52 



NA rURE 



[May 15, 1890 



into a shape something like the pointed half of the bowl 

 of a spoon. Another statement appears to me of ques- 

 tionable accuracy. The author notices the earth pillars 

 on the southern slopes of the Eggishorn, describing them 

 correctly, but saying of them, " Les pyramides des f^es, 

 aussi appeldes ' blocs perchds.' " Surely this is an 

 unwonted extension of the latter term. 



The pamphlet, in short, is rather disappointing. It is 

 beautifully printed on quarto pages with large margins, 

 and is illustrated with three photogravures of glacier 

 scenery, which would be improved by the omission of the 

 human figures, for these by contrast look like negroes in 

 mourning; but it tells us little that is new, and is a 

 " popular " article rather than a scientific memoir. 



T. G. BONNEY. 



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 anonyjnous communications. ] 



Panmixia. 



Private communications which I have received from natur- 

 alists interested in this controversy, and from Mr. Romanes 

 himself, have thrown light on the apparently irreconcilable 

 difference of the views which have been expressed. 



I think it desirable that an explanation should be afforded to 

 the readers of Nature. 



When Mr. Romanes contends that cessation of selection 

 leads to a dwindling in the size of a useless organ, he now tells 

 me that he assumes that the mean size of the part in all 

 born (what we may call the birth-mean) was smaller than the 

 mean size of that part in those individuals surviving under 

 selection. Hence the withdrawal of selection substitutes in the 

 adult survivors the lower birth-mean for the former higher 

 selection-mean. 



Mr. Romanes had not specifically stated that he made this 

 assumption. 



On the other hand, I had — for the purpose of estimating purely 

 and solely the result of panmixia and cessation of selection — 

 assumed that birth-mean and selection-mean were identical, in 

 which case the withdrawal of selection would, of course, not 

 alter the mean. 



To assume that birth-mean is smaller than selection-mean in 

 a given case seems to me to be introducing causes other than 

 panmixia or cessation of selection. 



It is evident that cases are possible in which the mean given 

 by selection is identical with the birth-mean — others in which it 

 is smaller than the birth-mean, and others in which it is larger. 

 Special causes of a complex character determine whether the 

 ratio is one or the other. If we are to consider the effects of 

 cessation of selection alone, apart from other causes, it seems to 

 me that we must not introduce causes which affect the ratio of 

 birth-mean and selection-mean ; we must eliminate them alto- 

 gether by assuming the ratio to be one of equality. Hence my 

 conclusion that panmixia or cessation of selection alone cannot 

 produce the dwindling of an organ. 



If, however, we admit the assumption that the selection-mean 

 is larger than the birth-mean, Mr, Romanes has my full con- 

 currence in stating that cessation of selection leads to dwindling, 

 and I am of course aware that, given that assumption, Weismann 

 and Galton are of the same mind. 



The point of interest therefore shifts. The question is, whether 

 we are justified in assuming that in organisms generally in a 

 state of nature the mean size of an organ or part in the selected 

 survivors is larger than in all born, or, to ]3ut it fully, larger than 

 would have been the mean size of the part in all born supposing 

 that they had all reached maturity. 



I do not think that we have data which warrant this assump- 

 tion. It is, I think, certain that some cases must some- 

 times occur in which this is the case, and others in which the 

 selection-mean-size is smaller than the birth-mean-size. It is 

 not improbable that in well-established species there is identity 

 of the two means. This is, however, a question which ought 



.to be settled by observation — not of domesticated races, but, if 

 possible, of wild forms. 



It seems to me that this assumption is precisely what Mr. 

 Darwin considered, and refused to make, so that he avoided 

 attributing dwindling of parts to the cessation of selection. He 

 says ("Origin," 6th ed., p. 401) : "If it could be proved that 

 every part of the organization tends to vary in a greater degree 

 towards diminution than augmentation of size, then we should 

 be able to understand how an organ which has become useless 

 would be rendered, independently of the effects of disuse, rudi- 

 mentary, and would at last be wholly suppressed." Mr. Darwin 

 says, "If it could be proved." This is really the whole point. 

 If the greater size of selection-mean than of birth-mean could 

 have been proved, Mr. Darwin was ready to formulate the doc- 

 trine of dwindling by cessation of selection. But, apparently, 

 it could not be proved then. It has not been proved yet. I 

 do not think it at all impossible that it may be proved. The 

 facts are as yet not recorded. E. Ray Lankester. 



May 10. 



Bertrand's Idiocyclophanous Spar-prism. 



It is a good thing that Prof. Silvanus Thompson has brought 

 the above prism to the notice of the Physical Society (see 

 Nature, vol. xli. p. 574) ; it is certainly remarkable that M. E. 

 Bertrand himself has never thought fit to publish any description 

 of his interesting invention. Perhaps it may be worth while to 

 mention a fairly simple method of constructing the prism (which 

 may easily have occurred to others besides myself, and) which 

 has the advantage of requiring only two artificially-worked 

 surfaces, and hence of interfering as little as possible with the 

 natural rhombohedral crystal of Iceland spar. 



Four plane, polished faces are required for the prism, which 

 i?, in fact, a four-sided parallelopipedon, having two opposite 

 sides parallel to the optic axis, while the two others make an 

 angle of 45° with it. 



Now, since in Iceland spar the faces of the natural rhombo- 

 hedron make angles of very approximately 45° (strictly, 45° 24' ) 

 with the optic axis, two of these faces can be utilized for the 

 last-mentioned pair of prism-sides. 



Take, then, a cleavage-rhomb of spar, about l cm. in thick- 

 ness, and having edges about 4 cm. in length (Fig. i) ; observing 



that both the face A B c D and the opposite one, a' b' g' d', are flat 

 and free from blemishes (such a crystal is easily found, even in 

 these spar-famine days). Grind away the solid angle a' down 

 to about the level shown by the dotted lines, working the face 

 thus obtained so that it makes an angle of 45° with the natural 

 face ABC D. Cut away the opposite solid angle c in a similar 

 way, so as to make another plane, parallel to the first. Polish 

 the two cut surfaces, and the prism is complete in all essential 

 particulars. 



Thus, if a beam of common white light is allowed to fall 

 normally on one of the worked surfaces, A, Fig. 2 (which is a 

 section of the prism), it will be (i) totally reflected at the natural 

 face B (corresponding to A B c D in Fig. i) ; (2) pass on through 

 the crystal parallel to the optic axis ; (3) undergo another total 

 reflexion at the opposite natural face c ; and (4) finally emerge 

 through the second worked plane d. An eye placed close to d 

 will then observe the well-known pair of ring-systems side by side, 

 one set complementary to the other. 



A very convenient source of illumination seems to be a lamp- 



