Изображения страниц
PDF
EPUB

THURSDAY, SEPTEMBER 28, 1871

EXPERIMENTAL SCIENCE IN SCHOOLS

The Elements of Physical Science. By Gustavus Hinrichs,
A.M., Professor of Physical Science in the State
University of Iowa, &c. In 3 vols. Vol. 1. Physics.
(Griggs, Watson, and Day, Davenport, Iowa, U.S.)
The School Laboratory of Physical Science. Edited by
Gustavus Hinrichs. Nos. 1 and 2.

"BY

Y resolution of the Board of Regents in 1870, the Iowa State University has finally cut loose from the old college course. Only by this resolution, placing the elements of Physical Science at the very beginning of the course, can instruction in science become thorough. For the first time the students in physical

science have been offered facilities not too inferior to

those they have for ten years enjoyed in other branches of learning." And with what result? "A marvel of studious industry there" (in the laboratory). "Young men and young women, boys and girls, measuring, weighing, testing, demonstrating, and recording fact upon fact in physics, that, at least in our school days, were pored over in a maze of bewilderment, in dryest of text-books, to be bolted in sections without question." We trust that these important reforms in science teaching will prove contagious, and spread rapidly from the plateau of Iowa City to a region of even greater extent than the American continent. Let us examine how Prof. Hinrichs is doing his part to attain this desirable result.

Bearing in mind the important fact that science teaching in schools must be of a practical nature from beginning to end, the American Professor has sketched out in his "School Laboratory" a plan which in the main will recommend itself to every competent teacher both in his own country and in ours. He proposes that the course shall be divided into three parts:-Rudiments, Elements, and General Principles. The Rudiments, which ought to be studied in the first year or so of a boy's school life, embrace only prominent general facts and determinations, easily observed and measured with a sufficient (but limited) degree of accuracy; together with the collective study of these facts, so as to bring to light several of the so-called laws. The Elements comprise the same subjects, treated however, more fully, and they should be completed "in the first year of the high school course." The General Principles embrace mathematical deductions of a concise and simple nature, together with some of the most important hypotheses of Physical Science; this portion should be completed in the last year of the high school course. Prof. Hinrichs is careful to point out that technical instruction in schools will not result in the advancement of science; but that a thorough general training in the phenomena of Nature, together with that already given in languages and mathematics, will lead to hitherto unimagined progress.

Such is Prof. Hinrichs' idea of a sound scientific training, and a very admirable one it is. To carry it out we must strive after good teachers, capacious laboratories,

VOL. IV.

and trustworthy text-books. For our own part, we think that good teachers would not be found so scarce as is imagined, if there were only a genuine demand for them; from a variety of causes, however, such as parental ignorance, false economy on the part of schools, and the ridiculous demands of public examiners, science has been kept, up to the present time, at the lowest possible ebb, except in the wealthiest of our public schools. It is deplorable to think how few school laboratories there are in England which could in any way vie with that in the Iowa State University, where "more than two hundred students have experimented within six months;" and we fear that this state of things will continue for the most part unaltered until the public examiners require a practical knowledge of the sciences taught in schools.

We are perhaps as deficient in good text-books as we are in laboratories; and the reason for this is not far to

seek. If a candidate is asked to explain a phenomenon or a class of phenomena, but is never required to exhibit it to the examiner, it is natural that he should content himself with learning the explanation without performing the experiment. Hence we find that the great majority of our text books are merely explanatory, and not at all experimental; the phenomena are fully described and most ably explained, but the work which should be done in the laboratory to bring about these phenomena is forgotten by the teacher and the taught, because-it is not required at public examinations. It was therefore a bold undertaking for Prof. Hinrichs to bring out his "Elements of Physics," which is an excellent and almost unique specimen of a practical treatise; and we trust that it will meet with a reception worthy of it.

In the first volume of this work, the student is taken, in about 150 pages, through a course of simple and easy experiments relating to Magnitude, Weight, Machines, Properties of Matter, Light, Electricity, and Magnetism. Each operation is so clearly described that the book might almost be employed by a solitary student, and many of the experiments, we are convinced, not only could but ought to be performed by children at the very commencement of their school career.

