164 



NATURE 



\_Dec. 15, 1887 



abundance of seeds, grains, nuts, acorns, &c., plainly indicates the 

 vegetable character of the diet of these lake-dwellers, the appear- 

 ance of masses of husked wheat and barley proves that they 

 practised agriculture, and understood how to thrash and winnow 

 the grain. Considerable interest attaches to the discovery below 

 the peat, in what is characterized as the archaic bed, of large 

 masses of seeds, determined by Prof. Sordelli as identical 

 with those of the cultivated so-called Indian poppy {Papaver 

 somniferum). Heer has recorded in the Swiss pile-dwellings 

 the presence of poppy seeds which he referred to P. seligeriim, 

 but whether the Italian and the Swiss remains belong to the 

 same or different species of poppy, the use to which they were 

 put by primaeval men in the two countries remains an unsolved 

 problem. — On the Polynesians, their origin, migrations, &c., by 

 MM. Lesson and Martinet. The purpose of this work is to 

 refute the three most generally accepted theories regarding the 

 origin of these races, viz. whether they are survivals from an 

 almost wholly submerged continent, or whether they are of 

 American, or of Asiatic descent ; and to maintain the novel 

 hypothesis that they are descendants of Maoris of the Middle 

 Island of New Zealand. These views the authors endeavour to 

 support by showing close analogies of language between the two 

 peoples, affinities between certain names of places and of deities 

 used by both, and frequent identity in forms of belief, rites, and 

 superstitions. They further point out that the natives of the 

 Marquesas, who are regarded as of the purest Polynesian race, 

 use the same word, Havaiki, as the Maoris to denote their 

 original ancestral home. From these and numerous other lin- 

 guistic affinities the writers conclude that the Maoris are the auto- 

 chthonic ancestors of the Polynesians, and that the Maori language 

 is the mother speech of all the Polynesian dialects. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, November 24. — "On the Motion of a 

 Sphere in a Viscous Liquid." By A. B. Basset, M. A. Com- 

 municated by Lord Rayleigh, D.C.L. , Ssc. R.S. 



The determination of the small oscillations and steady motion 

 of a sphere which is immersed in a viscous liquid, and which is 

 moving in a straight line, was first effected by Prof. Stokes in 

 his well-known memoir " On the Effect of the Internal Friction 

 of Fluids on the Motion of Pendulums" (Camb. Phil. Soc. Traus., 

 vol. ix. part 2, p. 8) ; and in the appendix he also determines 

 the steady motion of a sphere which is rotating about a fixed 

 diameter. The same subject has also been subsequently con- 

 sidered by Helmholtz and other German writers ; but, so far as 

 I have been able to discover, very little appears to have been 

 effected with respect to the solution of problems in which a solid 

 body is set in motion in a viscous liquid in any given manner, 

 and then left to itself. 



In the present paper I have endeavoured to determine the 

 motion of a sphere which is projected vertically upwards or 

 downwards with given velocity, and allowed to ascend or descend 

 under the action of gravity (or any constant force), and which 

 is surrounded by a viscous liquid of unlimited extent, which is 

 initially at rest excepting so far as it is disturbed by the initial 

 motion of the sphere. 



In solving this prol)lem, mathematical difficulties have com- 

 pelled me to neglect the squares and products of velocities, and 

 quantities depending thereon, which involves the assumption 

 that the velocity of the sphere is always small throughout the 

 motion ; and I have also assumed that no slipping takes place 

 at the surface of the sphere. The problem is thus reduced to 

 obtaining a suitable solution of the differential equation — 





where 



D = 



dr' 



sin % d 

 r de 



(cosec b'^ V 

 dd) 



^ is Stokes's current function, and /u is the kinematic coefficient 

 of viscosity. The required solution is obtained in the form of a 

 definite integral by a method similar to that employed by Fourier 

 in solving analogous problems in the conduction of heat ; the 

 resistance experienced by the sphere is then calculated, and the 

 equation of motion] written down and integrated by successive 



approximation on the supposition that ju is a small quantity. 

