5^8 



NA TURE 



[March 28, 1901 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Mr. W. E. Thrift has been elected Erasmus Smith 

 professor of natural and experimental philosophy in Trinity 

 College, Dublin, in succession to the late Prof, G. F. 

 Fitzgerald. 



We are glad to notice in the report of the committee of the 

 Bristol Museum that interest in nature study is encouraged by 

 various means. In one of the rooms of the Museum, three 

 aquaria containing the ova of the common frog, and the common 

 and crested newts, were arranged, in order that the various 

 stages of development passed through by these forms might be 

 seen by visitors. The aquaria proved of especial interest to 

 young people from schools. Lectures have been given by Mr. 

 H. Bolton, the curator, to the students of evening continuation 

 schools, and the Museum has been visited by a number of classes 

 from other schools. The committee record that definite steps 

 have been taken to provide the additional accommodation that 

 has long been needed. The proposal took the form of providing 

 for museum extension in conjunction with the establishment of 

 a municipal art gallery, and the generosity and public spirit of 

 Sir William Henry Wills has made this possible. Upon the 

 basis that the sum of about 30,000/. would be required to provide 

 a suitable building for both purposes, Sir W. H. Wills offered 

 that if 10,000/. were provided for museum extension on the site 

 adjoining the present building, he would provide for the comple- 

 tion of the scheme. This munificent offer was accepted by the 

 council, who also accepted a report of the joint libraries and 

 museum committees recommending ihe requisite application to 

 Parliament, and placing the administration of the proposed art 

 gallery in the hands of the museum committee. 



In connection with the London School of Economics and 

 Political Science, Lord Rosebery delivered an address on 

 commercial education at the Mansion House on Thursday last. 

 The Lord Mayor, in opening the proceedings, stated that the 

 •object of the school was to provide a scientific training in the 

 structure and organisation of modern industry and commerce 

 and the general causes and criteria of prosperity as they were 

 illustrated or explained in the policy and the experience of the 

 British Empire and foreign countries. Mr. Passmore Edwards 

 had generously contributed 10,000/. towards the erection of a 

 building for the faculty of economics and political science ; 

 and Lord Rothschild had given 5000/. In the course of his 

 address. Lord Rosebery said : "From whatever standpoint we 

 may regard the age, I think we must all be aware that we are 

 coming to a time of stress and of competition for which it is 

 necessary that we should be fully prepared. It is not necessary 

 here to indicate what form that stress or that competition may 

 take, but in military matters, in naval matters, in commercial 

 matters, in educational matters, we see more clearly day by day 

 that we shall not be allowed to rest on any reputation that we 

 possess already, but that we shall have to fight for our own hand 

 in every department of human activity and human industry if we 

 wish to keep our place. It is necessary for a nation in these 

 days to train itself by every available method to meet the stress 

 and the competition which is before it. Lord Salisbury said 

 the other day- and I think with some truth — that it was im- 

 possible to define technical education. Well, I do not think it 

 is impossible, but I think it is difficult. The way in which I 

 should define it — very imperfectly, I am aware — is this. I 

 should define it as education having a direct practical bearing on 

 any definite industry or calling ; that is to say, an education, 

 not as we are accustomed to see secondary education as carried 

 «utin this country — an education for the training and elevation 

 of the mind — but a practical training having a business bearing." 

 The United States Ambassador, in proposing a vote of thanks to 

 the Lord Mayor, said there was no doubt that colleges of 

 economics and of political science were the latest development 

 in the theory and practice of that education which was to fit 

 men for the great affairs of life as they were developing in the 

 complex and rapidly varying phases of modern civilisation. In 

 the United States they regarded them as among the chief means 

 of maintaining their part in that rivalry which they were main- 

 taining, and meant to maintain with all their force, with their 

 sister nations of the world, and especially with this country, to 

 which they were so much attached — a rivalry not of arms or of 

 warfare, but a rivalry of brains, of skill, of courage in the great 

 industries of life. 



SCIENTIFIC SERIALS. 



Transactions of the American Mathematical Society, vol. ii. 