There is great difference of opinion as to whether qualitative and quantitative observations of natural phenomena should be performed simultaneously or consecutively-we are disposed to hold the latter view rather tenaciously, believing that science should be one of the first subjects taught in all schools. However, no one need be dismayed by the simple measurements of length, area, weight, and so on, which form the main portion of Professor Hinrichs' first chapter. The metrical system is taught by him in the only practicable manner, by means of actual measurements performed by the pupils themselves, without any reference, beyond a passing contemptuous notice, to the English system. The student is also familiarised with various forms of surfaces and solids, learns the management and the use of very simple apparatus, such as could well be provided in any village school, constructs his own measures of weight and length, makes numerous determinations, and enters his results in a journal. The exercises in mensuration and co-ordinates are especially useful, both from a scientific and a mathematical point of view; and the Journal of Experiments-blank pages at the end of the volume to be filled up by the pupil-fs

[ocr errors]

perhaps the most suggestive portion of this original work. In short, the experimental method is adopted in every chapter; and it is thus that the inquirer after truth is taught, step by step, to appeal to the fountain source for most, if not all, information concerning "the wonder and mystery of Nature."

There is, however, a very marked disproportion in the amount of space allotted to each subject. Machines occupy only sixteen pages-probably the feeblest chapter in the book; while Crystallography extends over as many as thirteen pages. We think also that too much attention (relatively, at least) has been paid to Electricity and Magnetism. Pure and simple observation, even of natural phenomena, cannot properly be said to educate the mind, unless the reasoning faculties are called into play; and such subjects as Electricity, Botany, and Crystallography, if made an essential portion of school training, would doubtless tend to bring the whole question of science-teaching into disrepute. The only experiments that should be performed in the laboratory are such as will bring to light a scientific fact; and it should be remembered that a fact is scientific only in so far as it is interconnected with other facts. The more intimate this interconnection is, the better suited is the fact for elementary education; because it gives rise to a greater amount of rational explanation, and tends, by reaction, to imprint upon the mind knowledge already acquired. Professor Hinrichs does not appear to us to attach sufficient importance to these views; his work has therefore a disjointed aspect, and is wanting in large general ideas which should be cautiously introduced at proper intervals for the purpose of increasing the scope of the pupil's understanding. We agree with him that the quantitative study of such subjects as the Law of Gravitation should be postponed to the last year of the school course; but its qualitative study might be carried on with great advantage at a much earlier period; for previous familiarity with such theoretical views as are capable of some sort of experimental proof will make a student anxious to examine the subject quantitatively at the earliest opportunity. For these reasons we regret to find certain, points omitted in the present volume, such as the Laws of Motion, which are so admirably adapted, not only for experimental verification, but as a means of explaining the principles of scientific induction. Still, if Prof. Hinrichs has not discovered every gem, he has nevertheless succeeded in pointing out the right path of discovery, along which he has acted on the whole as a faithful and thoroughly painstaking guide.

The idea of the "School Laboratory" is also a very admirable one. It is, in fact, a monthly magazine, the aim of which is to inculcate the system of experimental work upon which Prof. Hinrichs so strongly insists; to give examples of methods and results; and to aid both teacher and pupil.

We trust that the efforts of this able reformer of scienceteaching will be amply seconded; and we believe that these Elements will be found of great service to every conscientious teacher, who will be able to glean from them many valuable suggestions both as to method and treatment; and we recommend them especially, because a widely-spread knowledge of a work of this kind will tend very much towards the introduction of experimental science into the curriculum of our schools.

OUR BOOK SHELF

Phrenology, and how to use it in Analysing Character. By Nicholas Morgan. (London: Longmans, Green, and Co. 1871.)