 The values of the acceleration and velocity of the sphere to a 

 third approximation are found to be 



-f^- 



Va« 



fka h^ !(i - \t)m + 'Jt\ +f^rd'-f.t, -^'{i- IXt), 



V T 



V = ((I 



■') + Vf 



-f"^/:{i'^r>-'^-'i!-\''^^'-^"'-'"'- 



where 





90 



<p{l) = f',-^^{(-r)-ldr, 



\=/cti. 



p being the density of the liquid, <r that of the sphere, and a its 

 radius. 



It thus appears that, after a very long time has elapsed, the 

 acceleration will vanish and the motion will become steady. 

 The terminal velocity of the sphere is /A. — ', which is seen to 

 agree with Prof Stokes's result. 



If the sphere were projected with velocity V, and compelled 

 by means of frictionless constraint to move in a horizontal 

 straight line, the values of the acceleration and velocity would 

 be obtained from the preceding formula; by expunging the terms 

 /e-^', /A- " (i -<-\0, in the expressions for v and z/ respect- 

 ively, and then changing/" into - Va. 



The preceding resulls can only be regarded as a somewhat 

 rough representation of the actual motion, for (i) the square of 

 the velocity has been neglected ; (2) no account has been taken 

 of the possibility of hollow spaces being formed in the liquid ; 

 (3) if the velocity of the sphere became large, the amount of 

 heat developed would be sufficient to vaporize the liquid in the 

 immediate neighbourhood of the sphere, and the circumstances 

 of the problem would be materially changed. 



In the latter part of the paper I have considered the problem 

 of a sphere, surrounded by a viscous liquid, which is set in rota- 

 tion with given angular velocity, H, about a fixed diameter, and 

 similar results are obtained. To a first approximation the angu- 

 lar velocity is equal to n,€-\ where A is a positive constant, 

 which shows that the motion ultimately dies away. 



December 8. — "The Sexual Reproduction of Millepora 

 plicata." By Dr. Sydney J. Hickson. 



Considerable attention has of recent years been paid by 

 naturalists to the phenomena connected with tha sexual repro- 

 duction of the Hydromedusa;. Stimulated by the brilliant results 

 obtained by Allman and Weismann, several naturalists have 

 investigated the structure of the various Medusa; and medusoid 

 gonophores found in the group, the origin of the sexual cells, 

 and the development of the embryo. These results have, on 

 the whole, been so interesting and important that it was confi- 

 dently anticipated that an investigation of the phenomena con- 

 nected with the sexual reproduction of Milleporidre would yield 

 results of considerable interest. The systematic position of this 

 family has always l)een a doubtful one, and naturalists were 

 agreed that until the sexual reproduction was described, the 

 position assigned to them could only be considered a temporary 

 one. 



It was my good fortune when in Talisse Island, North 

 Celebes, to find on the reef just opposite my hut a fine specimen 

 of j^////^/ora//2V«/« in vigorous growth. I visited it whenever 

 the tide allowed, in the hopes of seeing the polyps fully ex- 

 panded, and of beinj able to search them for any form of 

 gonophore they might possess. In this, however, I was dis- 

 appointed. Notwithstanding all my precautions, I never 

 succeeded in finding the polyps more than partially expanded, 

 and I could find no gonophores. 



Having collected some specimens and dissolved the cal- 

 careous skeleton in strong acid, I discovered in the canals 

 of the ccenosarc both the ova and the spermospores ; but the 

 unforeseen difficulties to be met with in working in a hot little 

 bamboo hut in a tropical island prevented me from making 

 any satisfactory series of sections, and I was reluctantly obliged 

 to leave the further investigation of the subject until I returned 

 to a laboratory in Europe. 



Since my return home I have made a large number of prepa- 



