2l8 



NATURE 



I'/niy 8, 1 8 So 



surface outflow, he could trace an underflow of sea-w.iter up the 

 channel ; and this he could attribute to nothing else than the sli^^ht 

 excess of dmvmvard and therefore lateral pressure in the outside 

 column, depending on the continually-maintained reduction in 

 the mean salinity of the iniidc column, which more than com- 

 jiensated for any slight excess in its level. 



William B. Carpenter 

 56, Regent's Park Road, London, N.W. 



The Freshwater Medusa 

 In Nature (vol. xxii. p. 190) Prof. Lankester refers to a 

 statement of mine in the preceding number, that I had arranged 

 with Mr. Sowerby some methods of observation from which I 

 h jped to obtain data for the determination of important points 

 regarding the development of the freshwater Medusa, aud ex- 

 p.-esses a desire to be infcrmed as to the nature of the proposed 

 methods. 



The obvious and only practicable course to be adopted with 

 this view was arranged with Mr. Sowerby by Mr. Busk and 

 myself, and consisted in the separation of specimens from the 

 Victoria tank and their confinement in glass jars, which, in 

 order to secure a continuance of the necessary temperature con- 

 ditions, were to be relained in the same house with the tank 

 in which the Medusa had shown itself. The examination from 

 lime to time of these jars would probably bring to light facts 

 having a direct bearing on the develoi^ment of the animal. This 

 method of observation, indeed, is sj obvious that it must have 

 occurred to any one engaged in the investigation it was designed 

 to aid. 



Prof. Lankester now says that Mr. Sowerby informs him that 

 he had undertal;en no experiments except such as had been 

 caiTied out at his request ; but as it seems that the-e are iden- 

 tical with those proposed by Mr. Busk and myself, nothing has 

 been thereby lost. 



Residing at a distance from London, my opportunities of 

 studying the life-history of the Medusa are at this moment 

 comparatively few. Prof. Lankester, however, being on the 

 s,X)t, and having an unlimited supply of subjects for investiga- 

 tion, will doubtless avail him- elf of the advantage thus afforded, 

 and will render our knowledge of thi-; remarkable little animal 

 more complete than would otherwise have been possible. 



Prof. Lankester refers to the difference of opinion between 

 himself and me, and promises to bring proofs of his own views. 

 When these proofs are offered I shall gladly accept them. My 

 desire is that no previous expression of opinion shall blind me to 

 evidence in favour of a contrary position. The only important 

 points, however, on which my conclusions have been absolutely 

 at variance with those of Prof. Lankester are the presence of a 

 c'rcular canal and the pervionsness of the distal extremities of 

 the radial canals. With regard to these there cannot in my 

 opinion be the slightcat doubt. 



The nature of the marjinal bodies is also a point of much im- 

 portance in this investigation, but I have expressed only a con- 

 ditional opinijn with legard to it. While Prof. Lankester 

 consideied these bodies as undoubtedly tentacular, I held that the 

 evidence afforded by adult and by comparatively young speci- 

 mens is in favour of their velar origin ; but at the same time I 

 stated that this point cannot be decided without the evidence 

 obtained from development. 



I also drew attention to the remarkable attachment of the 

 tentacles, whose adnate b.isal portion occupies exactly the posi- 

 tion of \\\& pcronia in the Narcomedu-re and Trachomedux, but 

 1 failed to find evidence of the presence of true peronia as 

 described by Prof. Lankester, who now admits that the peronia 

 while present are rudimental. 



The other jioints, namely those which concern the systematic 

 position of the Medusa, are necessarily only hypothetical. It 

 appeared to me that while there are certain features in the 

 structure of the adult Medusa which point towards the Tracho- 

 medusa:, there are others which connect it with the Leptomedu.a:, 

 to which on the whole it seemed to be more closely allied, though 

 holding a position intermediate between the two ; but I regarded 

 the data in our possession as insufficient for the final determina- 

 tion of this point, which can be absolutely settled by the study of 

 development alone. 



Prof. Lankester promises details of his observations in this 

 month's number of the Quarterly Journal of Microscopic ScUnee, 

 and I look forward to what I doubt not will be a valuable 

 contribution to hydroid 20olo7y. 