THE appearance of a book of this kind from time to time shows what a deep hold phrenology took upon the popular mind. Had it not been so, we should have neither writers nor readers of works upon "The Science of Phrenology," now that almost the whole foundations of the system have been shown to be either untrue or based upon misconceptions. The present work is illustrated by numerous portraits and other engravings, and several of the former are remarkably truthful representations of living or recently-living celebrities; though we doubt whether the accompanying analyses of character will prove as agreeable to the originals as they are destined to be edifying to the public.

[ocr errors]

The Dependence of Life on Decomposition. By Henry Freke, M.D., T.C.D., &c., Professor of the Practice of Physic and Lecturer on Chemical Medicine in Steven's Hospital Medical College. (London: Trübner and Co.) THIS is a pamphlet of a controversial character, which would not prove interesting to the general reader. Dr. Freke's views were originally published in 1848 in a work "On Organisation." They are peculiar in many respects, but contain the germs of some important biological truths. The following passage (p. 28) may serve as an example :— Why, with an adequate supply of food, are we not able to work our brains, muscles, &c., for an indefinite period, like a steam-engine with an adequate supply of steam? Because the tissues are disintegrated, and require nutritive repair. If the animal tissues did not undergo disintegration during the active discharge of their functions, why should not the animal, like the vegetable, continue to increase in dimensions during the entire period of its organic existence? It is because the organic tissues developed by the vegetable do not undergo disintegration when their construction has been completed, that the vegetable continues to grow and increase in dimensions animal, and that for this reason, namely, when the conduring its entire life. Such is not the case with the struction of the animal tissues, brain, muscle, &c., is completed, those tissues undergo disorganisation while discharging their functions."

The Estuary of the Forth and adjoining Districts viewed Geologically. By David Milne Home, of Wedderburn. (Edinburgh: Edmonston and Douglas.)

MR. MILNE HOME'S name has long been known in connection with Scottish geology. His memoir on the Coalfields of the Lothians was for many years the only trustthis he has from time to time communicated to various In addition to worthy geological account of those areas. scientific journals a number of papers chiefly on subjects relating to glacial geology. In this present volume he returns to these subjects, and gives us a description of the superficial formations of the basin of the feasible explanation of the somewhat intricate details he Forth, together with what he considers to be the most brings before his readers. He treats first of the form and physical features of the Estuary and the districts adjoining; secondly, of the formation or origin of the Estuary; and, thirdly, of the superficial deposits met with in the area described. He conceives that the faults which intersect the strata along both sides of the Firth, and which not only have the same general bearing as the Estuary, but are also for the most part downthrows to south, in Fifeshire, Clackmannan, &c., and, in the Lothians, downthrows to north, have formed the deep trough or valley of the having reached at least 2,000 feet. "Along the lines of Forth-the depression caused by this series of step-faults these slips great precipices, or cliffs, were formed, several hundred feet in height, which, under the action of the sea

or the atmosphere, crumbled down." The materials thus supplied went to form the superficial deposits, it being supposed that almost the whole of Scotland was under the sea at the time these changes took place. We feel sure that Mr. Milne Home will get few geologists to agree with him in these conclusions. In the first place, it may very well be doubted whether the faults which cut the strata ever actually showed at the surface in the manner supposed. It is much more probable that the dislocations took place so gradually that any inequalities arising therefrom were planed away by denudation as fast as they appeared. But even were this not the case, it is quite certain that the faults referred to by Mr. Milne Home must date back to a vastly more remote antiquity than the later Tertiary periods. The Scottish Coal-fields, indeed, would appear to be traversed by some faults which, according to the Geological Survey's map and description of the South Ayrshire Coal-fields, do not influence the overlying Permian. It is also indisputable that the igneous dykes, which Professor Geikie has shown to be of Miocene age, are all posterior in date to the faults which shift the Coalmeasures. Mr. Milne Home does not take into consideration the prodigious amount of denudation that the paleozoic strata of the valley of the Forth must have undergone in the long ages that intervened between the close of the Carboniferous period and the advent of the glacial epoch. There cannot be any reasonable doubt that the valley of the Estuary of the Forth existed as a valley long before the dawn of the age of ice. But Mr. Milne Home's memoir is taken up chiefly with the history of the drift deposits, which he describes in considerable detail. Especially valuable are the numerous sections given, and the long lists of localities where glacial-striæ, erratic blocks, kaims, and the other phenomena of the drift, may be studied. The author inclines to the iceberg theory of the formation of the boulder-clay, and thinks it may have originated at a time when "the ocean over and around Scotland was full of icebergs and shore-ice, which spread fragments of rocks over the sea-bottom, and often stranded on the sea-bottom, ploughing through beds of mud, sand, and gravel, and blocks of stone, and mixing them together in such a way as to form the boulder-clay." Mr. Milne Home points to the presence of beds of sand included in the boulder-clay as one of several objections to the landice origin of that peculiar deposit. He thinks that if the iceberg theory be adopted, the explanation would be simply this, "that icebergs came at different periods, new sea-bottoms being formed in the intervals." But, on the other hand, if the glacier theory be accepted, then it would have to be admitted that the land must have sunk under the sea for every bed of sand we find in the boulder-clay. The author, however, does not seem to be aware that fresh-water beds are found interstratified with the boulder

