io6 



NATURE 



[June 4, 1891 



general systems of Sets, Matrices, or Algebras ; and without 

 much further knowledge I should not attempt to write in any 

 detail about such subjects. I may, however, call attention to 

 the facts which follow ; for they appear to be decisive of 

 the question now raised. Cauchy {Comptes Rendus, 10/1/53) 

 claimed (7«fl;/tfr«/a as a special case of his "clefs algebriques." 

 Grassmann, in turn, {Comftes Kendus,_ 17/4/54; and Crelle, 49) 

 ■declared Cauchy's methods to be precisely those of the Ausdehn- 

 ungslehre. But Hamilton {Lectures, Pref. p. (64), foot-note) 

 says of the clefs algebriques (and therefore, on Grassmann's 

 own showing, of the methods of the Ausdehnungslehre) that 



they are " j«c/M(/^a' in that theory of Sets in algebra 



announced by me in 1835 of which Sets I have 



always considered the Quaternions to be merely 



a particular CASE. " 



But all this has nothing to do with Quaternions, regarded as 

 a calculus " uniquely adapted to Euclidian space." Grassmann 

 Jived to have his fling at them, but (so fiir as I know) he 

 ventured on no claim to priority. Hamilton, on the other 

 hand, even after reading the first Ausdehnungslehre, did claim 

 priority and was never answered. He quoted, and commented 

 upon, the very passage (of the Preface to that work) my allusion 

 to which is censured by Prof. Gibb*;. [Lectzires, Pref. p. (62), 

 foot-note.] I still think, and it would seem that Hamilton also 

 thought, that it was solely because Grassmann had not realized 

 the conception of the quaternion, whether as )3a or as ;3a~\ that 

 he felt those difficulties (as to angles in space) which he says he 

 had not had leisure to overcome. I have not seen the original 

 work, but I have consulted what professes to be a verbatim 

 reprint, produced under the author's supervision. \Die Ausdehn- 

 ungslehre von 1844, oder die lincale Ausdehnungslehre, S^c. 

 Zweite, im Text unverdnderte Auflage. Leipzig, 1878.] Prof. 

 Gibbs' citations from my article give a very incomplete and one- 

 sided representation of the few remarks I felt it necessary and 

 sufficient to make' about Grassmann. I need not quote them 

 here, as anyone interested in the matter can readily consult the 

 article. 



In regard to Matrices, I do not think I have ever claimed 

 anything for Hamilton beyond the separable <p, and the symbolic 

 cubic (or biquadratic, as the case may be) with its linear factors ; 

 and these I still assert to be exclusively his. My own work in 

 this direction has been confined to Hamilton's cp, with its square- 

 root, its applications to stress and strain, &c. 



As to the general history, of which (as I have said above) I 

 claim no exact or extensive knowledge, Cayley and Sylvester 

 will, no doubt, defend themselves if they see fit. It would be 

 at once ridiculous and impertinent on my part were 1 to take up 

 the cudgels in their behalf. P. G. Tait. 



The Spinning Ring. 



I cannot suppose that the mathematicians are all in error ; 

 but venture modestly to ask what are the assumed conditions 

 under which a girdle round the earth at the equator would be 

 subject to strain. If the surface of our globe at the equator 

 were continuous and level land, about 30,000,000 of persons — 

 more than 1000 to a mile— standing at equal distances and join- 

 ing hands, would form a girdle without any strain, or the girdle 

 might be formed of separate pieces of wire placed end to end in 

 close contact, which, if afterwards soldered, would form a girdle, 

 without strain. 



Then, it is stated, in Nature, vol. xliii. p. 514, that a wire 

 girdle supported on poles, if "relieved from gravitation," but 

 acted upon by a (greatly augmented) "centrifugal force equal 

 to the cable's weight "—that is, by an equal force acting in the 

 opposite direction— would be subjected to a 20 fold strain. 

 Why ? Reginald Courtenay. 



