Materials for the Study of Variation Treated with Especial Regard to Discontinuity in the Origin of Species

Fin. 124. Various forms of antenna; of adult Earwigs (Forficula auricularia), all from one garden and taken at one time. I. Specimen having the left antenna normally 14-jointed, and the right 13-jointed. No. (VJ1. IV. Eight antenna normally 14-jointed ; left antenna 12-joiuted. No. 624. Note that the rights and lefts are arranged as marked by letters r and /. The antenna; were so fixed for drawing in order to bring them side by side after the bend from the first joint. This figure was drawn with the camera lucida by Mr Edwin Wilson.

ment was much as shewn in this figure. As shewn, the 3rd joint especially is henratlinlonger than in the 14-jointed form, but srvn-al of the peripheral joints are also a little longer, so that though the 13-jointed antenna is not as a whole so long as the 14-jointed antenna of the same individual it is longer than its first 13 joints. G22. But besides the common 13-jointed form occasional specimens are as shewn in Fig. 124, II. Here both antennas are 13-jointed, the 3rd joint being much longer, and the 4th a little longer than the corresponding joints of the normal with 14 joints. Two specimens were seen having this structure in both antennae, thus presenting a difference which, did it occur in a form known from but few specimens, would assuredly be held to be of classificatory importance.

*G23. In another case (Fig. 124, III) each antenna contained only 12 joints, the 3rd, 4th and 5th being all of greater length than in the normal. 624. Fig. 124, IV shews a case in which there was on the right side a normally 14-jointed antenna but that of the left side was 12-jointed, agreeing nearly with those in Fig. 124, III. In considering these facts the possibility that some or all the abnormal states may result from or be connected with regeneration must be remembered ; but from the frequency of the variations, from their diversity, and from the fact that symmetrically varying individuals are not rare, it is on the whole unlikely that all can owe their origin to regeneration. It will besides be noticed that it is in the proximal joints that the greatest changes are seen, and it must surely be rarely that these are lost by mutilation.

The difficulty — indeed the futility — of attempting to adjust a scheme of individuality among such series of segments must here be apparent to all. We can see the change in number and the change in proportions, and we are doubtless entitled to affirm that the differences between these several kinds of antennae are reached by changes occurring chiefly in the neighbourhood of the 3rd and 4th joints ; but not only is there no proof that the changes are restricted to these joints, but the appearances suggest that there are correlated changes in many, and perhaps in all of the joints.

*625. Among the families of the class Orthoptera the number of tarsal joints differ. In Forficularia the number of tarsal joints 1 In connexion with variation in the number of joints in legs I may mention the case of Stenopterus rufus ? (Longicorn) described by GADEAU DE KERVILLE as having each tibia divided into two parts by an articulation (Le Naturaliste, 1889, s. 2, xi. p. 9, Jig.)- but upon examination it proved that each tibia had been sharply bent at each of these points, and there was no real articulation. I have to thank M. Gadeau de Kerville for lending me this insect together with many interesting specimens of which mention will be made hereafter.

The fa.-t, originally observed by BRISOUT DE BARXEVILLE", that in various sp.-ei.-s of Blattid» the number of tarsal joints may \arv from /nr to /',,///• is therefore of considerable importance in a consideration of th.- manner in which these several forms ha\r been evolved from .-ach other. The species in which BRISOUT oh-crved tlii> variation \\.-iv tdi in number and belonged to four genera of Blatt ida-. At mv -ii'_ru' -tion Mr H. H. BRiNDLEY has made an extended investigation of the matter and a preliminary account of the results arrived at was ^ivun in the Introduction (p. 63). It was found that of Blatta americana 25°/0 of adults have one or

I-'K,. 11~>. I. Normal five-jointed left tarsus of Blatta americana. II. Eight tarsus of the same having four joints. more tarsi 4-jointe<l. In Blatta orientalis these cases amounted to 15°/,, , and of li»2 B. germanica examined, 16 had one or more 4- joint I'd tarsi. Tluabnormality occurred soniftimos in one leg and sometimes in another, being more frequent in the legs of the second pair than in those "f the tirst, and much more frequent in the third pair than in either. In some specimens legs of the two sides were symmetrically affected, but this was exceptional. Only one specimen has hitherto been met with having all the tarsi 4-jointed. There was a slightly greater frequency in females than in males.

When the examination of these abnormal tarsi was begun it was supposed that the variation was congenital, but as explained in a note to the Introduction (p. 65) doubt subsequently arose as to this. It is well known th.-it Blattiche like many other Orthoptera have the power of renewing the appendices ;ifter loss, and Mr Brindley found by experiment ilmt when the tarsus of Jjlu/fn orientalis is renewed after mutilation the resulting tarsus is 4-jointed. It was also found that I y.inted tarsi were much more frequent in adults than in the young. The question therefore arises, is the 4-jointed tarsus ever congenital1?