clay, so that the difficulty in either case is equal. We have not space to notice several other interesting points treated of in this memoir, which contains so many important data, that we can recommend it confidently to our geological readers. We may dispute some of the author's conclusions, but it matters not what interpretation may eventually be put upon the facts, many of the facts are here, and Mr. Milne Home has done good service in bringing them together. J. G.

LETTERS TO THE EDITOR

[The Editor does not hold himself responsible for opinions expressed by his Correspondents. No notice is taken of anonymous communications.]

Phenomena of Contact

IN NATURE for August 24, Mr. Stone controverts two pro positions incidentally put forward in a review of Mr. Proctor's book, "The Sun." They are:

[merged small][ocr errors][merged small]

"2. That when seen they are due to insufficient optical power or bad definition."

proposition I could not fully sustain, and therefore very willingly In writing that review, I tried to avoid the assertion of any give the evidence on which these propositions rest. At the outset, however, I beg leave to call especial attention to the fact that I did not assert the second in an absolute manner, but only said that it was "indicated" by observations and experiments. The first proposition is sustained by the fact that at the last transit of Mercury, the majority of those observers who have described the phenomena saw neither ligament nor distortion, but only the geometrical phenomena of contact, the planet preserving its rotundity to the last.

The following is a statistical summary of the evidence on both the monthly notices, fourteen describe the phenomena. Of these sides :-Among the numerous English observations published in three saw the phenomena go on regularly, while eleven saw ligament, black drop, or distortion either before or after the contact. Among these eleven there is little agreement as to the exact nature of the distortion. Owing to the low altitude of the sun in England, I take it that the atmosphere was much less favourable than on the Continent.

At Marseilles Le Verrier saw the black drop. He used a seven-inch glass, of which both the centre and circumference were covered by a screen, which is sufficient to account for the phenomenon by the diffraction thus produced. Mr. Stephen, who observed at the same place with a very large reflector, "déclare n'avoir rien vu de pareil." *

Of the five observers at the Paris Observatory, Le Verrier sayst:-"Les observateurs ont remarqué qu'il ne s'est rien présenté de particulier, ni au moment du contact intérieur, ni après ce contact. Mercure a touché le bord du Soleil en amincessant progressivement le filet de lumière, mais sans produire le phénomène de la goutte." Le Verrier was, therefore, so far as we know, the only observer in France who saw the black drop. At Madrid Ventosa may have seen several black drops "toutà-coup." His description, however, is rather obscure. + At Lund the egress was observed by Duner under very favourHe says §:"Die able circumstances with a nine-inch glass. Weise, dass der Lichtfaden Zwischen den Rändern des Mercurs Bilder waren sehr ruhig, und die innere Berührung geschah in der

und der Sonne erst dann brach als seine Breite verschwindend klein geworden war. Es zeigte keine Spur einer Verdrehung der Bilder oder des von anderen Beobachtern erwähnten schwarzen Tropfens."

