October 17, 1895] 



NA TURE 



595 



I do not think Sir John Lubbock can know the facts of the 

 case, or he woukl not permit bis name to appear as the god- 

 parent of a liook thus flyblown : nor should its publishers con- 

 tinue to issue it, and this not because the book contains mistakes 

 — all books do that — but because its mistakes have been ]X)inted 

 out, and because its author is a great deal more than Sir Robert 

 Ball, and cannot therefore escape the penalty of such a position. 



The Athen.eum Club, IIknkv II. HoudKin. 



October 4. 



MacCuUagh's Theory of Double Refraction. 



.\n attempt has recently been made l>y Mr. Larnior to re- 

 suscitate MacCuUagh's dynamical theory of double refraction 

 (Kril. Assoc. Rep., 1893 : Phil. Trans., 1894, .\, part ii.), but 

 on examination this theory appears to me to infringe one of the 

 fundamental principles of dynamics, viz. the principle of angular 

 momentum. 



Whatever the constitution of the medium may be, the forces 

 which act upon any element consist of two distinct classes : (l) 

 forces due to the action of contiguous parts of the medium ; (2) 

 forces arising from causes external ttt the element. The forces 

 comi)rised in ibe first class are usually termed stresses ; they act 

 U]>on the surface of the element, and are ctimpletely specified by 

 the nine quantities X,, .\>, &c. The forces comprised in the 

 second' class act upon each element of mass, and arise from 

 attraction or repulsion due to external causes or to the action of 

 the medium upon itself. These forces, from whatever cause 

 they may arise, are capable of being compounded into a single 

 force along a line through the centre of inertia of the element, 

 and a couple altout some axis through this point. In t)rdinary 

 gravitating matter the couple vanishes. 



The equations of motion of the element in terms of the stresses 

 and the force iOiistitiieiit of external action are the analytical 

 ex|>ressions for the principle of linear momentum : but this 

 principle is not sufficient to determine the motion of the medium 

 — it is furthei necessary to satisfy the principle of angular 

 m<mienlum, and any theory which violates the latter principle 

 is dynamically luisound. Now the principle of angular mo- 

 mentum requires that three relations of the form \,v = Vi should 

 exist between the six shearing stresses, thereby reducing their 

 number from six to three, except in the following two special 

 cases. The first case occurs when the medium, previously to 

 being disturbed by the pa.ssage of a wave of light, is not at rest, 

 but ])ossesses an independent angular momentum : that is to say, 

 the medium is what has been termed a gyrostatic one. The 

 second case occurs when the resultant of the external forces 

 which act upon the element consists of a (oiipU as well as a 

 force. In the first case the kinetic energy of the disturbed 

 motion of an element will not be proportional to the square of 

 its velocity of translation, but will contain a term depending on 

 the gyrostatic momentum : whilst in the second case the poten- 

 tial energy must necessarily contain a term due to external 

 action. 



Mr. I.armor assumes that the kinetic; energy of an element is 

 proportional to the .square of its velocity of translation, so that 

 the medium he considers is not a gyrostatic one ; whilst the 

 potential energy is supposed to be a quadratic function of the 

 rotations, and he obtains his equations of motion by means of 

 the principle of least action. Now, as we have pointed out, the 

 potential energy of an element may consist of two distinct parts, 

 viz. one due to deformation, and the other due to the action of 

 external causes : anil it is (juite legitimate to assume l>y way of 

 trial that the former part contains rotational terms. But it is 

 well know 11 that a (piadratic expression which contains rotational 

 terms will not .satisfy the conjugate relation between the .six 

 shearing stresses, and consequently the principle of angular 

 moinenlum will be violated, unless e\ery element of the medium 

 is under the influence of .some system of forces, of the kind 

 belonging to the .second class, the couple con.siituent of whose 

 resultant does not vanisli. The potential energy ought therefore 

 to be of the form W + \ , where W is the portion due to deforma- 

 tion, whilst \' is the portion due to external causes which 

 supplies the couple which is necessary in ortler to prevent the 

 principle of angular momentum being violated ; and unless 

 Mr. l.aimor is able to sui mount this difficulty, I am at a loss to 

 unilerstand how his paper is an improvement upon theories 

 which are at any rate dynaiitually sound, whatever other imper- 

 fections they may possess. The question is one which cannot 

 be disposed of by pages of vague and obscuie generalities, but 



requires a detailed and carefiil mathematical investigation for its- 

 elucidation. A. B. Basset. 