 No. I. — Invariants of systems of linear differential equations, 

 by E. J. Wilczjnski. The author has elsewhere shown that 

 the most general point-transformation, which converts a system 

 of n homogeneous linear differential equations into another of 

 the same form and order, is 



X = /(4), n = ^ «*/ (1)"^ • . . (^= I, 2, 



«), 



NO. 1639, VOL. 63] 



where /(|) and a^,- (|) are arbitrary functions of |, and the deter- 

 minant I a*; (I) I does not vanish identically {American Jotirnal 

 ofMathe>naiics,]2iVi\ia,xy 1901). In the present paper he con- 

 siders those combinations of the coefficients of a system of 

 linear differential equations which remain invariant when the 

 system is transformed by the above transformation. These 

 transformations form an infinite continuous group, and the author 

 employs Lie's theory throughout, as Dr. Bouton has done in 

 the American Journal of Mathematics, vol. xxi. No. 2. The 

 applications of the theory are but lightly touched upon, and only a 

 passing mention is made of covariants (p. 23) in this (first) paper. 

 — Divergent and conditionally convergent series whose product 

 is absolutely conveigent, by Florian Cajori. Tests of the con- 

 vergence of the product of conditionally convergent series have 

 been worked out by Pringsheim, A. Voss and by Cajori (see 

 American Journal of Mathematics, vol. xv. and vol. xviii.. 

 and Bnlle'in of the American Mathematical Society, vol. i. 

 (1895) Two typical examples are discussed and also the 

 author's general method. — Sets of coincidence points on the 

 non-singular cubics of a syzygetic sheaf, by M. B. Porter. The 

 points where a cubic can have an eighth order contact with 

 cubics of the syzygetic sheaf are called by Halphen coincidence 

 points of the cubic. The author considers certain geometrical 

 relations that subsist between an inflexion triangle and its asso- 

 ciated group of in- and circumscribed rectilinear triangles. 

 The number of these triangles is 24. We give one pro- 

 perty. Each in -circumscribed triangle is in six ways 

 perspective with its associated inflexion triangle. — Note on 

 non -quaternion number systems, by W. M. Strong. All 

 number systems have been divided into the quaternion and 

 non-quaternion systems, and Scheffers has shown that the n 

 fundamental units of a non-quaternion system may be so chosen 

 that the multiplication table takes a particularly simple form, 

 which is in turn characteristic of the non-quaternion systems. 

 The present paper shows that the choice of the units may be 

 so regulated that the multiplication table becomes still simpler. — 

 On the reduction of the general Abelian integral, by J. C. Field, 

 embodies results (in 38 pp.) which were presented at the annual 

 meeting of the Society held in 1897. MM. Appell and Goursat, in 

 their " Theorie des fonctions aigebriques et de leurs Integrales " 

 (pp. 344-345) give a brief sketch of Hermite's method for obtain- 

 ing by lational operations the reduced form for a hyperelliptic 

 integral, in which note they make a remark which seems to imply 

 that the more general problem in the case of the Abelian 

 integrals was still awaiting a solution. The present paper is 

 the auth r's solution of the problem. — " Ueber flachen von 

 constanter Gausscher Kriimmung," by D. Hilbert. The greater 

 part is concerned with Flachen von negativer and the rest with 

 Flachen von positiver constanter Kriimmung {cf. Dini, Annali 

 di Mat. Bd. 4. 1870; Darboux, " Le9ons sur la theorie generate 

 des surfaces," Bd. 3, and Bianchi, " Lezioni di geometria differ- 

 enziale"). — A short note follows on the functions of the form 

 f{x) = ^{x)+a^x'"-^'^ + a^'^~'^-\- ... -fa» which in a given 

 interval differ the least possible from zero, by H. F. Blichfeldt. 

 This gives Tchebycheff^s solution (from Bertrand, " Calcul differ- 

 entiel," p. 5i"2)and then the author's solution. As this gentle- 

 man has not had access to TchebychefTs memoirs his method 

 may not be altogether novel. 



Annalen der Physik, March. — On the production and 

 measurement of sinoidal currents, by Max Wien. The ideal 

 electrical oscillations for use in wireless telegraphy would con- 

 sist of a continuous, purely sinoidal current, the oscillationi 

 frequency of which could be varied slowly and continuously 

 from a low figure up to frequencies that could be seen. Th« 

 arrangement described in the present paper, although still fai 

 short of this, constitutes a considerable advance upon previous 

 work, as a purely sinoidal current can be obtained with an osciI< 

 lation frequency up to 8500 per second, and with a slight depat: 



