final meeting of the congress it was 

 resolved to accept the invitation to Stockholm for 

 the next meeting in igi6. Informal invitations to 

 Budapest and Athens for subsequent meetings 

 were also noted. 



THE BRiriSH ASSOCIATION AT DUNDEE. 

 TI) Y the time this issue reaches the reader the 

 -L* British Association will be in full session, 

 and meanwhile there seems to be every prospect 

 of an unusually successful meeting. Dundee is a 

 town of comparatively small population, largely 

 made up of the working classes, but the number 



NO. 2236, VOL. ^o] 



of persons resident in the town and neighbour- 

 hood who have joined the Association is remark- 

 able. The various towns in which the Associa- 

 tion meets are found to differ greatly in this 

 respect, and it occasionally happens that the 

 number of local associates is exceedingly small. 

 Since the year 1901 the Association has held its 

 annual meetings on two occasions abroad and on 

 nine occasions at places within the United King- 

 dom. The average number of tickets sold at these 

 nine centres before the opening of the reception 

 rooms is 460, and the highest number so sold at 

 any one of the nine was 643 ; but considerably 

 more than iioo tickets had already been sold in 

 Dundee by the local committee before the opening 

 of the reception rooms, and by Tuesday evening 

 some 2000 tickets were issued. 



This large local addition to the ordinary mem- 

 bership of the Association, together uath the 

 unusually large attendance of foreign, American, 

 and Colonial guests, however gratifying it may 

 be to the officers of the Association, renders the 

 task of the local committee a difficult and anxious 

 one. The various halls and Section rooms will be 

 taxed to the utmost, and the various excursions and 

 entertainments will scarcely be sufficient for an at- 

 tendance so greatly in excess of the estimates that 

 were based on the statistics of recent meetings. 



As has already been stated in these columns, 

 the attendance of scientific men from abroad is 

 unusually great, beyond anything indeed that has 

 been seen since the great meeting at Manchester ; 

 and this large gathering of foreigners has had its 

 effect in helping to attract the scientific men of 

 our own country. Within the last few days a 

 number of eminent mathematicians, who have 

 attended the recent congress at Cambridge, have 

 made known their intention to be present ; geolo- 

 gists are mustering in strength from many coun- 

 tries, tempted to a large extent by the promise of 

 excursions of unusual interest, and a still larger 

 gathering of notable physiologists are coming to 

 do honour to a physiological President. 



Every nook and corner of the town is filled 

 almost to overflowing, and members who arrive 

 without having made their arrangements before- 

 hand will have little chance of finding even the 

 simplest houseroom. Private hospitality has pro- 

 vided for between 700 and 800 guests, and every 

 hotel in the town and in the near neighbourhood 

 was filled up many days ago. 



It is sometimes said that the British Associa- 

 tion is losing ground, but the experience of this 

 meeting shows that the belief is without founda- 

 tion ; not only is the attendance this year fully 

 comparable to the average attendance in the best 

 days of the Association, but there is every prospect 

 also of animated discussion and abundant scien- 

 tific work. We print this week the inaugural 

 address 'delivered last night by the president. Prof. 

 E. A. Schafer, F.R.S., and also the address to be 

 delivered by Prof. H. L. Callendar, F.R.S., 

 before Section A this morning. Other addresses, 

 and reports of the proceedings of the various 

 Sections, will appear in later issues. 



