April 23. 1908] 



I^A TURE 



.S8; 



last half of the nineteenth century. Prof. Volterra 

 discussed the work of Cremona, Betti, Brioschi, Bel- 

 trami, Fergola, Battaglini, and Dini, and directed at- 

 tention to the recent publication of Galileo's complete 

 works under the patronage of the King. 



The subsequent meetings were held in the magnifi- 

 cent suite of rooms occupied by the Reale Accademia 

 dei Lincei at the Palazzo Corsini, where ample 

 accommodation was available for general and sec- 

 tional meetings, as well as secretarial and post offices 

 and a buffet. The pretty garden behind the palace 

 was also thrown open, and in the groves the wild 

 BellevalUa romaua was in full flower. A service of 

 automobiles running intermittently to and from the 

 middle of the town was placed at the disposal of the 

 members. At the first general meeting a report was 

 presented by Profs. Segre, Noether and Poincare, 

 awarding the Guccia medal to Prof. Francesco Severi 

 lor his work on geometry of algebraic surfaces. 

 -Subsequently Prof. .Mittag-Leffler gave a lecture on 

 the arithmetic representation of analytic functions of 

 a complex variable, and Prof. Forsyth lectured on the 

 present condition of partial differential equations of 

 the second order as regards formal integration. 



The sectional meetings commenced on Tuesday 

 morning, .-Vpril 7, the sections being as follows : — i., 

 analysis; ii., geometry; iii.a, dynamics and mathe- 

 matical physics; iii.6, statistical and practical applica- 

 tions; iv., philosophy, history, and teaching of 

 mathematics. 



In the section of analysis. Prof. Marcolongo directed 

 attention to the lamentable death on March 30 of 

 Dr. Laura Pisati, who was at that time preparing her 

 paper for the congress entitled "An Essay on a Syn- 

 thetic Theory of Functions of a Complex Variable." 

 From a long list of subsequent papers the following 

 may be selected: — Jordan, solution of the sextic ; 

 Borel, theory of groups ; Frizel, power of continuum ; 

 Young, applications of semi-continuous functions ; 

 Schlesinger, parametric problems in the theory of 

 linear differential equations ; Remoundos, zeros of in- 

 tegrals of a class of differential equations; Volterra, 

 method of images in the hyperbolic type ; E. G. 

 Moore, a form of general analysis; Fredholm, 

 Fourier's integrals and theory of linear integral equa- 

 tions ; .\dhemar, equations of Fredholm and Volterra ; 

 Orlando, resolution of integral equations; Stephanos, 

 extension of invariant and covariant theory of binary 

 forms. 



In the geometry section, we note Andrade, theorem 

 of Ampere-Stockes and Euclid's postulate; Bagnera, 

 algebraic equations resolvable by meromorphic func- 

 tions which are quadruply periodic in two parameters ; 

 Severi, certain results in algebraic geometry with 

 special reference to the irregularities of a linear 

 system; Bianchi, Darboux's transformation of sur- 

 faces of minimal area ; Brouwer, a theory of groups 

 independent of the axioms of Sophus Lie. 



In section iii.a, Sir G. H. Darwin gave a com- 

 munication on the rigidity of the earth, illustrated 

 bv diagrams showing the displacement of the vertical 

 when the moon has a high north or south declination. 

 It was estimated that the earth's surface rose and 

 fell 17 cm. with the tides, and 20 cm. with variations 

 of barometric pressure. Among other papers we 

 notice Lauricella, certain extensions of the equation 

 of elasticity; Lamb, a theoretical confirmation of the 

 engineers' approximate treatment of bending of 

 beams; E. E. Levi, discussion of certain elastic de- 

 formations which satisfy Weingastein's but not Vol- 

 terra's condition; .A. Korn, an attempt to build up a 

 theory of pulsating spheres capable of accounting for 

 electrical as well as gravitational phenomena ; Levi 

 Civita, retarded potentials; Garbasso, white light; 



NO. 2008, VOL. 77] 



Greenhill, geometry of gyroscopic motion, descripti\i 

 of a method of drawing families of curves hodographic 

 lo the Poinsot herpolhode ; Sommerfeld, an attempt 

 to account for turbulent motion of viscous liquids; 

 Genese, reciprocal polars applied to statics ; Kolosoff , 

 elastic problems in two dimensions treated by com- 

 plex variables. 



Section iii.b met on three days only, the first two 

 being devoted to statistical problems, with especial 

 reference to life assurance. An address was given by 

 the chairman, Signor Guido Toja, on the relations 

 between mathematics and actuarial science, and the 

 papers included Dawson, on necessary cautions in deal- 

 ing with actuarial problems ; Borel, application of 

 probability to biology; Castelli, the teaching of 

 actuarial science; Poussin and Elderton, papers of a 

 graphical character; March, population statistics. 

 The third sitting was devoted to the mathematics of 

 engineering and building, a subject introduced by 

 Prof. L. Luiggi. Papers were read by Prof. D'Ocagne, 

 representing the French Office of Works, on the cal- 

 culus in engineering, and the approximate rectifica- 

 tion of circular arcs; by Swain, on teaching of mathe- 

 matics for engineers; by Canevazzi, and finally by 

 Claxton Fidler, on the theory of construction. The 

 last-named communication derives considerable import- 

 ance from the reference to the comparatively recent 

 bridge disaster in America, which a mathematical in- 

 vestigation proved to have originated through one of 

 the stays having had to play the part of a strut during 

 the process of construction, thereby causing buckling, 

 which would not have occurred in the completed 

 structure. 



The fourth section was devoted on the Tuesday 

 morning mainly to philosophical aspects of mathe- 

 matics, the subject being introduced by Prof. Fedengo 

 Enriques. A discussion between Profs. Itelson and 

 Pastor was a noticeable feature of the proceedings. 

 On the Wednesday and Saturday the discussions were 

 mostly historical. Prof. Krazer directed attention to 

 the publication of Euler's works, in accordance 

 with a wish expressed at the previous congress, 

 and proposed a vote of congratulation to the Swiss 

 Society of Naturalists, which had undertaken the ini- 

 tiative in this task. It was further proposed to invite 

 the Association of Academies, and the Academies of 

 Berlin and St. Petersburg in particular, to assist in 

 preparing the volumes. A proposal was made bv 

 Prof. Amodeo in favour of the publication of the col- 

 lected works of Bonaventura Cavalieri. Thursday 

 and Friday were devoted to the teaching of mathe- 

 matics. A number of reports had been invited as to 

 the position of mathematical teaching in the schools 

 of various countries. Germany was represented bv 

 Gutzmer, France by Borel, Great Britain by Godfrey 

 (whose paper was summarised by Vailati, and dis- 

 cussed by Gibson), the United States by D. T. Smith. 

 .Austria by Suppantschitsk, Hungary by Beke, Italy 

 by Vailati and Conti, Switzerland by Fehr, Greece 

 by Stephanos. Prof. Archenhold proposed that a 

 standing committee should be formed for the studv of 

 questions regarding the teaching of mathematics in 

 secondary schools, this motion being carried in the 

 section. Prof. Loria presented the first copy of the 

 fourth volume of Moritz Cantor's " Vorlesungen uber 

 Geschichte der Matematik," and a volume containing 

 the report of the educational committee of the German 

 Association of Naturalists and Physicians was pre- 

 sented by Prof. Gutzmer. 



The sectional meetings have, as a rule, lasted onlv 

 about a couple of hours, leaving plentv of time for 

 exchange of ideas between individual congressists out- 

 side the formal meetings. 

 I The discourses, occupying a little under an hour 



