io6 



NATURE 



[November 29, 1894 



either he mast accept the complete idea of the relativity of all 

 molioD, of rotation as well as of translation, as professed by 

 Milton, Mach, and Mr. I.ove ; or else he must follow N'ewton, 

 Maxwell, and the German writers Streintz and Lange (attacked 

 by Mach in Appendix iv. ), and distinguish between the relativity 

 of the motion of translation and the absoluteness of rotation. 

 Euler, it appears, was a waverer, and according to Lange never 

 arrived at any settled and intelligible opinion upon the subject. 

 The first theory appears more analogically complete, but in- 

 troduces unnecessary complication at an early stage ; and 

 stronger arguments than those of Mach, and others that I have 

 yet met with, will be required to convert me to their side of the 



question. 



November 26. 



A. G. Greenhii.l. 



Science Teaching in Schools. 



In the discussion on the teaching of science, and in the 

 schemes put forward for reorganising this teaching, mathematics 

 has so far been Itft out of consideration. 



At present mathematics is taught for itsowneducalional value, 

 which has been traditional since the time of Plato ; only in 

 modern times has its great practical value been recognised. 

 The teaching in schools takes little account, however, of 

 the applications of mathematics, and whatever Prof. Green- 

 hill may say (in his review of Prof. Mach 's excellent book), there 

 is still wanting complete harmony between those two points of 

 view ; not perhaps in the higher branches of the subject and its 

 applications, but certainly in school teaching. 



Boys, and girls too, in public schools are taught the elemenis 

 of mathematics as if all were expected to become mathema- 

 ticians, and the practical side is kept out of view. In the 

 modern, or science side, which has been introduced at many 

 schools, one finds too often chiefly those boys who show no 

 talent either for classics or mathematics. Many of these have 

 made little or no progress in Euclid ; they cannot grasp the 

 altogether abstract notions and symbols of algebra, and they 

 therefore never come near trigonometry. But they are expected 

 to understand the elements of chemistry, mechanics and 

 physics ; and it is instructive to find that they very often do 

 understand a good deal of what is taught under these heading-:. 

 Now none of these subjects can be accurately taught — and 

 Inaccurate leaching is worse than waste of time— without 

 the introduction of mathematical reasoning. Here we are 

 in a vicious circle : the boys are considered incapable of learn- 

 ing mathematics, and therefore mechanics and physics have to 

 be taught without any more than the most elementary notions 

 of geometry and algebra ; hence not much progress can be 

 made. 



In my opinion the order of procedure might be reversed 

 Mathematics might be taught through experimental science. If 

 the boys themselves make, as they should do, experiments 

 where they perform actual measurements, they will learn there 

 are certain laws connecting various quantities ; they will see 

 that such laws can be exprosed in simple symbols, and they 

 will thus grasp in the concrete form the meaning of a formula 

 or an equation which in the abstract form of pure mathematics 

 remained a mystery to them. 



Mathematics could in this manner be made very much easier 

 and more interesting to the majority of boys. Geometry can be 

 treated to a very great extent experimentally by aid of geo- 

 metrical drawing and a development of the Kindergarten 

 methods ; the abstract logic of Euclid can then follow, or it 

 can be treated at the same time. 



Trigonometry need not be at once as fully gone into as is 

 generally done, but the definitions of sine, cosine, &c. , as 

 Dames for certain ratios, can be easily and early introduced and 

 made use of at or.ce in mechanics or physics. Here also special 

 experiments may easily be devised where measurements of 

 angles or lines are made, and lines and angles calculated. 



To explain fully what I mean I should reiiuire a great deal 

 of space ; in (act it would be almost necessary to draw up a 

 distinct syllabuj for a course on the above lines, or to give at 

 least a great number of examples. 



At prcient I wish only to urge that, while many attempts are 



being made to improve science teaching, and with it technical 



education, mathematics should be included, and to express my 



opinion that this science also allows of experimental treatment. 



November 19. O. IIENRICI. 



