190 



NATURE 



[June 24, 1897 



correlative principle utilised by Poynting is valid, that the actual 

 rate of change with time of the organised or mechanical energy 

 within any region is expressible explicitly as a surface-integral 

 over its boundary. 



The mechanical effects of light- waves are reconsidered in the 

 light of this molecular theory. The conclusion is reached that 

 such effects are wholly associated with absorption of the radia- 

 tion, that no influence of perfectly transparent media on radiation 

 can provoke a mechanical reaction. There is a mechanical force 

 acting on an absorbing mass, in the direction of the incident 

 radiation and equal to E(i -;«-"), where E is the energy 

 absorbed per unit time and rii is the real part of the index of 

 refraction. Partial analogies are furnished by the mechanical 

 effects of Hertzian radiation on a medium built up of conducting 

 linear circuits, and of sound waves on a medium formed of a 

 system of resonators. 



As an application of the law of the mechanical forcive on 

 dielectrics, the changes of dimensions of a condenser under 

 electrification are considered. The problem is found to admit 

 of exact solution if the condenser layer consists of a closed sheet, 

 of any form, but of uniform thickness. In that case the 

 mechanical stress in the material of the sheet proves to be 

 simply of the type of the Faraday-Maxwell stress. The theory 

 is compared with Quincke's experimental results : their main 

 features are verified, including those which led Quincke to 

 assign a wholly non-mechanical origin to the effect : but some- 

 thing less than half the change of volume remains over as an 

 intrinsic electric deformation, not due to the transmitted 

 mechanical forces. 



Finally a series of practical illustrations of the mechanical 

 theory are treated, some of which have already been employed 

 for experimental measurement, and which are capable of still 

 further application. The mechanical circumstances attending 

 the refraction of uniform fields of electric force by fluid media are 

 developed. The theory of various arrangements for measuring 

 electric tractions and pressures in fluid dielectrics is worked out. 

 The etiect of an electric field on the velocity of ripples on the 

 surface of a conducting or a dielectric fluid is determined : as 

 also are the relations of electric polarisation to vapour tension 

 and fluid equilibrium. The internal mechanical forces in a 

 complete magnetic circuit are examined, and also the traction 

 between the interfaces when it is divided : and the mode of 

 calculation of the stress in a sphere of iron in a uniform magnetic 

 field is indicated, agreeing for this case with Kirchhoff. The 

 mutual influence of stress and magnetisation is analysed, with 

 reference to the experimental investigations of Bidwell. 



June 3. — " Mathematical Contributions to the Theory 

 of Evolution. On the Relative Variation and Correlation in 

 Civilised and Uncivilised Races." By Miss Alice Lee, Bed- 

 ford College, and Karl Pearson, University College. Received 

 April 9. 



The numerical constants of this paper were calculated in the 

 hope of 1 caching some general ideas on comparative variation and 

 comparative correlation in the case of civilised and uncivilised 

 races, and further of determining, if possible, any general law 

 connecting relative sexual variation and relative sexual corre- 

 lation with the degree of civilisation, and so, with what is 

 probably inversely proportional to the degree of civilisation, 

 namely, the intensity ol natural selection. 



The following two principles seem to flow from a study of 

 variation in the organs of man : — ^ 



(a) Civilised man is more variable than uncivilised man. 



(b) There is a greater equality of variation for the two sexes 

 in uncivilised than in civilised races. Civilised woman appears, 

 on the whole, to be slightly more variable than civilised man. 



Both these principles are in accordance with the intensity of 

 the struggle for existence— and the amount, consequently, of 

 natural selection — being greater for uncivilised than for civilised 

 races, and, further, greater for men than for women in the latter 

 races. 



Tl)e ]:)roblem of correlation is, however, of a less simple 

 chi racier. While the action of selection can be shown theoreti- 

 cally to reduce variation, it by no means follows that it reduces 

 correlation. Indeed, selection may increase, decrease, or reverse 

 correlation at the very same time as it is reducing variation. 

 We have then the following problems to' guide us in the treat- 

 ment of actual statistics : — 



1 See "Variation in Man and Woman," by K. Pearson : " The Chances 

 of Death," vol. i. pp. 256-377, where some 155 cases of human variation for 

 both sexes are dealt with. 



