January 24, 19 18] 



NATURE 



415 



according to the older (say Newtonian) definition. In 

 particular, the function to be integrated might have a 

 finite number of isolated discontinuities in the range of 

 integration ; isolated, that is, in the sense of being 

 separated by finite intervals. Thus a new type of in- 

 tegrals, the Riemann integrals, had come under ob- 

 servation. 



Quite recently the whole theory of integration has 

 entered upon a new phase, mainly through the develop- 

 ment of the theory of sets of points, and the enlarged 

 notion of " function " now established. To Lebesgue 

 is due a definition of a definite integral which is applic- 

 able in certain cases even when Riemann 's is not. The 

 Lebesgue integral agrees in value with the Riemann 

 integral when the latter exists; just as the Riemann 

 integral agrees in value with the ordinary integral when 

 the latter exists. The very latest contributions to the 

 theory are mainly due to Vallee Poussin and Baire, 

 and apparently a kind of finality has been reached in the 

 mathematical notion of an integral, at least in the light 

 of our present mathematical knowledge. Students will 

 find an excellent summary in Prof. G. A. Bliss's lec- 

 ture, " Integrals of Lebesgue," published in the Bulle- 

 tin of the American Mathematical Society for October, 

 T017. The reader must have a fair acquaintance with 

 the theory of sets (including the notions of measure and 

 content); otherwise the lecture is self-contained. Refer- 

 ences to recent works on the subject are also given. 



Few things are more remarkable than the mathe- 

 matical discoveries of the present generation, dis- 

 coveries which have profoundly affected the very rudi- 

 ments and foundations of logic, analysis, and geometry. 

 They cannot be ignored even by the elementary teacher, 

 and the problem of making them familjar to students is 

 one that must be resolutelv faced. G. B. M. 



METEOROLOGY IN THE ARGENTINE 

 REPUBLIC. 



A COPY has reached us of the Boletin Mensiial 

 of the Argentine Meteorological Office — a new 

 monthly weather review that has now been running 

 for more than a year. The data summarised refer to 

 the year 1916, and are given in useful form. The 

 tri-daily meteorological observations for twenty-five 

 stations are printed in extenso, and an abstract of these, 

 along with returns from other fifty-two stations, are 

 given in an expended table. The elements summarised 

 are pressure, temperature, relative and absolute 

 humidity, direction of the wind, rainfall, cloud, and 

 the number of frosts experienced. 



The stations range in latitude from 55° S. to 22° S., 

 and in height from 4 to 3447 metres, so that all 

 climates are represented. Tables of daily rainfall are 

 given for more than 1400 stations. The distribution, 

 as is to be expected in a country like Argentina, where 

 the meteorological posts are in general also railway 

 stations, is very irregular. In the province of Buenos 

 .Aires, which embraces an area equal to that of the 

 United Kingdom without Wales, there are 556 rain- 

 gauge stations, but in the equally large territory of 

 ^ inta Cruz there are only eleven stations. The results 

 le shown in six coloured maps, giving the rainfall, 

 h.^ departure of the rainfall from the average, the 

 accumulated rainfall since the beginning of the agri- 

 cultural vear, viz. July i, with departures from the 

 average, the mean temperature, pressure, and prevail- 

 ing winds, and the extremes of temperature. Detailed 

 hourly values of declination, horizontal force, and ver- 

 tical force as recorded at the Central Magnetic Ob- 

 servatory at Pilar (lat. 31° 40' S., long. 63° 53' W.) also 

 appear, along with a summary of the seismic pheno- 

 mena recordel at several points with the Milne or 

 Bosch-Omori seismographs. 



NO. 2517, VOL. 100] 



The hydrometric branch of the service gives in each 

 number of the Boletin the daily height of the principal 

 rivers and lakes of the Republic as observed at fifty- 

 eight places, with the departure from the average, also 

 a special study month by month of the conditions at an 

 individual station. So far the discussions refer to gauges 

 at various points on the River Parana, where there are 

 more than thirty years' observations available. Vari- 

 ous interesting articles by members of the staff appear 

 from time to time, and it is to be hoped that the prompt 

 issue of meteorological data initiated by Mr. Wiggin, 

 director of the Argentine service, will extend to other 

 South American weather bureaux. 



THE NEEDS OF OUR EDUCATION AT 

 THE PRESENT DAY, WITH SPECIAL 

 REFERENCE TO SCIENCE TEACHING.-^ 

 ■p.ARLY in the past year a work was published 

 -'-' by a recently retired Ambassador which was 

 understood in a special way to reflect the opinion of 

 the Foreign Office. In this book he set forth the 

 '• necessary qualifications " for the diplomatic career, 

 which in his opinion were " good birth, good breeding, 

 good looks, and good health," and went on to say :— 

 ■■ Science is not necessary. Geography beyond elemen- 

 tary notions is not of great value. The diplomatist 

 will acquire what geographical knowledge he needs of 

 the country to which he is appointed while residing 

 at the post. Few men can know it in sufficient detail 

 beforehand." 



We drifted into this war through sheer lack of expert 

 knowledge of foreign countries and foreign languages. 

 We have muddled and misconducted our war opera- 

 tions on sea and land through lack of expert know- 

 ledge, of science, on the part of those commandiiig at 

 home, and sometimes^happily not always — of those 

 commanding abroad. If by the proverbial good luck 

 which saves Great Britain ever and again ; if, still more, 

 by the unparalleled bravery of our men in all branches 

 of the combatant Services, by their innate common 

 sense and coolness, and by the occasional streak of 

 genius among their leaders, which not even a War 

 Office or an Admiralty can occlude, we are sufficientlv 

 victorious to make peace on satisfactory terms, we 

 shall need more than ever to reform our system of 

 education and the general curriculum to be applied in 

 all schools to the children and youth of both sexes. 

 We shall not, I believe, conquer the Germans suffi- 

 ciently in this round to be sure they will remain in the 

 sphere allotted to them. We shall at best be able with 

 the help of our Allies to turn them out of France, 

 Belgium, and Italy. .Serbia and Rumania, and leave 

 them temporarily exhausted behind a frontier they only 

 intend to respect until they regain strength. The one 

 sure way to beat the Germans and keep them in their 

 place is to become better educated than they are, and 

 apply our new education to developing the resources of 

 our own land and of the four or five million square miles 

 in the tropics dependent on the London Government 

 for direction. 



Prior to the war, because of our contempt of a 

 scientific education, we offered little or no inducement 

 to our young men and women to serve the Home Coun- 

 try and the Empire in the application of science to 

 industry, commerce, and the enlargement of the 

 national intelligence. Therefore, we had to recruit 

 our science teachers frequently from Germany. A 

 great influx of clever men came to Britain from Ger- 

 many under the aegis of the Prince Consort and from 



1 From the presidential ad''re«s delivered before the Association of Public- 

 School Science Masters on January 8 by Sir H. U. lohnston. G.C.M.G., 

 K.C.B. 



