NATURE 



[September 5, 1912 



at all rounded by the shearing^ movement of the ice in 

 which they were once embedded, are often scratched 

 and grooved. (See further my paper on the 

 mechanics of glaciers, Q.J.G.S., February, 1883; 

 also Nature, June 20, 1912.) 



I can assure Mr. Reid Moir that the delicate and 

 interesting subject of patinatwn presents difficulties 

 to those "who (in microscopic and laboratory work) 

 have brought some knowledge of physics and 

 chemistry to bear on the Uthology of the flint, and 

 that it is' not to be dismissed in the easy way he seems 

 to suppose. Nor do I think that even Dr. Sturge 

 (Proc. Prehis. Soc. of E. Anglia) has adequately dealt 

 with the subject or with the possible causes of some 

 phases of " striation." A. Irvin'G. 



Bishop's Stortford, August 22. 



THE FIFTH INTERNATIONAL CONGRESS 

 OF MATHEMATICIANS AT CAMBRIDGE. 



THE first Mathematical Congress was held at 

 Ziu-jch in 1897, the second at Paris in 1900, 

 the third at Heidelberg in 1904, and the fourth 

 at Rome in 1908. This year's congress met at 

 Cambridge, August 21-28, under the presidency 

 of Sir G. H. Darwin, and was divided into sections 

 as follows: — I, Analysis; H, Geometry; HI (a), 

 Physical Mathematics; HI [b). Statistics; IV (a), 

 Philosophy and History ; IV (b), Didactics. 

 Several meetings of the last section were held in 

 connection with the International Commission on 

 the Teaching of Mathematics, which was formed 

 by a resolution of the fourth congress to study 

 and report on the actual state of mathematical 

 teaching in various countries. 



Receptions were given by the Chancellor, Lord 

 Rayleigh, in the Fitzwilliam Museum, by Sir 

 G. H. Darwin in St. John's and Christ's Colleges, 

 and by the Master and Fellows of Trinity College. 

 Msits were made to the University observatory 

 and to the works of the Cambridge Scientific In- 

 strument Company. Excursions were arranged 

 to Ely Cathedral, Oxford and Hatfield House. 

 Throughout the week the University and colleges 

 displayed their customary hospitality to the full, 

 and the appreciation of the visitors, both English 

 and foreign, was very evident. The members 

 numbered 572, as compared with 535 at the fourth 

 congress, and included representatives from 

 Brazil, Chile, Egypt, India, Japan, and Mexico. 

 An exhibition organised by the Mathematical 

 Association was arranged in the Cavendish 

 Laboratory, and included English and foreign 

 text-books, examples of school work, models and 

 apparatus, and a most interesting and complete 

 collection of calculating machines. Eight lectures 

 were delivered to the whole congress, and we 

 mention below a few of the less technical points 

 occurring in these, and in the meetings of the 

 didactic section. 



Sir G. H. Darwin (Cambridge), in welcoming the 

 congress at the first meeting, referred to the death 

 of Henri Poincare, whom he described as the one 

 man who alone of all mathematicians might have 

 occupied the position of president of the congress 

 without misgivings as to his fitness. It brought 

 vividly home to him how great a man Poincare 

 NO. 2236, VOL. 90] 



was, when he rellected that, to one incompetent 

 to appreciate fully one half of his work, he yet 

 appeared as a star of the first magnitude. 



Prof. E. W. Brown (Yale) lectured on " Period- 

 icity in the Solar System." Newton and his con- 

 temporaries aimed at obtaining functions which 

 should express the positions of individual bodies 

 at all epochs. This is now recognised as unattain- 

 able ; and the position within certain limits of 

 time is expressed by infinite series of terms, some 

 of which are harmonic representing periodic 

 motions, and others expressed as powers of the 

 time representing secular motions. These series 

 are carried to a degree of accuracy exceeding that 

 of the most delicate observation ; so that where 

 the calculated positions differ from those observed 

 by a quantity exceeding the possible error of 

 observation, it may be safely assumed that forces 

 are in action other than those postulated in the 

 theory. This is notably the case in the theory of 

 the moon, where the outstanding discrepancy is 

 comparable with the largest of' the perturbations 

 due to the planets. Dynamical theory in the case 

 of the asteroids has shown that in the particular 

 case of the problem of four bodies when the mass 

 of one is small, the motion of the latter is imstable 

 for certain ranges of value of the radius vector; 

 and no asteroids have, in fact, been found within 

 these limits. It is possible that an explanation may 

 here be foreshadowed of the dark intervals in 

 Saturn's rings. 



Prince B. Galitzin (St. Petersburg) lectured on 

 "The Principles of Instrumental Seismologv." 

 The usual seismographic record shows three chief 

 groups of disturbances, due respectively to the 

 longitudinal and transverse waves through the 

 core of the earth, and to the superficial wave, 

 round the crust. These, however, are complicated 

 and supplemented by reflections of the deep waves 

 at the surface, and sometimes also by twin earth- 

 quakes caused by the primarv. The relations 

 between the elastic constants of the core deduced 

 from seismographic observations are in fair agree- 

 ment with the theory of elasticity of an isotropic 

 medium. But an attempt has been made to con- 

 struct a more general theory assuming hetero- 

 geneity depending on depth. The ideal aim of 

 seismometry must be the determination of the six 

 components of motion of a particle of the earth's 

 crust throughout the whole of a disturbance. 

 Hitherto attention has been confined to the three 

 components of translation. The practical problem 

 of recording the three components of rotation 

 seems to have been solved recently in an apparatus 

 in which induced currents from two pendulums 

 are passed simultaneously in opposite directions 

 through the same galvanometer. There is even 

 reason to believe that the problem of predicting 

 earthquakes is not so hopeless as it would a priori 

 seem to be. 



Sir W. H. White lectured on "The Place of 

 Mathematics in Engineering Practice." It is 

 matter for surprise that many of the great engin- 

 eering discoveries of the last century were made 

 by men who had little or no mathematical or 



