December 4, 1919] 



NATURE 



365 



Mr. J. G. Legge, Mr. R. VV. Livingstone, Mr. G. A. 

 Macmillan, Prof. Gilbert Murray, Mr. Cyril Norwood, 

 Prof. W. Rhys Roberts, Mr. C. E. Robinson, Prof. 

 A. N. Wfiitehead, and Mr. C. Cookson (secretary). 

 Communications intended for the Committee should 

 be addressed to Mr. C. Cookson at the offices of the 

 Board of Education, Victoria and Albert Museum, 

 Exhibition Road, South Kensington, S.W.y. 



The eighth annual Conference of Educational Asso- 

 ciations \\\\\ be held in Uniyersity College, Gower 

 Street, London, W.C.i, from Wednesday, Decem- 

 ber 31, 19 19, to Saturday, January lo, 1920. Mr. 

 H. \. L. Fisher, President of the Board of Education, 

 will give an address at the inaugural meeting, and the 

 following are among the subjects to be discussed at 

 meetings of some of the associations : — National .Asso- 

 ciation of Manual Training Teachers and Educational 

 Handwork .Association : (a) The Measurement of 

 Practical .Ability and (ft) Handwork and Science. 

 British Psychological Society — Education Section : 

 The Development of Mental Tests. .Association of 

 Science Teachers : Anti-gas Fans — with E.xperiments. 

 Geographical Association : The Present Position of 

 Geography in the Upper Forms — Some Causes and 

 Possible Remedies; Spitsbergen; Islands, Peninsulas, 

 and Empires; and Rainfall Considered as a Geo- 

 graphical Function. The .Association of Science 

 Teachers has arranged for a demonstration of Dr. 

 \\'ilson"s astronomical model at intervals throughout 

 Monday, January 5. 



The inauguration of the University of Strasbourg 

 under the new regime, which took place on Novem- 

 ber 22, was naturally an event of importance. The 

 position of Strasbourg as the eastern outpost of French 

 culture gives to its University a position of outstand- 

 ing prestige. The authorities responsible for its "re- 

 construction " under the tricolour intend to maintain 

 a very high standard of studies, and are especially 

 anxious to attract students from this country. There 

 are six faculties (law, sciences, letters, medicine, and 

 Protestant and Catholic theology) and a personnel 

 enscignant of 170 professors and maitres de conference. 

 \ well-endowed Societd des .Amis de I'Universite 

 (2 rue Geiler, Strasbourg) has just t)een founded, and 

 one of its chief obj'^cts will be that of welcomin<i t-lude.i"s 

 (of either sex) from abroad and of making life attrac- 

 tive to them. Inquiries should be addressed to the 

 society. The cost of living is much to the advantage 

 of British residents on account of the verv favouraiile 

 rate of exchange. The imposing university buildings 

 (opened in 1884 at a cost of 2,000,000/.) stand in the 

 centre of the city, and close at hand is the magnificent 

 library of 1,200,000 volumes, so rich in German litera- 

 ture. Strasbourg itself is, without doubt, one of the 

 most attractive and wiell-governed cities in Western 

 Europe, and its close proximity to the beautiful forests 

 of the Vosges gives it a further advantage as a place 

 of residence for British students. 



SOCIETIES AND ACADEWES. 



London. 

 Royal Society, November 20.— Sir J. J. Thomson, 

 president, in the chair. — W. J. Johnston : A linear 

 associative algebra suitable for electro-magnetic rela- 

 tions and the theory of relativity. The algebra is 

 based on four fundamental units i, ;', fe, o. The 

 square of each unit is — i, while the other binary 

 products are polar (ij=-ji, io^ — oi, etc.). This 

 algebra is associative. i, ;', fe are intierpreted as 

 mutually rectangular unit vectors in Euclidean space, 

 while o is a unit vector in the fourth dimension per- 

 pendicular to the other three. Let lu be the pure 

 imaginary scalar ct-J — i and W = c-Vv'— i, where 

 NO. 2614, VOL. 104] 



is the scalar potential, then if (F, G, H) is the 

 ordinary vector potential the vector 



U = iF-l-;G-t-feH-l-oW 



is the fourfold vector potential. If Vj is the operator 



ox •'oy 02 do) 



then the electric and magnetic forces are the six 

 components of fViU, the scalar part of which 

 vanishes ; and the eight scalar equations of the electro- 

 dynamic field which connect these forces are expressed 

 by the single equation Vi(ViU) = o. This equation in 

 the equivalent form Vi^U=o, when interpreted in 

 terms of ordinary space, expresses that all the dis- 

 turbances are propagated from their point-sources with 

 uniform velocity c. — Sir Joseph Larmor : Generalised 

 relativity, in connection with Mr. W. J. Johnston's 

 symbolic calculus. If ijk are polar units, so that 

 i'= — I, ij=—ji, then ik + jy + ks is a binary form 

 involving the position of a point xyz and that of a 

 trihedron ijk. So far as regards relative position, a 

 displacement of the one is the same thing as a dis- 

 placement of the other. .A vector I'F-l-jG-i-fcH repre- 

 sents an entity independent of the trihedron of refer- 

 ence, so is invariant for changes of the latter. Opera- 

 tions of addition and multiplication of vectors give 

 results which are also invariant. Similar statements 

 apply in geometric algebras of higher dimensions, and 

 the scalars involved may be ordinary imaginaries. 

 With the four dimensions x, y, z, ctiZ—i of Min- 

 kowski, Mr. Johnston has shown that the vector 

 forces of the electro-dynamic field are specified by 

 ViU, where U is the fourfold vector potential, and 

 the eight equations of the field are summed up in 

 ■^j'-Urso. But a source, naturally conceived as a 

 singular point in ordinary space, complicates now 

 into a Minkowski line. .Again, all the geometric 

 quantities natural to any Euclidean hyperspace are 

 those which are evolved immediately from the addition 

 and multiplication of vectors in it. It is proved that 

 the possible types of disturbance propagated through 

 an aether, which conform to the principle of relativity, 

 are restricted to the single one specified by Maxwell's 

 electro-dvnamic scheme. In an appendix the Einstein 

 idea of gravitation is developed as a theory of corre- 

 spondence of modes of action of a physical system ; 

 it appears, at any rate on this view, that it does not 

 involve displacement of the solar spectral lines. — 

 G. E. Bairsto : The variation with frequency of the 

 conductivity and dielectric constant of dielectrics for 

 high-frequency oscillations.— F. J. W. Whipple: Equal 

 parallel cylindrical conductors in electrical problems. 

 Dr. .Alexander Russell has recently directed attention 

 to the practical importance of determining the mutual 

 induction between currents of high frequency carried 

 by parallel cylindrical conductors, and pointed out that 

 the problem is mathematically equivalent to that of 

 finding the distribution of static charge on two elec- 

 trified conductors. The first part of the present paper 

 is devoted to the solution of this problem. The co- 

 etTicientS of mutual and self-induction and the force 

 between the cylinders, regarded as carriers of high- 

 frequency currents, concentrated on the surfaces, are 

 also investigated.— G. A. Schott : The scattering of 

 X- and 7-ravs by rings of electrons. .A crucial test 

 of the electron-ring theory of atoms. This paper 

 investigates the effect of the regular spacing of the 

 electrons of a ring on the scattering of X- and 7-rays, 

 treated as undamped simple harmonic wave-trains of 

 high frequency. The ring, whether at rest or 

 revolving "uniformly about its axis, diffracts the waves 

 incident on it in all directions, but not equally. For 

 a single electron the law of distribution is that of 

 Sir J. J. Thomson's simoU -pulse theory, but it deviates 