As to the nane of the Medusa, Prof. Lankester, while aban- 

 doning his generic name in favour of mine, declares it to be his 

 intention to retain his own specific name for the animal. This 

 is to me a matter of complete indifference. Science can gain 

 nothing from personal contention about names, and the time so 

 occupied miglit with far greater advantage be devoted to more 

 useful and lasting work. 



J. Allman 



On the Simplest Continuous Manifold of Two 

 Dimensions and of Finite Extent 

 So far as I am concerned Mr. Frankland answers too soon 

 (p. 170), for I am sorry to say I have not read Klein in the 

 meantime. Therefore my reply is provisional. A hint was 

 given of Mr. Frankland's exijlanation by Mr. Newcomb in a 

 phrase quoted by Mr. HalsteJ (American Jjurii. of Math., I. 

 iii. 275, paper on the bibliography of hyperspace, &c.) : "The 

 first elements of complex functions imply that a line can change 

 direction without passing through infinity or zero." We do not 

 require even the first elements of complex functions to tell us 

 that we can get to the other side of a point without pajsing 

 through it, provided we can go round it. But the question was not 

 whether "a line" simply could be thus reversed, but whether it 

 could be so with the geodetic perpendicular in question described 

 in a uniform continuous manifold of two dimensions. Mr. 

 Frankland's explanation expressly takes account of a third 

 di nension. It supposes the moving line to generate a sort of 

 skew helicoid about the fixed line to which it is perpendicular. 

 But how can even initial portions of successive generators be in 

 the same plane, Euclidean or other? This point may seem 

 incidental, but I think it is essential, so I omit further 

 questions. 



Somewhere in his "Dynamic" Clifford says that Klein's 

 double surface is a sphere in which opposite points are con- 

 sidered as one. In this light the mystery disappears. There 

 are two perpendiculars : considered as one they never change 

 sign ; because, considered as two, they periodically exchange 

 signs. But if opposite points do not coincide, they may be "one," 

 but they are not one point ; if they do, is the manifold they 

 compose a surface? Mr. Fran'dand has not called it a surface : 

 but is it continuous? 



There is a very well-known manifold which obviously obeys the 

 laws worked out by Mr. Frankland and Mr. Newcomb, a system 

 of straight lines, not vectors, through a common point ; or, 

 reciprocally, a system of planes. To measure of curvature 

 answers density ; if this is constant, the geodetic distance from 

 a point to a geodetic line is represented by the angle between a 

 straight line and a plane. 



It may be worth while to note one or two oversights in the 

 writing or printing of Mr. Frankland's letter. For \l >J -\ we 

 ought to have an expression involving the angle between the 

 geodetics. The sentence "If a being," &c., is a quotation, and 

 the last word should be "position," not "poise." 



Both Mr. Newcomb and Mr. Frankland understand my 

 intention as more negative than it was. I said (xv. 547) "it 

 could hardly fail to be instructive if Mr. Frankland would 

 explain," &c. Probably I underrated the difficulty, in this 

 Euclidean world, of making it clear that one means just what 

 one says. C. J. MONRO 



lladley, June 29 



A Fourth State of Matter 



It seems to nie that Mr. Tolver Preston in his letter on the 

 above to Nature {vol xxii. p. 192) has somewhat overlooked 

 the con ext in the objections he urges against Mr. Crookes's 

 remark that " an isolated molecule is an inconceivable entity." 

 It i, p'ain that Mr. Crookes meant this statement to apply to the 

 quality, not the existence of a molecule, and granting Mr. 

 Crookes's premisses regarding the constitution of matter, it 

 appears a very fair deduction ; since if the three states of matter 

 (as we know it), v'z., solid, liquid, and gas, owe their different 

 qualities merely to different modes of motion of the ultimate 

 molecules, it is quite conceivable as well as logical to suppose 

 that the latter have a nature totally unlike that of the effects of 

 their motion, and therefore inc mceivable to us by reason of its 

 dissimilarity to anything of which we at present possess any 

 knowledge. 



Again, with reference to the remark, "solid it cannot be," 



