it 



Dec. 6, 1888] 



A^A TURE 



143 



Poincare's analysis, however, did not appear to admit of any 

 ! Wi definite conclusions being formed as to the nature and fre- 

 quencies of the various periodic free waves. The present paper 

 contains an application of Poincare's methods to the simpler 

 . ise when the fluid ellipsoid is one of revolution (Maclaurin's 

 heroid). The solution is effected by the use of the ordinary 

 sseral or zonal harmonics applicable to the fluid spheroid and 

 I he auxiliary spheroid required in solving the differential 

 equation. 



Denoting by k the ratio of the frequency of the free waves to 

 twice the frequency of rotation of the liquid about its axis, the 

 values of K are the roots of a rational algebraic equation, and 

 depend only on the eccentricity of the spheroid as well as the 

 degree and rank of the harmonic, while the number of different 

 free waves depends on the degree of the equation in k. At any 

 iistaut the height of the disturbance at any point of the surface 

 proportional to the corresponding surface harmonic on the 

 he;oid multiplied by the central perpendicular on the tangent 

 jilane, and is of the same form for all waves determined by 

 harmonics of any given degree and rank, whatever be their 

 frequency, but the motions of the fluid particles in the interior 

 will differ in nature in every case. 



Taking first the case of zonal harmonics of the «th degree, we 

 lind that according as n is even or odd there will be \n or 

 \ \{n + I), different periodic motions of the liquid. These are 

 ! essentially oscillatory in character, and symmetrical about the 

 I axis of the spheroid. Taking next the tesseral harmonics of 

 j degree // and rank s, we find that they determine n - s + 2 

 ! periodic small motions. These are e>sentially tidal waves 

 I rotating with various angular velocities about the axis of the 

 spheroid, the angular velocities of those rotating in opposite 

 directions being in general different. 

 j With regard to the question of stabilhy, the author shows that 



I in the present problem, in which the liquid forming the spheroid 

 is supposed perfect, the criteiia are entirely different from the 

 conditions of secular stability obtained by Poincare for the case 

 when the liquid possesses any amount of viscosity, which latter 

 depend on the energy being a minimum. In fact for a disturb- 

 ance initially determined by any harmonic (provided that it is 

 symmetrical with respect to the equatorial plane, since for 

 unsymmetrical displacements the spheroid cannot be unstable), 

 the limits of eccentricity consistent with stability are wider for a 

 perfect liquid spheroid than for one possessing any viscosity. If 

 we assume that the disturbed surface initially becomes ellipsoidal, 

 the conditions of stability found by the methods of this paper 

 agree with those of Riemann. 



Finally the methods of treating forced tides are further 

 discussed. 



The general cases of a "semi-diurnal" forced tide or of per- 

 manent deformations due to constant disturbing forces are men- 

 tioned in connection with some peculiarities they present, and 

 the paper concludes with examples of the determination of the 

 forced tides due to the presence of an attracting mass, first when 

 the latter moves in any orbit about the spheroid, secondly when 

 it rotates uniformly about the spheroid in its equatorial plane. 



The effects of such a body in destroying the equilibrium of the 

 spheroid when the forced tide coincides with one of the free 

 tides are then considered. 



