June 15, 19 16] 



NATURE 



19 



ot publications, may unfortunately have been 

 overlooked. And there is, I am afraid, the in- 

 stable personal equation of the author, which 

 ids him to take a greater interest in some 

 anches of the subject than in others." 

 -Most readers will be of opinion that the author 

 as held the balance fairly. Formal proofs of 

 existence theorems " are excluded. Some of 

 these, though demanded by the upholders of 

 mathematical rigour, tell us only what we knew 

 before, as Kelvin used to say. Take, for example, 

 the existence of a possible stationary temperature 

 within a solid when the temperature at the sur- 

 face is arbitrarily given, A physicist feels that 

 nothing can make this any clearer or more certain. 

 ^Vhat is strange is that there should be so wide 

 a gap between his intuition and the lines of argu- 

 ment necessary to satisfy the pure mathematician. 

 Apart from this question it may be said that ever}- 

 where the mathematical foundation is well and 

 truly laid, and that in not a few cases the author's 

 formulations will be found the most convenient 

 starting point for investigations in other subjects 

 as well as in hydrodynamics. To almost all parts 

 of his subject he has made entirely original con- 

 tributions ; and, even when this could not be 

 claimed, his exposition of the work of others is 

 often so much simplified and improved as to be of 

 not inferior value. As examples may be men- 

 tioned the account of Cauchy and Poisson's theory 

 of the waves produced in deep water by a local 

 disturbance of the surface (§ 238) — the first satis- 

 factory treatment of what is called in Optics a 

 dispersive medium— and of Sommerf eld's investi- 

 gation of the diffraction of plane waves of sound 

 at the edge of a semi-infinite screen (§308). 



Naturally a good deal of space is devoted to the 

 motion of a liquid devoid of rotation, and to the 

 reaction upon immersed solids. When the solids 

 are "fairly " shaped this theory gives a reasonable 

 approximation to what actually occurs ; but when 

 a real liquid flows past projecting angles the 

 motion is entirely different, and unfortunately this 

 is the case of greatest practical importance. The 

 author, following Helmholtz, lays stress upon the 

 negative pressure demanded at sharp corners in 

 order to maintain what may be called the electric 

 character of flow. This explanation may be ade- 

 quate in some cases ; but it is now well known 

 that liquids are capable of sustaining negative 

 pressures of several atmospheres. How, too, does 

 the explanation apply to gases, which form jets 

 under quite low-pressure differences?^ It seems 

 probable that viscosity must be appealed to. 

 This is a matter which much needs further eluci- 

 dation. It is the one on which Kelvin and Stokes 

 held strongly divergent views. 



The later chapters deal with vortex motion, 



1 The fact that liquids do not hreak under moderate negative pressure 

 \va<i known to T. Youns. " The maenitude of the cohesion between liquids 

 and solids, as well as of the particles of fluid with each other, is more 

 directly shown hy an experiment "n the continuance of a column of mercurj-, 

 in the tub» of a barometer, at a height considc^ibly greater than that at 

 which it usuallv stands, on account of the pressure of the atmosphere If 

 the mercury has been wU boiled in the tube, it may be made to remain in 

 contact with the closed end at the height of 70 in. or more" (Young's 

 " Lecture-^," p. 626, 1807). If the errury he wet, boilin? may be dispensed 

 with, and negative pressures of two atmospheres are easily demonstrated. 



tidal waves, surface waves, waves of expansion 

 i (sound), viscosity, and equilibrium of rotating 

 ; masses. On all these subjects the reader will find 

 I expositions which could scarcely be improved, to- 

 gether with references to original writings of the 

 author and others where further developments 

 may be followed. 



It would not have accorded with the author's 

 scheme to go into detail upon experimental 

 matters, but one feels that there is room for a 

 supplementary volume which should have regard 

 more especially to the practical side of the sub- 

 ject. Perhaps the time for this has not yet come. 

 During the last few years much work has been 

 done in connection with artificial flight. We may 

 hope that before long this may be co-ordinated 

 and brought into closer relation with theoretical 

 hydrodynamics. In the meantime one can 

 scarcely deny that much of the latter science is out 

 of touch with reality. Rayleigh. 



PREHISTORY IX IXDIA. 



Madras Government Museum. The Foote Col- 

 lection of Indian Prehistoric and Protohistoric 

 Antiquities. Notes on their Ages and Distri- 

 bution. By Robert Bruce Foote. Pp. xv-f- 

 246 -f plates 64. (Madras: Government Press, 

 igi6.) Price 145. 8d. 



THIS book must be welcomed, in default of any 

 systematic study of the prehistoric remains. 

 The late Mr. Bruce Foote had, for more than 

 forty years, been collecting stone implements as 

 a bye-issue of his professional work as Govern- 

 ment geologist. In 1901 he published a valuable 

 catalogue of the collection in the Government 

 Museum at Madras. Since then he drew up the 

 present catalogue of his own collection, which 

 has lately been added to that museum. The 

 photographic plates here are sufficiently good, and 

 a large map of India (in end pocket) shows seven 

 distinct classes of prehistoric sites by coloured 

 signs. The arrangement by locality is useful for 

 the future worker, but it makes the grasp of the 

 historical results more difficult to follow. 



The main question, for which no answer seems 

 forthcoming, is that of the relative and absolute 

 age of prehistory in India. Some assurances given 

 here are surprising, as that in India "the iron 

 industry is one of great antiquity (far greater, 

 indeed, than in Europe — e.g., at Hallstatt or La 

 Tene) " (p. 25). Also that " the iron workers 

 were the direct successors and probably lineal 

 descendants of the neolithic people " (p, 3). 

 Further, that only in "the Later Iron Age we 

 reach a period in which we find Indian man had 

 become acquainted with three additional metals — 

 gold, copper, and tin " (p. 3). We see here a 

 position so different from that of western Asia 

 and Europe that some convincing evidences are 

 needed. Yet, unhappily, there is no stratified site 

 to prove the succession of periods (p. 29), nor is 

 there a single evidence stated of the relative ages. 

 The mention of iron in the Ramayana is quoted, 

 but that is onlv of the fourth centurv B.C. Xo 



NO. 2433, VOL. 97] 



