June 5, 1890] 



NATURE 



heard them, and that they may therefore be regarded as 

 faithfully reflecting the Pawnee character. As genuine 

 documents, throwing light on the ideas and habits of a 

 primitive people, the stories are of some scientific value ; 

 and students of anthropology will find in them a good 

 deal that is interesting and suggestive. Mr. Grinnell 

 adds various notes, in which he gives much well-arranged 

 information as to the history, racial affinities, and institu- 

 tions of the Pawnees. 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself responsible for opinions ex- 

 pressed 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 of anonymous communications. "[ 



The Influences at Work in producing the Cerebral 

 Convolutions. 



Dr. G. Jelgersma, of Meerenberg, has recently published 

 two remarkable papers, ^ in which he endeavours to explain 

 the influence which leads to the production of the convolutions 

 on the surface of the cerebrum and cerebellum. Many theories 

 have been advanced to account for these. Several authorities 

 have ascribed their presence to mechanical forces operating upon 

 the brain from without, whilst others have sought to explain 

 them by the supposition of different degrees of growth-tension 

 acting upon the brain-surface ; but in every case these theories, 

 when submitted to the test, have broken down, in so far that it 

 is impossible, by means of any of them, to show how it comes 

 about that small animals have smooth brains, and large animals 

 convoluted brains ; how, in short, we should find in the beaver 

 — an animal remarkable for its intelligence — a cerebrum almost 

 entirely smooth, and in the sheep — an animal, shall we say 

 remarkable for its dullness? — a brain with a high convolutionary 

 system. Jelgersma not only explains this, but makes the ap- 

 parent discrepancy the strongest pedestal of support to his theory. 

 Briefly put, his views are as follows : — 



The grey cortex of the cerebrum, which in different forms of 

 the same animal group preserves a tolerably constant thickness, 

 increases by surface extension. Now, if we extend the surface 

 of a smooth-brained animal say four times, we must provide 

 eight times as much white matter to fill the interior of the grey 

 capsule, if we desire to keep the surface even ; or, to put it in 

 different terms, if we lengthen out the radius of the brain say 

 ten times, we acquire a surface extension one hundred times 

 greater, and an internal capacity one thousand times greater. 

 The geometrical law involved is simply this, that in the growth 

 of a body the surface increases with the second, but the interior 

 with the third power of the radius.^ 



Such being the case, it is very evident, seeing that the propor- 

 tion of internal white matter and external grey matter is in all 

 cases a uniform one, that in the evolution of a large animal out 

 of a small animal, a disproportion between the grey capsule 

 and the white core of the cerebrum must result. This is com- 

 pensated for by the extended cortex placing itself in folds or 

 puckers, and thereby reducing the capacity of the capsule to a 

 d^ree which brings it into correspondence with the white con- 

 tents. Consequently, "the formation of the convolutions and 

 furrows is simply the result of the tendency on the part of the 

 superficial layer to increase by surface extension and of a mutual 

 space-accommodation {Rnujtiaccovuitodation) of the grey sub- 

 stance and of the white conducting paths." 



I have not written this short account of Jelgersma's views — 

 important though they be — simply for the purpose of giving 

 them a wider circulation through the pages of Nature, but 

 with the object of stating that the theory advanced has received 

 independent testimony in its favour at the hands of my col- 

 league, Prof George F. Fitzgerald. For two years or more I 

 have been engaged in a research bearing upon the growth of the 

 cerebral hemispheres, and have constantly had occasion to ap- 



' "Uber den Bau des Saugethiergehirns," Mor/>hologisches Jahrbuch, 

 June 1889 ; " DasGehim ohne Balken : eia Beitrag zur Windungstheorie," 

 Neurologisches Centralblatt, March 1890. 



* It is right to state, although, indeed, Jelgersma does not mention it, 

 ■that many years ago Baillarger ascribed the increase of the convolutions 

 with the increase in the size of the animal to the same geometrical law. 



NO. 1075, VOL. 42] 



preciate the unsatisfactory nature of the current theories as to the 

 formation of the convolutions of the brain. Consequently, in 

 February last, before I had read Jelgersma's first article, and 

 before the appearance of the second, 1 explained to Prof Fitz- 

 gerald, as far as I could, the conditions of cerebral development, 

 and asked him if he could offer any geometrical explanation 

 which would account for the appearance of the convolutions. 

 The views which he then advanced were identical with those of 

 Jelgersma, and further, they were expressed in very similar 

 terms. I feel that this adds greatly to the weight of the 

 hypothesis. 



But Prof Fitzgerald went further than Jelgersma, because the 

 latter states that he is unable to explain why the fissures and 

 convolutions should, within certain limits, assume the same for- 

 mation in different animals, Fitzgerald, however, saw the im- 

 portance of his theory in regard to the localization of function 

 in different areas of the cerebral cortex. The surface extension 

 of the cerebrum cannot be a uniform one : the bulgings out in 

 the shape of the convolutions must necessarily be connected 

 with the functions which the areas involved have to perform. 

 Therefore if a given area of grey matter increases it must 

 pucker out, unless an undue quantity of white matter grows all 

 over the inside of the grey cortex. 



D. J. Cunningham. 



Anatomy School, Trinity College, Dublin, 

 May 24, 



The Bourdon Gauge. 



From Prof. Greenhill's letter on this subject in Nature, 

 vol. xli. p. 517, as well as from that of a writer in Engineering, 

 I gather that I did not succeed by my letter (Nature, vol. xli, 

 p. 296) in making quite clear the point of my explanation of the 

 action, since Prof. Greenhill argues that consideration of the 

 longitudinal stresses in the walls leads to the conclusion that the 

 tube would curl up under internal pressure rather than uncurl. 



Towards the top of the second column on p. 296 in my letter 

 I used the words " Consider now the equilibrium of any portion 

 . . . when the internal pressure is applied and before uncurling 

 takes place." Perhaps it would have been clearer to have written 

 '■^ after the internal pressure has been applied,''' &c. In the 

 last figure on the same page the tension T is that exerted by the 

 outer wall of the already distended gauge as it contracts, while 

 p is the thrust of the inner wall, each on the part BC supposed 

 solidified. 



I desire specially to emphasize the words italicized, for my 

 method of explanation amounts to an artifice for taking the 

 distension into account. It is because Prof Greenhill has over- 

 looked this that he arrives at an opposite conclusion, and wishes 

 apparently to reverse the forces in the figure referred to. 



I hope to make this clear by putting the argument again in a 

 slightly different form. 



Starting, as before, with a tube of rectangular section, with the 

 end aa' fixed and bb' free, we arrive at the uncurled condition 

 by taking the tube in imagination through the following series 

 of steps : — 



(i) Remove the ends aa' and Bu', and complete the annulus 

 as indicated by the dotted lines of the figure. 