At Pulkowa fourteen observers observed the egress. I learn that not one saw anything but the geometrical phenomena of

contact.

To avoid a tedious collation of accounts which nearly all say the same thing, I remark that only two observers on the Continent saw any abnormal phenomena, namely, Kaiser at Leiden, and Oppolzer at Vienna. The first saw an elongation of the planet, which he thought might be due to maladjustment of his instrument. The second saw the sun's limb pushed out by that of of the thread of light." Mercury, so that apparent contact took place before the breaking

**

39

Summing up all the accounts, I find the result to be:Total number of observers who describe phenomena Number who saw the planet remain perfectly round, and the phenomena of contact occur with entire regularity, and without distortion, ligament, or drop 24 Number who saw ligament, distortion, one or more drops, or other abnormal phenomena .. 15 The twenty or thirty observers who do not describe the phenomena probably saw nothing abnormal, but they are not counted in the above list.

The first proposition is, I conceive, fully established by the statistical facts cited.

Passing now to the second, it may be remarked that when different observers give different descriptions of the same

[blocks in formation]

phenomena, there must be some corresponding difference in the circumstances of observation, and that when among five observers three see the phenomena exactly as we know they are, while two see them as we know they are not, and even then do not agree between themselves, there is a strong presumption that the latter do not see them rightly. I am aware of but a single attempt to determine experimentally the causes why one-third of the observers of the late transit, and many observers of former transits, saw the planet distorted, namely, that of Wolf and André, to which Mr. Stone alludes. They found, in observations of artificial transits under various circumstances, that when they used a telescope of at least twenty centimetres aperture, with a good object glass, well adjusted to focus, they saw only the geometrical phenomena of contact, while, if the object glass was small, or not well corrected for aberration, or not well adjusted to focus, they saw the phenomena of distortion.*

In the absence of farther investigation, which is much to be desired, these results seem to me, at least, to "indicate" that the phenomena in question are due to insufficient optical power, or bad definition either in the object glass or the atmosphere. At the same time I by no means insist on this proposition as established, and it is a great defect in the experiments in ques tion that they do not extend to the effects of using shades of different degrees of darkness in observing the sun; but of this anon.

In his letter Mr. Stone quotes the observations of Chappe, Wales, Dymond, &c., in 1769; but I cannot admit that they bear strongly on either of the points in question, till we have some better evidence than now exists that their object glasses were such as Clarke or Foucault would call good.

Again, the argument from irradiation, if it proves anything, proves too much. I do not see why, upon the theory of Mr. Stone, the distortion should not always be seen. To be satisfactory, any theory of the matter must explain why it is that A, B, C, &c., see the phenomena, while X, Y, Z, &c., do not, and that of Wolf and André is the only one which does this.

Mr. Stone objects to the experiments of the Paris astronomers, that their disc was not sufficiently illuminated to exhibit any optical enlargement.

Solar Parallax

I HAVE waited somewhat anxiously for Prof. Newcomb's statement of the errors in a chapter on the Sun's distance ("The Sun," Chapter 1.). His review was certainly so worded as to imply very gross inaccuracy, and his explanatory letter, in which he remarked that more than a column of NATURE would be needed for the mere record of my errors, did not improve matters. This morning I have received his notes. The errors enumerated amount but to seven in all; I will leave your readers to judge of their importance.

1. At p. 50, I assign to Hansen's letter of 1854 the announcement of the value 8" 9159 for the solar parallax; whereas this value was not announced by Hansen until 1863. Tanquam referat. Hansen's priority remains unaffected by the change.

2. At p. 53, I mention that Prof. Newcomb deduced a value of 8" 84 (probably a misprint for 8" 81) for the solar parallax by a certain method. His real result was 8" 809. Again my comment is tanquam referat.

