May 9. 1895] 



NA TURE 



which occur in the epithelium of the gills and latjial tentacles of 

 the Marcnnes oyster. 



I also showed that such cells are present in the common 

 oysters, but that the granules they contain are not green. I ! 

 further showed that these cells occur abundantly on the [ 

 siiffaic of the gills, crawling about an<l exhibiting amceboid 

 movement. I also showed that the Marennes oysters are specially 

 fed u\v.m Naviciila ostrearia which contains a highly refractory 

 blue pigment " Marennin,"'and I ?«/fr;-(Y/ that the granular cells 

 of the gills derive their colour from the blue pigment of the 

 naricula; — since it was shown long ago by Claillon (in 1824) that 

 the /mitres de Marennes are ijurjxisely placed by the oyster- 

 culturist into tanks containing the Navicula ostrearia : that when 

 placed there they have gills of the usual yellow-brown colour, 

 but rapidly acquire the green colour ; that they actually feed on 

 the A'az'iiti/a ostrearia. an<l that when removed from this article 

 of diet, they lose the green colour of gills. 



The inference that the " granular cells" are to be regarded as 

 wandering phagocytes, was not first published by me ; and, 

 though I have no doubt of its justification, I may point out that 

 it is an interpretation, and not an observation of fact. 



Lasitly, let me say that I showed by chemical analysis that the 

 green colour of the oyster's gill is not due to any metallic base 

 — either copper, iron, or chromium. The statement made by 

 Carazzi that there is "abbondanra di sesqui-ossido di ferro " in 

 the mud of the tanks where the oysters are fed, is therefore 

 iloubly futile. Every one knows that such mud contains 

 abundance of iron ; but as there is no iron in the green pigment 

 of the i>yster, it is useless to draw attention to the iron in 

 the mud. E. Ray L.ankkster. 



Oxford, May 4. 



immediately gave up the illustration as not coming within my 

 own knowledge, and substituted that of the Apple, of which I 

 myself know several kinds to have distinct and characteristic 

 foliage. Such examples may be multiplied indefinitely. Now 

 the passage in Darwin is as follows: — "Verlot mentions a 

 gardener who could distinguish 1 50 kinds of Camellia when not 

 in flower" {*' Animals and Plants," ed. 18S5, II. chap. xxii. 

 p. 23S) : but Darwin takes the case as an illustration of the fact 

 that structures " though appearing to an unpractised eye abso- 

 lutely undistinguishable, yet really dificr." ^ly use of this case 

 was therefore a wrong one, and as Mr. Dyer has thought fit 

 again to refer to the matter, I take the opportunity of withdraw- 

 ing it once more. W. B.meson. 

 St. John's College, Cambridge. May 5. 



The Origin of the Cultivated Cineraria. 



I M.\I)Ii two objections to Mr. Dyer's account of the history of 

 the Cineraria ; the careful reader w ill observe that his letter meets 

 neither. Mr. Dyer informed us that the cultivated Cinerarias 

 were produced ^^ dy the ^i^euiual accitmulation of smait -'aria- 

 tions,' i.e. without the selection of definite sports. My object 

 in adducing historical evidence of Cineraria sports was to pre- 

 \ent Mr. Dyer's pronouncement from being repeated without 

 further endence. That purpose I think has been attained ; for 

 I notice that in now restating his account Mr. Dyer does not 

 refer to the |)oint, though it was the object of his original exhi- 

 bition of the Cineraria to the Royal Society. That the Cineraria 

 was an excellent " illustration of the amount of variation which 

 could l>e brought about under artificial conditions in a limited 

 time " I should be the last to dispute. .\s I showed in my first 

 letter, there is evidence that the time was very short indeetl. 



Compared with this |Hiint, the second question — that of the 

 hybrid origin of cultivated Cinerarias — is of subordinate interest. 

 For the view that they were originally hybrids, resulting from 

 crosses between C. cruenta^ C. lanata., and other species, I have 

 given the evidence, <)Uoting the explicit statement of contem- 

 ixiraries and the almost universal opinion of practical gardeners, 

 with references to the sources of information. .Mr. Dyer, how- 

 ever (with him Mr. Kolfe) declares that the) arc descended frmn 

 C. erueiita alone. Is this statement a mere inference from the 

 want of likertess between particular cultivated Cinerarias and the 

 wild species, or have -Mr. Dyer and Mr. Rolfe evidence of a 

 more substantial character ? Of course these authorities may be 

 right, and the rest who have written on the matter may be wrong ; 

 Imt I ask for proof of this, and the request can hardly be thought 

 mireasonable. 



