262 



NATURE 



[January i6, 1902 



the debt — 7500/. — in order that the debt of the College may be 

 extinguished altogether. 



At a special meeting of the Court of the Victoria University, 

 the recent movements to estabhsh separate Universities in Liver- 

 pool, Manchester and Leeds were discussed. .\s the University 

 College, Liverpool ; Owens College, Manchester ; and the 

 Vorkshire College are the three constituent colleges of the 

 Victoria University, the establishment of the three proposed 

 Universities would mean the disruption of the present federated 

 University. The two alternatives which the Court had to con- 

 sider were as follows : — " Having regard to the resolutions of 

 the three con.stituent colleges of the University, the question for 

 decision must be whether (a) the three colleges are to remain as 

 constituent colleges of the University ; or whether {b) there 

 should be a separate University in Liverpool and a ' University 

 in Manchester without liability to admit or to remain in associa- 

 tion with any other college," and also a ' University established 

 having its seat in Leeds.' " The latter view was accepted, and a 

 committee was appointed to consider the terms and conditions 

 on which it should be carried into effect. 



The New York correspondent of the Moniiiig Leader says 

 that the gifts to education in the United States in 1901 amount 

 to more than 15,000,000/. Of this sum 9,000,000/. was con- 

 tributed by three individuals. Mrs. Leland Sanford gave the 

 magnificent sum of 6,000,000/. to the western University which 

 bears her husband's name. Mr. John D. Rockefeller made an 

 endowment of 1,000,000/. for the law school in the University 

 of Chicago, and Mr. Andrew Carnegie has given 2,000,000/. to 

 found an institution for scientific research at Washington. Mrs. 

 Leland Sanford's gift of 6,000,000/. was in real estate and bonds 

 and stocks. In making her gift Mrs. Sanford was actuated by the 

 example of many wealthy persons in making bequests before 

 their death in order to avoid possible will contests which might 

 tie up the property for years. Mr. Carnegie's gift to endow 

 research provides the United States with a fund which, wisely 

 administered, will greatly strengthen university work in America 

 and give an impetus to investigation which will have a profound 

 influence upon the progress of the country. 



That there is a widespread desire to modify the traditional 

 methods of teaching the subjects of the ordinary secondary 

 school curriculum and to bring them more into harmony with 

 the practical needs of present everyday life, is strikingly shown 

 by the frequent discussions on the desirability of reform in the 

 teaching of mathematics which have taken place in the last few 

 months. One of the most recent of such discussions was that 

 which followed an address by Mr. W. C. Fletcher, headmaster 

 of Liverpool Institute, at the meeting of the Incorporated Asso- 

 ciation of Headma.sters held in London last week. Mr. Fletcher 

 moved the following resolution, which was eventually adopted : 

 " That this Association desires to press upon the universities 

 and other examining bodies the desirability of greater elasticity 

 in their regulations as to mathematical teaching, and is of 

 opinion that to insist upon adherence to the order of propositions 

 in Euclid is mischievous." Mr. Fletcher said that six years' 

 experience of teaching geometry has led him to believe that 

 Euclid is a great hindrance to ninety-nine boys out of every hun- 

 dred in training and knowledge. A great deal of damage is done 

 by insistence, not only upon the particular method, but on the par- 

 ticular order, of Euclid. As the result of his experience he had 

 re-written the first half of Euclid's first book, omitted the second 

 book, and introduced two or three propositions about propor- 

 tion, in this way forming an interesting, sound and coherent 

 plan. The headmasters were so impressed with the value of 

 Mr. Fletcher's remarks that they decided to have his speech 

 printed and circulated among teachers. 



The position of the University of Birmingham was described 

 by the Vice-Chancellor, Mr. Chamberlain, at the second annual 

 Court of Governors held on January S. On the occasion of the 

 former annual meeting the fund raised for the purpose of the 

 University amounted to 330,000/. ; it has now reached 420,000/. 

 The Birmingham City Council has made a grant equal to a 

 halfpenny in the pound on the borough rate, and this will 

 provide about 5500/. per annum towards the ordinary mainten- 

 ance of the University. The Staffordshire County Council has 

 similarly identified itself with the aims of the University by 

 making a grant of 500/. a year lor five years in aid of the 

 'School o( Mining and Metallurgy. It is hoped that the example 



NO. 1 68 I, VOL. 65] 



will be followed by the county councils of Worcestershire, War- 

 wickshire and Shropshire, and that the annual contributions 

 from all these sources will amount to at least 7000/. per annum. 