3. At p. 53, Foucault's "parallax is given as 8"'942, whereas the result actually deduced was 8" 86." The matter again is utterly insignificant; but it chances that I have not given Foucault's estimate of the parallax as 8"942. I remark only that if Foucault's estimate of the velocity of light is correct, the parallax would be 8" 942. I deduced this result by a calculation made on my thumb-nail as I wrote. It is correct, however, and Foucault's was not.

4. At p. 59, I say that Mr. Stone deduced the solar parallax from observations of Mars made at Greenwich alone, and then by combining these observations with others deduced the solar parallax at 8"'943. Now, Prof. Newcomb says that he "finds no discussion of the observations at Greenwich alone, in the paper here referred to." But I refer to no paper whatever. A rough calculation of the parallax was certainly made from the Greenwich observations alone, though, as Mr. Dunkin remarks at p. 507 of his edition of "Lardner's Astronomy," ""the observations by this method (single-station observations) were comparatively owing to unfavourable weather at Greenwich." Apart from the facts, which fully justify my statementwhat could the correction be worth in any case? Only the final result was insisted upon.

unsuccessful," I do not know his authority for this

assumption, but, whether well founded or not, it seems to me that if the sun were viewed through a dark glass, it would present the same optical phenomena of irradiation with a disc so illumi nated as to appear of the same brilliancy with the darkened sun. Thus, in the absence of evidence to the contrary, the Paris experiments may be taken as showing how the phenomena would present themselves in the case of the sun viewed through a shade of a certain (unknown) degree of darkness.

I

Before we can make any application of the theory of irradiation to the phenomena of contact, we require to know whether the irradiation of an extremely minute thread of light, darkened so as to be barely visible, is the same with that of a large disc. am decidedly of opinion that it is not, and, if not, the fact that the sun's disc is optically enlarged by the telescope or the eye of the observer, cannot be directly applied to the phenomena of a transit.

To sum up my views ;-neither Mr. Stowe nor any one else will claim that the ligament he saw before the time of internal contact was a celestial reality-he considers it a result of irradiation, but whether of telescopic or purely ocular irradiation I do not understand. If the former, this is simply a species of bad definition, and there is little difference between us. I also admit, on my part, that if the telescope and the eye are such that from any cause whatever an exceedingly thin thread of light presents itself to the sense as a band several times thicker than it really is, then, as the real thread becomes invisible, the seeming band will appear to be broken through by what some may consider a ligament and others a black drop, and the really sharp cusps will seem to be rounded off at their points. If I rightly understand Mr. Stone, he holds that these results of the thickening of the thread of light by what he considers irradiation are unavoidable. But this view is conclusively negatived by the fact that they actually were avoided by a large majority of the observers of the late transit. Admitting, then, that these spurious phenomena are not unavoid. able, it matters little whether we call their cause irradiation or bad definition, though it is important that we should know its exact nature. The only attempt I know of to determine this is that of Wolf and André, and their results seem to me so nearly in accordance with what we should expect, as to be quite worthy of acceptance, at least in the total absence of rebutting evidence. SIMON NEWCOMB

* Comptes Rendus, 1868, i. p. 921.

66

In a note on this matter, Prof. Newcomb makes "in passing" the really important observation that the method of determining the sun's distance by observations on Mars from a single station was applied by the Bonds as far back as 1849. Mr. Carrington had already told me that he believed the Bonds had anticipated the Astronomer Royal. I wrote to Prof. Young asking for further information, and was waiting for his reply, I am obliged to Prof. Newcomb for aiding me in this matter. The priority of the Bonds in this matter should certainly be more widely known than it is.