 Ilolyport, Berks, October 3. 



The Southern Carboniferous Flora. 



So far as I am aware, Ur. Kurtz's paper on the newly dis- 

 covered Carboniferous Flora in Argentina had not been noticed 

 in print in this country until the appearance of the number ot 

 N.^TiRi-; for September 26, which contained a note (p. 523) 

 giving a brief abstract from the translation published in the 

 Records of the Cieological Survey' of India. "The circumstance 

 that the original paper, which appeared nearly a year ago, was 

 in Spanish, may have caused its being f)verlooked. 



The subject of the ancient Southern floras is naturally un- 

 familiar to most Kuropean geologists, and I hojie I may be 

 allowed to point out why the present discovery is important. 

 It completes a mass of evidence gradually accumulated. It 

 is, of course, well know n that several successive floras of Upper 

 Palaeozoic and Lower and Middle Mesozoic .Vge have been found 

 a.ssociated with beds mainly of freshwater origin, some of which 

 combine valuable coal seams, in India, .\ustralia, and South 

 .\frica. The most ancient of these beds in .Australia and South 

 Africa contain certain plants, amongst them a Lepidodendron , 

 allied to the ordinary Carboniferous flora of Europe and North 

 -\nierica. f^rom the upper beds in all the three regions named, 

 Ferns, Cycads, and a few other plants have been obtained that 

 are related to the Rhatic and Jurassic types found in European 

 rocks. Between the upper and lower plant-bearing strata \\\ 

 South .Vfrica and .\ustralia, and beneath the upper .series in 

 India, are found beds, with coal seams in places, containing by 

 far the most remarkable flora of the whole, the Glossopteris- 

 flora, as it has been called. The particular interest attaching to 

 this flora is mainly due to two circumstances. (I) It is clearly 

 Upper Takvozoic, for in .Australia the coal measures con- 

 taining it are interstratified with marine beds abounding in 

 carboniferous fossils, and yet it differs radically from any known 

 European or North .American flora of that age. (2| The basal 

 betls, in India, .Australia, and South -Africa, are boulder beds, re- 

 sembling the Pleistocene glacial l)oulder clay more than they do 

 any other formation. 



Now in -Argentina the occurrence of the Southern Jurassic or 

 Rha'tic flora has been known for some years, and Prof. Derby 

 has called attention to the presence in Southern Brazil of a great 

 boulder bed, that very probably corresponds in character and 

 geological position to the Talchir beds of India and the Dwyka 

 beds of South Africa. More recently traces of the ancient 

 Lejiidodentlron flora have been discovered in .Argentina, anil 

 some additions to that flora are described in Dr. Kurtz's paper. 

 But the important announcement in this paper is the discovery 

 in .Argentina of thr^e Indian lower Ciondwana plants, Xenrop- 

 tcridiiim '.•alidtait, Gangamopleris cyilopteroides, and Naggera- 

 tliiopsis liislofi, all three as.sociated in India w ith the Karharb.iri 

 coal-seams near the base of the lA)wer Ciondwana. Two of the 

 species are also found or represented by closely allied forms in 

 .\ustralia and South .Africa. In .Argentina, as in India, 

 .Australia, and South .\frica, there is a remarkable absence in 

 this particular flora of forms characteristic of the I'pper Pakvozoic 

 of Europe, no representati\'e (>f Lepidodendron tir Sigillaria 

 occurs, and the Kerns, ("ycads, and Equisetacea' that constitute 

 the flora are related to European Mesozoic types. 



It is flifiicult to understand how two floras diflering from each 

 other far more widely than do any two continental floras living 

 on the earth's surface at the present day, can have coexisteil 

 unless there was, for a long iieriod of geological time, a great 

 .southern continent — the tlondw.ina-land of Sucss — isolated by a 

 wide sea, probably an ocean, from the land that occupied in 

 Carboniferous and Permian days so wide an area in the northern 

 hemisphere. The importance of the new discovery is the 

 immense extension that it gives to Ciondw.ina-land, and the 

 proof it affords that the region with its flora extended to the 

 western hemisphere, and included a part, at all events, of South 

 .Vmerica. This appears to indicate that a ct)nsiderable area now 

 occupied by ocean in the southern hemisphere was land in the 

 Carboniferous period. Further research is needed to show 

 whether the various tracts of Gondwana-land were connected by 

 a South Polar land area. W. T. Bi-AMOKU. 



October 4. 



NO. 1355, VOL. 52] 