4 Serjeants' Inn, Fleet Street, April 30. 



Bishop Courtenay's questions may perhaps be clearly 

 answered as follows. The centrifugal force of a free spinning 

 hoop has to be balanced by its peripheral tension ; but this, 

 having a large tangential and a small radial component, acts at 

 a disadvantage, and may have to be very big to balance even a 

 moderate centrifugal force. The larger the hoop the more 

 marked is the magnitude of the tangential component as com- 

 pared with the radial or effective component ; so that a hoop 

 8000 miles in diameter could not rotate even once a day without 

 tearing itself asunder. 



NO. 1 127, VOL. 44] 



An actual girdle round the earth is not dependent on peri- 

 pheral tension for balancing its centrifugal force, since it is 

 subject to an overpowering centripetal force due to the earth's 

 gravitation. 



The statement made by Mr. Herschel on p. 514, vol. xliii., 

 involved not a 20-fold stress but a 20-fold speed, which means 

 a 400-fold stress. Oliver J, Lodge. 



The Use of Startling Colours and Noises. 



Last January a friend showed me a smew {Afergus albellus) 

 shot on the Dee, near Chester, the crop of which he had found 

 to be full of young flat-fish. He called attention to the dazzling 

 whiteness of the bird's breast, and suggested that it must frighten 

 the fish, and so be a disadvantage to it. A little consideration 

 showed that the effect would be precisely the reverse. As long 

 as the flat-fish remains at rest, its colouring assimilates so closely 

 to the sand on which it lies, and with which it partly covers 

 itself, that it would not be easily seen by the smew. But if, 

 startled by the white object flashing down on it from above, it 

 moves, it is seen at once, and of course captured. Anybody 

 who has ever collected small insects, such as beetles, will admit 

 the truth of this at once. 



The same effect is probably produced by the hooting or 

 screaming of owls when hunting at night. A mouse, which 

 would be invisible even to the sharp eyes of an owl when 

 motionless, would be seen at once if startled into motion by the 

 sudden " shout " of the bird, whose noiseless flight had brought 

 it unperceived into close proximity. 



Perhaps these suggestions may serve to explain other apparent 

 difficulties in the way of natural selection. 



The brown owl hoots throughout the winter here, so that it 

 cannot be a sexual call. Alfred O. Walker. 



Nantyglyn, Colwyn Bay, May 25. 



The Formation of Language. 



I PERCEIVE that my note on the evolution of speech in the 

 case of one of my children has excited some interest and called 

 out communications both to myself and to you ; but I must tres- 

 pass again on your kindness to explain that what I considered 

 noteworthy in that case was not the invention of words, which 

 is not of rare occurrence, but the, to me, far more important 

 phenomenon of the evolution of the habit of speech through 

 the three stages, so distinctly marked in this case — of simula- 

 tion, the faculty we share with the monkey, and which does not 

 imply the possession of the idea ; of invention of symbols, which 

 indicates the birth of the power of conception, and perhaps 

 the formation of what Max Miilier calls "concepts," and the 

 perception by the young mind of a community of interest and 

 intelligence ; and, finally, the faculty of learning from others 

 ideas already formed, or what must be considered the germ of 

 science : and it was the clear demarcation of the three states 

 which interested me more than the mere invention of words. 

 And this interest is the greater as the case appears to illustrate 

 a law that the development of the individual follows the lines of 

 the universal, so that the child but repeats, in a very much 

 abbreviated sequence, what humanity had gone through as a 

 whole. My purpose in bringing the case before your readers was 

 rather to invite the repetitions of my observations with a view 

 to the establishing of the law, than to publish an isolated 

 phenomenon. W. J. Stillman. 



Rome, May 8. 



Cordylophora lacustris. 



It will be interesting to zoologists to know that Prof. Weldon 

 recently found very large quantities of Cordylophora lacustris on 

 submerged roots and stems in the Rivers Ant, about Ludham 

 Bridge, and Thurne, at Heigham Bridges, Norfolk. From my 

 own knowledge, I can say that it is very generally met'with 

 throughout the whole system of rivers and broads in connection 

 with the Bure. At the places spoken of, a fresh-water tide of 

 from 6 to 18 inches is felt. I think I am safe in saying that a 

 salt tide has but once been known so high up these rivers. 



John Bidgood. 



7 Richmond Terrace, Gateshead-on-Tyne. 