NO. 1443, VOL. 56] 



(a) Is correlation more intense among civilised than among 

 uncivilised race* ? 



{b) How does the relative correlation of the sexes differ in 

 civilised and uncivilised races? 



((-) Is there any marked prepotency of either sex in the matter 

 of correlation ? 



These are the problems which the present calculations were 

 designed, not to definitely solve, but to illustrate. 



Unfortunately, adequate measurements on living members of 

 uncivilised races are not very numerous, nor for the purposes of 

 correlation generally very satisfactory. Reasons are given in 

 the paper why long bones form more suitable material than skulls, 

 and the measurements made in France by Rollet, and on the 

 Ainos in Japan by Koganei, are discussed at length. 



The following results are suggested by a discussion of the 

 measurements. 



(i) Civilised man has progressed as a rule on primitive man 

 in size, variation, and correlation. 



(2) This progression can hardly be accounted for by increased 

 selection (because of the increased variation), not by decreased 

 selection (because it is inconsistent with the relative changes in 

 male and female size). It might possibly be accounted for by 

 decreased selection and improved physical conditions. 



(3) Woman is more variable than man in civilised races. 



(4) Woman is more highly correlated than man in civilised 

 races. 



(5) In uncivilised races the sexes are more nearly equal in the 

 matter of size, variation, and correlation than in the case of 

 civilised races. 



(6) It is impossible to say that civilised woman is nearer to the 

 primitive type than civilised man. While civilised man differs 

 more from the primitive type than civilised woman, so far, 

 probably, as absolute size is concerned, he has made only about 

 half her progress in variation, and hardly any progress at all in 

 correlation. 



(7) The causes {eg., lessening of selection) which tend to 

 increase variation may also increase correlation. In other 

 words, the intensity of the struggle for existence is not necessarily 

 a measure of the intensity of correlation. 



Mathematical Society, June 10.— Prof. Elliott, F.R.S., 

 President, in the chair, and subsequently Major MacMahon, 

 R.A., F.R.S., Vice-President— Mr. W. W. Taylor gave, in 

 some detail, a description of several models of the regular 

 convex and star solids. — The following papers were communi- 

 cated : — The calculus of equivalent statements (sixth paper), by 

 H. MacCoU ; on the primitive substitution groups of degree 

 fifteen, by Dr. G. A Miller ; and a generalised form of the 

 binomial theorem, by Rev. F. H. Jackson. 



Edinburgh. 

 Royal Society, June 7. — Prof. Geikie, F.R.S., inthechair. 

 — Sir. William Turner read a paper by Dr. Broom, South 

 Africa, on the comparative anatomy of the mammalian organ of 

 Jacobson. — Prof. C. G. Knott gave the concluding paper of the 

 series on magnetic strains, for which the Council has awarded 

 him the Keith Prize for 1893-95. His results may be sum- 

 marised thus : — All the iron and steel tubes follow appro.ximately 

 the same law as regards their longitudinal dilatation in a 

 longitudinal magnetic field. In moderate fields the dilatation 

 is positive ; but it is negative in higher fields. The maximum 

 occurs in field 150 ± 50, according to the thickness of the walls 

 — the thinner the wall, the lower the field corresponding to the 

 maximum dilatation. The great diversity in the volume changes 

 within the cores shows that the transverse dilatations must be of 

 such a value as to be in some cases less than half the longi- 

 tudinal dilatation, sometimes greater. This is particularly true 

 of the steel tubes. The behaviour of nickel is much simpler 

 than that of iron. On the whole, the cubical dilatation is 

 determined by the longitudinal dilatation, both being negative 

 and more nearly alike in order of magnitude than in the case of 

 iron. Excepting for the tubes of narrowest bore, the transverse 

 dilatation is positive, and about ^th or -1th of the longitudinal 

 dilatation. The change of volume of a mass of nickel turnings 

 enclosed in a brass tube and placed in the magnetic field is 

 much smaller than the volume-changes in the bores of the tubes. 

 The cubical dilatation is always positive, and increases steadily 

 from 1-56 X 10-^ in field 107, to 27-4 x lo-^n field 570.— In a 

 paper on the solution of equations connecting linear vector 

 functions. Prof. Tait derived a general proposition regarding 

 the commutativeness of strains, and noted connected questions. 



