June 25, 1903] 



NATURE 



179 



examinations is a necessary preliminary to any sub- 

 stantial improvement in teaching." 



The syndicate has, therefore, made recommend- 

 ations affecting the subject-matter of the Previous Ex- 

 amination. The alterations will begin to operate in 

 the Lent term of 1904, and will finally supersede the 

 present regulations after October, 1905. The principal 

 changes may be summarised as follows : — 



(i) In demonstrative geometry, Euclid's Elements 

 shall be optional as a text-book, and the sequence of 

 Euclid shall not be enforced. The examiners will 

 accept any proof of a proposition which they are satis- 

 fied forms part of a systematic treatment of the subject. 



(2) Practical geometry is to be introduced, along with 

 deductive geometry, and questions will be set re- 

 quiring careful draughtsmanship and the use of 

 efficient drawing instruments. 



(3) In arithmetic, the use of algebraical symbols and 

 processes will be permitted. 



(4) In algebra, graphs and squared paper work will 

 be introduced ; and a knowledge will be required of 

 fractional indices and the use of four figure tables of 

 logarithms. 



The scopetbf the subject-matter in geometry is set 

 out in tww ^dhedules. The first gives a list of con- 

 structions in practical geometry. We venture to take 

 exception to one detail in this list, that of requiring a 

 construction for drawing a common tangent to two 

 circles. Why insist on first finding the points of con- 

 tact? This may have been necessary under Euclid's 

 postulates, but it should now be discarded; it is not 

 practical geometry. 



The second schedule indicates the amount of book 

 work necessary in preparing for the Previous Examin- 

 ation. The propositions enumerated are nearly all 

 contained in the Elements, but a judicious amount of 

 pruning has been effected in the latter. Hypothetical 

 constructions are permitted. The theory of incom- 

 mensurables is not required. 



The increase of freedom now being given to teachers 

 should lead to further developments in the reform as 

 experience is gained. It will be one great advantage 

 to have the several branches of the subject brought into 

 closer association and reacting on one another. 



Geometry will be made generally interesting and 

 will at last have a chance of being taught in a manner 

 suited to boys. In looking out for suitable numerical 

 examples in geometry, we predict that a good teacher 

 will not fail to make use of functions of angles. Pro- 

 bably three figure tables of chords, sines, cosines and 

 tangents will be sufficient, reading to tenths of a 

 degree, and occupying a very modest space. A boy's 

 interest will be stimulated when he discovers the latent 

 power residing in these innocent looking tables. And 

 in checking his graphical results, he may be led on 

 to the numerical solution of right-angled triangles 

 before he has heard of trigonometry, and will never 

 ■ afterwards be repelled by the symbols sin,, cos., tan. 



The employment of logarithms is most important. 

 Their use illustrates the significance of fractional 

 indices. And here again the interest of a boy must 



r surely be aroused when he finds himself in possession 



of a new, unforeseen, and most valuable means of 

 calculation. 



The introduction of graphs is of great value. The 

 fundamentar idea of the representation of position and 

 change of position by means of rectangular coordinates 

 is thus acquired early and in an agreeable manner. 

 Some teachers find that it is quite possible to go on 

 without much delay to easy illustrations of the cal- 



I cuius. 



I ^ Looking ahead to possible developments, the graph- 



' ical use of polar coordinates to mark position and 



change of position, by the plotting of lengths and 



NO. 1756, VOL. 68] 



angles, might serve as an introduction to the study of 

 vectors, a subject of first importance, and at present 

 so woefuUv neglected. 



We regaVd this reform at Cambridge as an important 

 step in the movement now in progress throughout the 

 country, and we hope to see it carried much farther 

 before crystallisation takes place. 



THE UNIVERSITY OF LONDON. 



THE presentation for degrees of the University of 

 London, which is to take place in the Albert Hall 

 as we go to press, under the presidency of the Chan- 

 cellor, Lord Rosebery, is noteworthy in several respects. 

 For the first time in the history of the university, 

 honorary degrees are to be conferred, the recipients 

 being their Royal Highnesses the Prince and Princess 

 of Wales, Lord Kelvin, and Lord Lister. The Prince 

 is to receive the honorary degree of Doctor of Laws, 

 the Princess that of Doctor of Music, and Lord Kelvin 

 and Lord Lister that of Doctor of Science. Ordinary 

 degrees are also to be conferred on 414 persons who 

 have obtained them during the past year. Moreover, 

 the occasion is remarkable as being the first gathering 

 of representatives of all the different institutions and 

 groups of persons connected with the university. 



The reconstituted university has opened up new 

 avenues of work in connection with schools, with uni- 

 versity extension, with the colleges, medical schools, 

 and polytechnics; students are entering both for the 

 ordinary matriculation examination and for post- 

 graduate study and research in unexpected numbers. 

 The educational forces of London have, in fact, been 

 organised by the university, and public interest is being 

 shown in the work. But, as Sir Arthur Rucker, the 

 principal, has pointed out, while there are many 

 grounds for hope, and while the university is doing its 

 best to make itself worthy of public support, it can 

 never fulfil its duties without the supply of funds from 

 public or private sources on a very large scale. We 

 trust that one result of the brilliant ceremony on Wed- 

 nesday evening will be an increase of the endowment 

 of the university sufficient to secure the full develop- 

 ment of the scheme which has already produced such 

 satisfactory results. 



NOTES. 



For the first time for about forty years the Royal Society 

 of Edinburgh, on the evening of June 6, held a conversazione. 

 Lord and Lady Kelvin and Sir William Turner received 

 the guests. There were many interesting exhibits from 

 several departments of the Universities of Edinburgh, Glas- 

 gow, and St. Andrews, from the Geological Survey of 

 Scotland,' the Scottish Antarctic Expedition, &c. Prof. 

 Mcintosh, of St. Andrews, sent over a large collection 

 of pearl shells and animals, living and dead, and great 

 interest was taken in Prof. Ewart's exhibition of hybrid 

 ponies. Some of the lantern exhibits were particularly 

 attractive, notably the projection on the screen of tanks of 

 living worms, Crustacea, &c., and a fine selection of slides 

 made from Piazzi Smyth's " cloud " negatives. Among 

 the inventions and novelties exhibited, Dr. Halm's instru- 

 ments for mechanically correcting stellar observations and 

 for solving Kepler's problem in any given case, and Dr. 

 Hugh Marshall's petrol incandescence lamp are worthy of 

 mention. 



Captain Ammundsen's Magnetic North Pole Expedition 

 left Christiania on June 16 on board the ship Gjoa. 



