76 



NATURE 



[July 20, 191 1 



Indeed, it will be speedily ascertained by those who 

 start the course that the experiments indicated require 

 considerably more time than is ordinarily devoted to 

 this branch of botany; however, in this case there is 

 no great ob]ection to superfluity, as it is a simple 

 matter to leave out those experiments considered to 

 be less important. In the circumstances the author 

 was well advised to touch only lightly upon the sensi- 

 tivity of plants, which is discussed in the last chapter. 

 The general method of exposition is original, and a 

 certain number of experiments, such as that devised 

 by Dr. F. Blackman for illustrating the dependance 

 of germination upon oxygen supply are additions to 

 the courses generally followed in botanical labora- 

 tories. There is overmuch insistence on the correla- 

 tion of guessing, reasoning, and trying, and perhaps 

 a superabundance of chemical and physical tests. But 

 these are minor matters of opinion, whereas there can 

 be no question that the book is original, vigorous, and 

 stimulating. 



The Statesman's Year-Book. Statistical and Histo- 

 rical Annual of the States of the World for Hie Year 

 191 1. Edited by Dr. J. Scott Keltie. Pp. lxxii+ 1412. 

 (London: Macmillan and Co., Ltd., 1911.) Price 

 10s. 6d. net. 

 This is the forty-eighth annual issue of a work of 

 reference which has become indispensable to adminis- 

 trators, statesmen, and students of economics and 

 geography. The volume has been thoroughlv revised 

 and brought up to date — a preliminary section of addi- 

 tions and corrections including the results of the 191 1 

 census of the United Kingdom. A series of new maps 

 is provided, and these include maps of the new pro- 

 jected railway routes to India ; railways, navigable 

 waters, and steamship routes; the new Liberian 

 Boundary, iqoq; the northern territory of Australia; 

 and of the Panama Canal from the latest reports of 

 the Isthmian Canal Commission. 



Several sections of the book have been greatly im- 

 proved — those dealing with Turkey, Spain, and China 

 may be mentioned. Altogether this issue of the 

 "Year-Book" will preserve the high reputation the 

 work has secured, and the editor may well be con- 

 gratulated upon his efforts to maintain the accuracy 

 and usefulness of the volume. 



Catalogue of the Serial Publications in the Library of 

 the Manchester Literary and Philosophical Society. 

 Compiled, under the direction of the honorary 

 librarian, C. L. Barnes, by A. P. Hunt. -Pp. vi + 

 177. (Manchester: Published by the Society, 1911.) 

 Price 2s. 6d. 

 The object of this catalogue is to make known the 

 wealth of periodical scientific literature in the librarj 

 of the Manchester Literary and Philosophical Society. 

 The_ total number of current publications at presenl 

 received by the society is 810, and they come from all 

 parts of the world and cover every branch of science. 

 The catalogue is excellently arranged, and is provided 

 with an exhaustive index. It should be of greal ser- 

 vice to members of the society and to oilier- engaged 

 in scientific research. 



The Lore of the Honey-Bee. By Tickner Edwardes. 



Pp. xx f mo. (London: Methuen and Co., Ltd., 



191 1.) Price is. net. 

 The first edition of Mr. Edwardes's book on the 

 bee was reviewed in the issue of Naturi foi Novem- 

 ber 5, 1908 (vol. lxxix., p. 6). This fourth edition is 

 a cheap re-issue of whal has alread) proved a popular 

 work; and. at its present price, such an interesting 

 history of the folk-lore of the bee and accounl ol its 

 activities should become known to a widei circli ol 



NO. 2177, VOL. 87] 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken 0/ anonymous communications.] 



The Deformation of Rocks under Tidal Load. 



I have read with interest Prof. Milne's letter under the 

 above title in Nature of July 13, and congratulate him on 

 the promising character of the results. As he himself 

 remarks, the subject theoretically is not a new one. Its 

 geophysical interest lies largely in the possibility of deriving 

 information from the observed phenomena as to the elastic 

 character of the earth's crust. Several difficulties, however, 

 stand in the way of this information. The earliest mathe- 

 matical treatment of the problem, so far as I am aware, is 

 that by Sir G. H. Darwin, to which Prof. Milne refers, 

 lhe problem which he actually solved relates to the effect 

 of load on the surface of an elastic solid material which is 

 homogeneous, isotropic, and incompressible. In ignorance 

 of this solution, I obtained another ' in 1896 — a simple 

 deduction from the important solution by Prof. Boussinesq 

 for material bounded by an infinite plane — which is some- 

 what more general, in so far as it does not assume incom- 

 pressibility in the material, but otherwise is subject to the 

 same limitations. In practice, the most important of these 

 limitations are probably the assumptions of homogeneity 

 and isotropy. Very possibly, an expert mathematician 

 familiar with recent developments of the mathematical 

 theory of elasticity might have no serious difficulty in 

 removing these restrictions in part or in whole. For in- 

 stance, if a solution were obtained for the case where there 

 is a relatively thin superficial layer differing in elastic 

 quality from the remainder, it would immediately throw 

 light on what is to be expected from differences in the 

 surface strata. 



The solution derived from Boussinesq's for the homo- 

 geneous solid is simple, the formula for the vertical com- 

 ponent w of the elastic displacement at a point in the plane 

 of the loaded surface being J 



:{(l-,)/2,r«}J j(pfr)d<r, 



where p is the normal pressure over the element da oi 

 surface, situated at a distance r from the point where w 

 is being measured, n denotes the rigidity, and >; Poisson's 

 ratio for the material, dw/dx gives the slope measured in 

 the direction of file axis of v, supposed horizontal. We see 

 at once that however complex the distribution of load may 

 be, the slope varies directly as 1— i), and inversely as n. 

 For a given value of n it is 50 per cent, greater when 

 Poisson's ratio is 3 — as it approximately is in steel — than 

 when the material is incompressible. 



There is, however, another aspect of the case that has to 

 be taken into account. The influence of the tide does not 

 consist solely of the pressure effect. At high-tide we have a 

 large additional quantity of gravitating material, the attrac- 

 tion of which modifies the direction of gravity at the land 

 station. If we compare the readings of a delicate spirit 

 level at mid-tide and at high-water, there is an apparent 

 changi of level 4,,+^.,, made up of ii, due to the actual 

 slope of the surface carrying the level, and i„ due to the 

 alteration in the direction of local gravity. Under the con- 

 ditions postulated in my solution of the problem 



<VK> = 2(i ik-,W3"> 



where g is gravity, a the earth's radius, and p its mean 

 density. The ratio varies enormously for values of t/ and re 

 that exist in known materials. Thus we have, measuring 

 re in grammes weight per sq. cm., 



7) = o - 25, « = ?oxio 7 , i|/,/i(/o= 2 approximately, 

 = 0'5, 11= 1 1 ■ 10". =11 ,, 



The first thing to be considered is what does the instru- 

 ment used actually record? Is it ^orip, i . ? In the 

 lattei event, unless >{., i- relatively negligible] we must 



- See Phil. M<i£.. March, 1897, 1 



* Free. Fhysiial Society, vol \v , p. : < , and Phil. Mag., I., ., p 177. 