NO. 1309. VOL. 51] 



Mr. Crump i^:ide p. 56) though adopting a critical form and 

 tone, really endorses the grounds of my suggestion that the Science 

 and Art Department should dissever itself by an age limit from 

 school science. He is inclined to be especially severe upon the de- 

 fects of the Government examinations because they are controlled 

 by scientific men, and to excuse the proper school examining 

 boards because they have — according to Mr. Crump^attempted 

 to examine in science without any qualification to do so. Hut I 

 fail to see why eminent scientific men should be expected to be 

 experts in elementary science teaching, any more than distin- 

 guished litterateur.', in the art of teaching to read, and it seems 

 to me — in spite of Mr. Crump's "absolute" denial — that 

 examining boards, neither professedly literary nor scientific but 

 professedly educational, are more to blame in following and 

 abetting the Department's premium upon text-book cramming. 

 The fact remains that the London Matriculate ignores practical 

 teaching of any kind, and that the "practical chemistry" of 

 the Locals and College of Preceptors is essentially the same test- 

 tube analysis as the South Kensington examination. .-Vnyone 

 who knows the London Matriculation examination — witness 

 Miss Heath's concluding remark — will appreciate the quiet 

 humour of Mr. Crump's allusion to it as "awakening and de- 

 veloping the powers of observation and reasoning." 



II." G. Wells. 



The Explosion of a Mixture of Acetylene and Oxygen. 



With reference to your note in last week's Nature, I may 

 say that, whilst the thanks of chemists, and particularly of those 

 whose duty it is to perform lecture-experiments, are due to 

 Prof. Lothar Meyer for once more drawing attention to the 

 dangerously explosive nature of mixtures of acetylene and 

 oxygen, it may be assumed that the facts already known con- 

 cerning acetjlene account sufficiently well for the great violence 

 of the explosion, and hence for the circumstance that the 

 mixture will shatter even the open cylinder in which it is 

 detonated. What .M. Berthelot terms the molecular rapidity 

 of the reaction, as distinguished from the rapidity of propaga- 

 tion, in the case of mixtures of acetylene and oxygen is very 

 high. The heat of the reaction, too, is nearly five times 

 as much as in the cases of electrolytic gas and of carbonic oxide, 

 and more than twice as much as that of methane. It is slightly 

 exceeded by that of ethylene, but, on the other hand, the 

 theoretical temperature of ihe change with acetylene is 

 enormously greater than in the case of any other explosive 

 mixture of gases. The temperature, too, required to initiate 

 the change is, as Prof. Lothar Meyer showed indirectly some 

 ten years ago, much lower in the case of acetylene than in that 

 ol the other gaseous mixtures of which he speaks. All the 

 conditions tend to make the duration of the reaction so nearly 

 instantaneous that the initial pressure cannot be far removed 

 from the theoretical pressure, and this is sufficient to smash a 

 much stronger envelope than a glass cylinder, even if the 

 " tamping " be nothing more ihan the air. Everything we 

 know about acetylene combines to show that it is extremely 

 "sensitive" as an explosive, and th.at in this respect, as in its- 

 destructive action, it resembles mercuric fulminate. 



T. E. Thorpe. 



"Newth's Inorganic Chemistry." 



Thf.RE are one or two points in Mr. Pattison Muir's review, 

 upon which I should like to be allowed to say a few words. 

 Criticising the general plan of the book he says : 

 " It seems to me that the method of the author is radically 

 wrong. Descriptive statements of facts ought surely, neither to 

 precede, nor to follow, but to accompany the reasoning oi» 

 these facts whereby general principles are gained." 



It is not easy to see how the Jescriptivt slalevinits of/acts, ana 

 \^e reasoning on these fa,:ts a.ra\.o hi: printed in a book at all, 

 unless one either precedes or follows the other. I can only 

 suppose that my reviewer means, that such theoretical and 

 other considerations as I have included in part i., and have 

 ' called "introductory outlines," should in his opinion not be 

 I collected together cither at Ihe beginning or at the end of the 

 book, but should be sprinkled among the descrip'ive chapters. 

 It seems to me that the plan I have .i.lopied, beMdcs being a 