Mr. Dyer h.is referred to a remark I made at the meeting re- 

 specting the Camellia. .\t the risk of diverting attention from 

 the real issues, I feel bound to speak of this, for I was then in 

 the wrong. In justice the circumstances nnist be stated. Speak- 

 ing of the Cineraria, Mr. Dyer declared that though the flowers 

 have changed so much, the foliage, which had not been an ob- 

 ject of Selection, still resembled that of his wild plant. I re- 

 plied that though this might be true of the Cineraria, it led to 

 no universal induction, for it is well known that the foli.ige of 

 many plants selected .solely for their flowers or for their fruits had 

 varied greatly. .\s an illustration taken on the spur of the 

 moment, I said that though the m.atter had not come within my 

 own olKerv.-ition. there was. I believed, a |)assage in one of 

 Darwin's books to the efi'ect that the foliage of the several kinds 

 "I Camellia difl'ered so ntuch that they could be recognised by it 

 diHie. Upon .Mr. Dyer interjecting that this was not true, I 



NO. 1332, VOL. 52] 



The Assumptions in Boltzmann's Minimum Theorem. 



.Mr. Ci:i.VER\VELl/s letter in your issue of April 18 leaves 

 many important points in connection with the reversibility of 

 Boltzmann's .Minimum Theorem untouched. On the question as 

 to what different people mean (or think they mean) when they 

 assert that the theorem is true, enough has already been said. 

 What we want to know is what assumptions are involved in the 

 mathematical prciofs of the theorem, why they have to be made, 

 and for what systems they are likely to hold. This question has 

 been ably treated by Mr. Burbury, but in view of Prof. Boltz- 

 mann's assertion that the theorem is one of probability, it is 

 desirable to examine more fully where probability considerations 

 enter into proofs such as Dr. Watson's, w hich contain no explicit 

 reference to them. 



Dr. Watson starts by assuming two sets of molecules so dis- 

 tributed that the numbers haWng coordinates and momenta 

 within the limits of the corresponding differentials are 



F(Pi 



Q»,KP, 



dq„ and /(/, 



1«)ip\ 



. dq... 



If, however, the differential elements arc taken very small (as 

 when we consider a volume-element comparable with molecular 

 dimensions), these expressions no longer represent numbers of 

 molecules, and it is assumed that in this case they represent the 

 probabilities of a molecule having coordinates and momenta 

 within the given limits. 



It is then necessary to assume that the probabilities for the 

 two kinds of molecules are independent of each other. This as- 

 sumption was pointed out to me by Mr. Burbury, and is what 

 I intended to imply in my previous letter when I said that Dr. 

 Watson's assumption was more natural than any other. Under 

 these circumstances alone can we assert that the proliability of a 

 given combination of coordinates and momenta of two molecules 

 is proportional to 



K(/P, 



diiuXfdpi . . . d,j„ 



To make the proof independent of the choice of coordinates, 

 let yy . . . Vm+ii be any other system of coordinates specifying 

 the pair of molecules, so chosen that j'j = O at the beginning 

 of an encounter. Then if -v, . . . .v„,^.„ denote the correspond- 

 ing momenta, we may emjiloy the theorem jiroved in my last 

 British .\ssociation Report, § 14, to write the above expression 

 in the form 



Vfjdy^dy., . . . dy„d.Xi . . . <i'-i„,+«. 



and if we write (dy^jdt)dt for rf)-j, the probability of a con- 

 figuration in which an encounter will take place in the time- 

 element dt becomes 



Vfldy., . . . d.x-Z*„(dyJdt)dt 



corresponding to Watson's expression with (dyyjdt) in place of 

 (dij„',dt). This step involves the assumjition (made above) that 

 dy■^ is small in com|xirison with the dimensions of a molecule. 



From this jjoint on Dr. Watson's proof is easy. But it will 

 be seen that the proljabilities for two molecules are not indepen- 

 dent of each other (Z/Ztv- a collision between them. The method 

 woukl fail if the same pair of molecules were likely to collide 

 repeatedly. Thus the Minimum Theorem depends on the free 

 motions of the molecules quite as much as on the collisions 

 themselves, and it only applies to ga.ses whose molecules mix 

 freely among each other between collisions, not to media where 

 they are densely crowded. In such cases, however,- we have 

 .Mr. Burbury's investigation (Phil. Mag. January 1894). 



If we were to reverse the nu)tion exactly, we should have 

 one in which the probabilities for two molecules before an 