5. At p. 61. This is a very curious correction. I speak of Prof. Newcomb as having successfully treated the problem which was afterwards discussed by Mr. Stone; and he remarks that he knows nothing of the matter, and has read my statement with great bewilderment. I am not responsible for it. There is a letter in the Astronomical Register for December 1868, signed only "P. S.," but with unmistakable internal evidence of coming from the Astronomer Royal for Scotland, in which the following passage occurs :-"I must not say word about the pyramid sun-distance here, or my letter will never be allowed to see the light; something, however, on the score of modern justice to our contemporaries I must beg leave to put in. Admirable is the praise given to Mr. Stone, and worthy, in so far, the credit abundantly bestowed on him at every step of the undertaking; but why is there not one word about Prof. Simon Newcomb, of America, having already gone over that same problem similarly, and published the results a year sooner?" Of course, as Prof. Newcomb now writes that "he has no recollection of ever having made any independent investigation of the observations of the transit of Venus," Prof. Piazzi Smyth was mistaken, and "the abundant discussions of Prof. Newcomb's paper in various northern scientific societies last winter" (so speaks Smyth) were founded on some misconception of its purport. But Prof. Smyth's statements were permitted to remain uncorrected ;-hinc illa lacrymæ.

6. At pp. 61, 62. "The distortion of Venus at the time of internal contact is described as an ever-present phenomenon, and the apparent formation of the ligament as contemporaneous with true internal contact.' If what I say in pp. 61, 62 admits of being so misinterpreted (which I question), the same cannot be said of

[ocr errors]

my remarks in p. 63. My belief is now, as it has been for years (long before Mr. Stone's paper was published), that under favourable conditions an exceedingly fine ligament must be visible at the moment of real internal contact, the planet's ontline being otherwise undistorted. But in most instances a coarser ligament is formed not contemporaneously with the moment of real con. tact. I have shown that the true moment of contact can be inferred from the formation of a coarser ligament as exactly as when a fine ligament is observed. This I still maintain, and I further believe that Mr. Stone's opinion as to the cause of the phenomenon, an opinion independently enunciated by myself in November 1868 (see Scientific Opinion) is correct, and that the experimen al tests which have been supposed to disprove it, have in reality no sufficient bearing on the question at issue.

7. At p. 63. It is unfortunate if my account of Stone's proceed. ings suggests that I maintain he was the first to consider whether real or apparent contacts had been observed; for I have but lately been maintaining the contrary view in a correspondence with an ex-president of the Royal Astronomical Society. I have invariably opposed the opinion here ascribed to me. Mr. Stone himself has never claimed what I am said to have claimed for him, He has made a definite claim, and that claim I have repeated and still hold to be just.

Prof. Newcomb concludes with some general statements. He considers I am mistaken in supposing that astronomers generally regard observations on Venus in transit as the most trustworthy method of obtaining the solar parallax ; mistaken again in supposing that Mr. Stone has removed any "difficulties that had

Until

perplexed astronomers; " and so on. Such statements are so vague that I shall scarcely be expected to discuss them. proof, or at least some evidence to the contrary, is supplied, I can only say that now, as when I wrote "The Sun," my opinions on these points seem to me to be just. I am certainly not alone in holding them. RICHARD A. PROCTOR

Brighton, September 23

Elementary Geometry

THE question raised on this subject naturally consists of two parts. The first relates to the unsuitableness of Euclid as a textbook, and the need of a work which shall so commend itself to examiners and teachers, so to supplant it. The second question is -given the authoritative text-book, how is the geometry of which it treats to be taught to young students? The arguments on the first of these questions have been so ably and conclusively stated lately by several mathematicians, especially by Mr. Wilson, Dr. Joshua Jones, and Dr. Hirst, that there is no need to revive the discussion; but I entirely agree with your correspondent in his conclusion that the book which is to supplant Euclid is at present a desideratum, and that it will probably be the work of more heads than one. Several books have been written during the last four years, and have formed the basis of the discussions which have since taken place on the requirements of the new programme. By their means, the questions at issue between the opponents and supporters of Euclid have become more clearly defined, and a greater unanimity of action has resulted amongst those who are labouring to supply this desideratum of modern education. But I am sure that most of these authors will admit that the issue of works intended for permanent text-books was premature.