Anthropological Institute, November 13. — Francis Galton, 

 F.R. S., President, in the chair. — Dr. E. B. Tylor read a paper 

 on a method of investigating the development of institutions 

 applied to laws of marriage and descent. With the view of 

 applying direct numerical methods to anthropology, the author 

 had compiled schedules of the systems of marriage and descent 

 among some 350 peoples of the uoild, so as to ascertain, by 

 means of a " method of adhesions," how far each rule co-exi.sts 

 or not with other rules, and what have been the directions of 

 development from one rule to another. As a first test of the 

 results to be obtained by this means, Dr. Tylor first examined 

 the barbaric custom which forbids the husband and his wife's 

 parents (though on a friendly footing) to speak or lo 'k at one 

 another, or mention one another's names. Some seventy peoples 

 l^ractise this or the converse custom of the wife and her husbands 

 relatives being obliged ceremonially to " cut " one another. On 

 classifying the marriage rules of mankind, a marked distinction is 

 found to lie between those peoples whose custom is for the husband 

 to reside with his wife's family and those where he removes her to 

 his own home. It apoears that the avoidance custom between the 

 husband and the wift'^s family belongs preponderantly (in fourteen 

 cases, as compared with eight computed as likely to happen by 



chance) to the group of cases where the husband goes to live with 

 the wife's family. This implies a causal connection between the 

 customs of avoidance and residence, suggesting as a reason that 

 the husband, being an interloper in the wife's family, must be 

 treated as a stranger ; to use an English idiom expressing the 

 situation, he is not " recognized." Other varieties of the custom 

 show similar preponderant adhesions. Another custom, here 

 called tcknovymy, or naming the parent from the child, prevails 

 among more than thirty peoples ; as an example was mentioned 

 the name of Ra-mary, or Father of Mary, by which Moffat was- 

 generally known in Africa. TTiis custom proves on examination 

 to adhere closely to those of residence and avoidance, the three 

 occurring together among eleven peoples— that is, more than six 

 times as often as might be expected to happen by chance 

 concurrence. Their connection finds satisfactory explanation in 

 the accounts given of the Cree Indians of Canada, where the 

 husband lives in his wife's house, but never speaks to his 

 parents-in-law till his first child is born ; this alters the whole 

 situation, for though the father is not a member of the family, 

 his child is, and so confers on him the status of " Father of 

 Soand-so," which becomes his name, the whole being then 

 brought to a logical conclusion by the family ceasing to cut him. 

 These etiquettes of avoidance furnish an indication of the direction 

 of change ia social habit among mankind : there are eight 

 peoples (for instance, the Zulus) where residence is in the hus- 

 band's family, with the accompanying avoidances, but at the same 

 time avoidance is kept up between the husband and the wife's 

 family, indicating that at a recent period he may have habitually 

 lived with them. The method of tracing connection betweer> 

 customs was next applied, with the aid of diagrams, lo the two^ 

 great divisions of human society, the matriarchal and the patri- 

 archal, or, as Dr. Tylor preferred to call them, the maternal and 

 paternal systems ; and the method showed that the drift of society 

 has been from the maternal to the paternal system. Examination 

 was next made of the practice of wife capture, recorded among 

 about a hundred peoples, as a hostile act, a recognized and con- 

 doned mode of marriage, or a mere formality. It appears from the 

 tables that the rules of human conduct are amenable to classifica- 

 tion, so as to show by strict numerical treatment their relations to 

 one another. It is only at this point that speculative explanation 

 must begin, guided and limited in its course by lines of fact. 

 In the words of Prof. Bastian, the future of anthropology lies in 

 statistical investigation. Dr. Tylor's pajier showed that the 

 institutions of man are as distinctly stratified as the earth on 

 which he lives, succeeding one another independently of 

 difference of race and language, by similar human nature acting 

 through necessarily changing conditions of savage, barbaric, and 

 civilized life. 



Royal Meteorological Society, November 21.— Dr. W. 

 Marcet, F.R.S., President, in the chair.— The following papers- 

 were read : — Results of an investigation of the phenomena of 

 English thunderstorms during the years 1857-59, by Mr. G. J. 

 Symons, F.R.S, This paper was written nearly thirty years^ 

 ago ; it has now been communicated to the Society at the request 

 of the Thunderstorm Committee. The paper contains a sum- 

 mary, chiefly in statistical form, of some of the results of an- 

 investigation into English thunderstorms and the accidents pro- 

 duced by lightning during the years 1857-59. The author found 

 that in sheet-lightning the most prevalent colour is white, theiv 

 yellow, blue, and red. In forked lightning the order is nearly 

 reversed, blue being more than twice as frequent as any other 

 colour, then red, white, and most rarely yellow. Sheet-lightning 

 was seen about twice as often as forked. — Notes on the meeting 

 of the International Meteorological Commitee at Zurich in 

 September 1888, by Mr. R. li. Scott, F.K.S. The Committee 

 recommended certain rules for the publication of data by travel- 

 lers, &c., so as to insure their being useful for the advancement 

 of sound climatological knowledge. The proposals for an 

 international cloud nomenclature, as recommended by Mr. 

 Abercromby and Prof, llildebrandsson, did not commend them- 

 selves to the Committee, who suggested that the subject should 

 be further studied. At the conclusion of the meeting the Com- 

 mittee was dissolved. — On a method of photc^raphing cirrus- 

 clouds, by Dr. A. Riggenbach. The author exhibited some 

 photographs of cirruS and other fine clouds which had been 

 obtained by using the surface of the lake as a polarizing mirror. 

 — Mr. A. C. Stratten exhibited some models of very large hail- 

 stones — spheres about 24 inches in diameter — which fell at 

 Montereau, about forty miles southeast of Paris, on August 15, 



