S2 



NA TURE 



[November 27, 1902 



at last quite suddenly, and as if miraculously, like the 

 fall of the walls of Jericho. 



In criticism of the schedules, we may perhaps be allowed 

 to say that personally we wish the syndicate had not 

 followed Euclid so closely. All the practical geometry 

 of the syllabus is meie illustration of Euclid. There are, 

 for example, other angles than 90 easily to be drawn ; 

 arithmetical computation and experimental mensuration 

 give new avenues to geometrical ideas, and the more 

 avenues we can offer to pupils the better. Where the 

 syllabus says ''division of straight lines into a given 

 number of equal parts," there appears to us too much 

 restraint. There is no reason why a line should not be 

 divided into many parts in any proportions, and a most 

 educational exercise it would be. And what is the use 

 of hiding the fact that a " preliminary " candidate cannot 

 be prevented from having a good working knowledge of 

 Book vi., although it is wise enough to keep the demon- 

 strations to a later stage? Any boy understands that 

 maps may be drawn to different scales, and this is almost 

 the whole of the sixth book of Euclid. As for construc- 

 tion of tangents to a circle and " construction of common 

 tangents to two circles," we would let a student draw 

 these without introducing any idea of difficulty and we 

 would ask him, by dropping perpendiculars on tangents 

 from centres, to find the real points of contact. As soon 

 as a boy can draw a right-angled triangle, measuring the 

 sides and using arithmetic to find sines, cosines and 

 tangents, he ought to begin trigonometry. If he knows 

 the mere definition of tan A, he ought at once, by merely 

 exercising his common sense, to be able to draw the angle 

 the tangent of which is given. A common-sense know- 

 ledge of right-angled triangles is really a knowledge of 

 solution of triangles in general. But until the artificial 

 bulkheads between the various water-tight compartments 

 of mathematics are swept away, we suppose that it will 

 not be possible to give to very young schoolboys the 

 power to solve trigonometrical problems. If the syndicate 

 would condescend to study the elementary syllabuses of 

 Science Subjects I. and V,, of the Education Department, 

 we think these courses of studies might become much 

 easier and much more valuable. 



But is not ingratitude the meanest of sins? And may 

 it not show wisdom in the syndicate that it avoids 

 changes which may seem to be loo sudden and too great ? 

 Besides, it is to be recollected that almost every candidate 

 who has followed this course has also taken a course in 

 experimental science, into which weighing and measuring, 

 the uses of squared paper and logarithms, and the ideas 

 of the calculus have entered in all sorts of common- 

 sense ways. Even taken by themselves, the schedules 

 mark a great step in our experiment of finding a method 

 ot teaching mathematics suitable for boys of the Anglo- 

 Saxon race. A beginning has been made in disenchant- 

 ing the English school system of those pedagogic dogmas 

 which have tied teachers and pupils hand and foot. 

 Teachers and examiners will ask for more and more 

 freedom as they find that it is altogether good. Hitherto, 

 the average English boy has believed himself to be 

 stupid because he was unable to reason about things un- 

 known to him ; hitherto, the average English teacher of 

 mathematics has thought of himself as a dull, tired 

 usher because he has had no interest in teaching ; in 

 future, pupils and teachers will feel with complacent 

 pride that they have come to their inheritance as 

 thinking, useful human beings. We look forward to 

 very great results, and we are not going to give credit 

 in particular to any one of the ten or twenty names that 

 rise before us of the men who have helped to make this 

 reform. Those who are dead had their reward in 

 knowing that they helped towards a reform that was 

 certain to come ; those who are alive have the reward of 

 knowing that they were commissioned to keep alight the 

 torches lit by their much-loved predecessors. 



NO. 1/26, VOL. 67] 



With the exception of the Society of Arts, no institution 

 of the country has been so successful in initiating 

 scientific reform as the British Association. A Com- 

 mittee was appointed in 1874 (the present writer is proud 

 to think he was a member of it) for improving science 

 teaching in schools, and another for improving mathe- 

 matical teaching, and although the members of these 

 Committees were mostly men of influence, their efforts- 

 led to no important results for many years. But ten 

 years afterwards, the report of a British Association 

 Committee on the teaching of science acted on the 

 scholastic world like the prince's kiss in the story of the 

 Sleeping Beauty, and in 1901 the British Association 

 proceedings in the new Education Section acted in much 

 the same magical way in relation to the teaching of 

 mathematics. Many mathematical masters were feeling 

 hopeless about reform, but without jealousy, with great 

 enthusiasm, with the most wonderful forgetfulness of 

 differences in small matters, they joined together to 

 assist the British Association Committee of Mathe- 

 maticians. There can be no doubt that this evidence 

 of a desire for reform among the schoolmasters had 

 a great effect upon the members of the Committee 

 who were not in immediate touch with the schools. All 

 the tact, patience and resourcefulness of a chairman 

 eminent for these qualities might have been unavailing 

 in dealing with a Committee the members of which were 

 all men of great individuality had it not been for the 

 schoolmasters' memorial. Anyone who knows the history 

 of this reform must recognise its peculiarly English cha- 

 racteristics — the conservative clinging to past methods 

 because of the recognisable good in them, even among 

 the most radical reformers ; the efforts of individuals in 

 low and high positions gradually making converts in 

 spite of the seeming hopelessness of reform ; the un- 

 willingness of men in high positions to lend their names 

 to the movement, the virtue of which they were aware of, 

 so long as they thought that only unrest and disturbance 

 could accompany it ; and their concerted action as soon 

 as it was evident that a great reform was possible. And 

 now, because it has occurred in the English way. we 

 know that the reform is real, that it will have a fair 

 chance, that it will go on year after year for many a year 

 to come. This is no case of a thin end of a wedge, for 

 no force is really required. It would be bad policy to 

 make too great a change at once. Freedom has been 

 given to teachers, a freedom much sighed for, a freedom 

 which will create enthusiasm. Those who are most 

 determined to make the reform complete are most 

 anxious to proceed cautiously and to smother in- 

 temperate zeal. John Perry. 



THE THEORY OF THE GAS MANTLE. 



\ NUMBER of papers have been recently published 

 ■*■»■ which deal, either directly or indirectly, with the cause 

 of the high efficiency of the' incandescent gas mantle.' 

 Space does not permit us to enter at all fully into the 

 details of these papers, but it is of interest to consider 

 some of the questions which they raise. 



The high luminosity of the mantle and its still more 

 remarkable dependence on a particular composition have 

 long been recognised as facts calling for some special 

 explanation, and many have been the hypotheses advanced 

 to account for them. The simplest of these is that which 



1 " Zur Theorie des Auerlichtes." by \V. Nernst and E. Bosc {PkysikcU- 

 ische Zeitschrift, 1900, i. 289). 



"Theory of the [ncandescent Mantle," by A. H. White, H. Russell 

 and A. F. Tt.tvcr [Journal G is L ig -..<■). Ixxvii. p. S70, and Ixxix. p. 892). 



"Theory of the Incandescent Mantle," by A. H. White and A. 1. 

 Traver {Journ. Soc. Chem. Industry^ 1002, xxi. p. 1012). 



" The Conditions Determinative of Chemical Change and of Electrical 

 Conduction in Gases and on the Phenomena of Luminosity," by Prof. 

 H. E. Armstrong, F.R.S. (Tht Chemical AYrcs, May 23 and 30, 1902). 



" The History of the Invention of Incandescent Gas Lighting," by Auet 

 von Welsbach (TAe Chemical .\\:rs, May ;o, 1902. p O. 