When the first question is settled, the second remains. Geometry is not essentially difficult, nor is it generally distasteful to young students. It becomes so, however, when they are required to commit the propositions to memory before they understand them. The educational purpose which geometry serves is not the discipline and exercise of the memory. A choice and pregnant passage from a good author may be learnt and retained in the memory without much difficulty, although its meaning may be very imperfectly understood, and it will richly repay the labour of its acquisition. It will be recalled again and again, and receive new light, and afford new pleasure with every fresh associ ation. Not so with geometry; it is useless if not understood. A child should be made to comprehend even the definitions before he commits them to memory. Let us suppose, for instance, that the definition of a circle is to be learnt, the preliminary explanation should take some such form as the following.

The teacher at the black-board, with chalk and compasses, and the pupils at their desks, with paper and compasses-the teacher draws a circle and names the figure-he tells each boy also to make a circle, and then proceeds to question. What name is

given to such a surface as that on your drawing paper? What kind of a figure shall we call one which can be drawn on a plane surface? Compare a triangle and a circle, and say how many lines form the boundary of the triangle? How many lines contain the circle? Explain exactly what you do with the points of the compasses when you use them to make a circle? Why must the joint of the compasses be tight? Fix a drawing-pin in your drawing-board, and with a piece of thread construct a circle. What purpose does the thread serve in the construction? The defining properties of a circle are, therefore, these (1) it is a plane figure; (2) it is bounded by one line, termed the circumference (3); every point of the circumference is at the same distance from a fixed point, termed the centre.

After the definition is worded in its permanent form, and repeated, and written several times on paper, it will be remembered.

Again, let us suppose the propositions on the equality of triangles to be the subject; the following introductory questions and exercises suggest themselves. Draw two straight lines, one 5 in. long, and the other 8 in.; then make with your protractor an angle of 43°. Construct a triangle having one of its angles equal to the angle drawn, and the sides of this angle equal to the given straight lines. Take the figures drawn by different boys, and compare them as regards size. Now consider the parts of each; how many sides has each? How many angles? How many sides are drawn from given dimensions? Letter them and then name them. How many angles? Name it. How many angles were not originally given? Name them. How many sides? Name it. Compare this third side, B C, in two of the figures. If the figures are all accurately drawn throughout the class, what must necessarily follow with regard to this third side BC in all the figures, &c. ?

Finally, the proposition should be enunciated, and the proof learnt in the form in which it is to be remembered.

Then the teacher may give three angles which may form the angles of a triangle, and when the cons'ructions are made compare two figures from distant parts of the class. Similarly he may treat all the allied propositions. When taught in this way, the subject becomes so easy and attractive that it may be commenced at an early age.

If, as some teachers maintain, Spartan severity be necessary to secure mental discipline, then this plan of teaching elementary geometry will not be an improvement on that of forcing into the memory Euclid, pure and simple, without note or comment; bit when the test of success is applied, I am sure the plan of making the early school work as easy and as pleasant as possible will require no other argument to support it. R. WORMELL

Deschanel's "Heat"

Ir is remarkable that Prof. Everett asserts h to represent the reduced height of the mercurial column, when the unreduced height is carefully indicated in Fig. 264 by the same symbol h. Moreover it is distinctly stated on page 362 that "the tension of the vapour is evidently equal to the external pressure minus the height of the mercury in the tube."

Prof. Everett writes, "In some instances I have endeavoured to simplify the reasonings by which propositions are established or formulæ deduced" (Preface, part 1). This would lead most people to expect simplicity, which includes accuracy; and they may well be astounded when they find not only unexplained but inaccurate formula. Prof. Everett's promises, and not his complaint, were the grounds of expectations which have not been realised. THE REVIEWER OF DESCHANEL'S "HEAT"

Sept. 22

Newspaper Science

on

MR. FORBES does not stand alone in his experience of newspaper science. The Globe, however, is not generally looked or as a scientific paper, and no one would be likely to go to it for information on matters other than political. What shall we say, however, to the following paragraph, copied verbatim et literatim from the columns of the Mark Lane Express for September 4 ?—

"CHARLOCK.—A correspondent inquires what he must do to abate the annoyance of it in his crops. We do not believe there is any mode of preventing its presence. Some seasons are distinguished by its appearance. We do not think they come from

« ПредыдущаяПродолжить »