 With the practical assurance of this income, a sum of 300,000/. 

 is available for the new buildings of the University. It is esti- 

 mated that the buildings contemplated cannot be erected and 

 equipped for a less sum than a million sterling. Out of the ten 

 departmental blocks of the University, three are to be com- 

 menced, in the first instance, to accommodate the schools of 

 mining and metallurgy, and of civil, mechanical and electrical 

 engineering. A University Hall will also be erected. While the 

 University buildings are being erected, the Mason College must 

 be extended in some way and its equipment increased, in order 

 to accommodate the additional students who have entered 

 .since the University was founded. For this purpose 10,000/. 

 will be required, and Mr. Chamberlain announced that 6000/. 

 had already been subscribed. 



SCIENTIFIC SERIALS. 



Annals of Matheiiiatifs (July and October, 1901). — Concern- 

 ing Du Bois Reymond's two relative integrability theorems. 

 The two theorems considered by E. H. Moore are, ( I) a con- 

 tinuous function of (properly) integrable functions is integrable ; 

 (2) an integrable function of an integrable function is integrable. 

 (i) was announced in 1880 and a proof published two years 

 later (Math. Ann.., vols. xvi. and xx. ). In connection with 

 this proof (2) was announced. Dr. Moore in this note shows, 

 by means of a simple example, that (2) is not true. Reference 

 is made to a proof of (i) by Dini with an extension which is 

 not applicable to the general case, but Dr. Moore extends 

 Du Bois Reymond's general proof (1882). — P. Saurel, on a 

 theorem of kinematics, gives an elementary demonstration of 

 the well-known theorem that every displacement of a rigid 

 body is equivalent to a rotation followed by a translation parallel 

 to the axis of rotation. — The collineations of space which trans- 

 form a non-degenerate quadric surface into itself, by Ruth G. 

 Wood, discusses the cc'' collineations of sp.ace which transform 

 the surface. — J. Westland contributes a note on multiply perfect 

 numbers, with a view to determine all numbers of multiplicity 3 

 of the form m = px<'\p^ip-f where />„ /.,, p.^ are three distinct 

 primes and p\<pi<pt. — The isoperimelrical problem on any 

 surface, by J. K. Whittemore, gives a generalisation of the 

 problem known to Pappus (see W. Thomson, " Popular Lectures 

 and Addresses," vol. ii.' p. 578). He solves Pappus's problem 

 by the calculus of variations, and then solves, by an apparently 

 novel method, the problem " Find a curve, v=<f(H), joining the 

 two given points (h„, z',,) and («[, Wj) having a given length L, 

 and such that the area of the portion of the surface between the 

 two curves, v=J\u) and v = <f>(ii), shall be a maximum." — On a 

 surface of the sixth order which is touched by the axes of all 

 screws reciprocal to three given screws, by F. W. Hyde, has 

 for its main object the determination and discussion of the 

 envelope of a certain conicoid, which is touched by the axes of 

 all screws of a certain system, so enabling one to grasp the 

 nature of the system. The surface possesses other features of 

 interest. The paper is illustrated with diagrams. — D. Sintsof, 

 in a note sur revaluation d'une integrale definie, discusses a 

 previous note by M. Pell (evaluation of a definite integral. 

 Annals (2), tome I, No. 3).^The October number opens with 

 a lengthy article (18 pp.) on the convergence of the continued 

 fraction of Gauss and other continued fractions, by E. B. Van 

 VIeck. Numerous references are given. — M. B. Porter supplies 

 a short note on the differentiation of an infinite series term by 

 term. — A note on geodesic circles, by J. K. Whittemore, 

 discusses these circles in Bianchi's sense, viz. their definition is 

 the locus of a point on a surface at a constant geodesic distance 

 from a fixed point of the surface (" Vorlesungen iiber Differ- 

 entialgeometrie," p. 160). Darboux (" Theorie Generale des 

 Surfaces," vol. iii. p. 151) calls such a circle a curve of constant 

 geodesic curvature. Mr. Whittemore gives three theorems — 

 the first is. If, on a surface, there exists a family of concentric 

 geodesic circles, such that the geodesic curvature of each curve 

 of the family is constant, then the total curvature of the surface 

 is constant along e.ach curve of the family, and the surface is 

 applicable to a surface of revolution, so that the geodesic circles 

 fall on the circles of latitude of this surface. — Prof. Osgood 

 gives a note on the functions defined by infinite series whose 

 terms are analytic [functions of a complex variable, with cor- 