To this question a positive answer cannot yet be given ; but as about 200 young B. orientalis have since been hatched from the egg and no 4-jointed tarsus was found among them, while in every instance of regeneration the new tarsus had four perfect joints, there is now a presumption that the variation does not occur congenitally. On the other hand it should be mentioned that the 4-jointed tarsus was seen in 3 specimens, found by Mr Brindley, which by their size would be judged to have been newly hatched. But even if the variation shall hereafter be found to be sometimes congenital it is certain that this occurrence must be very rare, and there can be no doubt that in the majority of cases the 4-jointed tarsus has arisen on regeneration1.

As mentioned in the Introduction, the existence of the 4-jointed tarsus, whatever be the manner of its origin, raises two questions. Of these the first is morphological, relating to the degree to which the joints exhibit the property of individuality, and the second is of a more general nature, relating to the application of the theory of Natural Selection to such a case of discontinuous change. The interest of the case in its bearing on both of these questions arises from the Discontinuity, which was complete. All the tarsi seen were either 5-jointed or 4-jointed, and in none of the latter was any joint ever rudimentary, or any line of articulation imperfectly formed (except in a single specimen having a deformed tarsus). There were 5-jointed tarsi and 4-jointed tarsi : between them nothing.

Following the usual methods of Comparative Anatomy it must be asked which of the 5 joints is missing in the 4-jointed tarsus? With reference to this question careful measurements of the separate joints were made by Mr Brindley in 115 cases of 4-jointed tarsi occurring in legs of the third pair in B. americana; and for comparison the separate joints of 115 normal 5-jointed third tarsi of the same species were also measured. (It is clear that the legs compared must belong to the same pair, 1st, 2nd or 3rd, for there is considerable differentiation between them. From this circumstance it was comparatively difficult to obtain a large number of cases, and hence the smallness of the whole number measured. But though of course statistics respecting a larger number would be more satisfactory there is no reason to think that by examination of a greater number of cases the result would be materially affected. )

In the two sets of tarsi the total length of each tarsus was reduced to TOGO, the lengths of the joints heing correspondingly reduced. The arithmetic means of the ratios of the several joints to the whole lengths of the tarsi to which they belonged was as follows : 1 The circumstance that in Mr Brindley's observations the variation was in all species more frequent in females than in males, and that the frequency differed in The e\ id.-nce derived from these numbers lends no support to the expectation th.-it any one particular joint of the 5-jointed form is mi — ing from tli.- 1-jointed, <>r that any one joint of the 4-jointed form corn-pond^ with any two joints of the 5-jointed; for if the numbers are treated with a \ iew to either of these hypotheses it will be found iinp.i»ible ;,, make them agree with either. It appears rather that the four joints of tin- I jointed form collectively represent the five joints of the normal.

The other question upon which the statistics bear has already been .stated in the Introduction. In any appendage the ratio of the length of eachjoinl to the whole length of the appendage varies; but if it varies about one normal form it will be possible to find a normal or in. -an value for this ratio, and the frequency with which other values of the same ratio occur will be inversely proportional to the degree in which they depart, from the normal value. The curve representing the frequency of occurrence of these values will then be a normal Curve of Error. The form of this curve will indicate the constancy with which the normal proportions of the tarsal joints are approached. If the proportional lengths of the tarsal joints vary little then the curve representing the frequency of their departure from their normal value will be a steep curve, but if these proportions are very variable and have little must aney, then the curve will be natter. The probable error will thus in the case of each value be a measure of the constancy with which it conforms to its normal proportions. As explained in the Introduction, upon the hypothesis that all constancy of form is due to the control of Natural Selection, it would be anticipated that the 1 jointed tarsus, if a variation, would be very much less constant in the proportions of its joints than the 5-jointed tarsus. It was however found that as a matter of fact the proportions of the joints of the I jointed form were very nearly as constantly conformed to as those of the joints of the normal tarsus.

The evidence of this is as follows. The total length of the 5-jointed tarsus being L, and tl, t-, A:c, being the lengths of its several joints, I, T1, T3, &c. representing the same measurements in the 4-jointed form, the ratios — &c., — &c., represent the proportional length of the several joints in each case. The values of these ratios \\ere thru arranged in ascending order in their own series and the measures occupying tin positions of the first, second, and third quarterly divisions noted1

(indicated hen after hy v1. -1/ and V3 respectively). The probable error or fi j'i variation of each ratio — , — , Are. will then bo represented by the expression . Inasmuch as the joints are of different lengths, to compare the results each must he oonvi rte.l into percentages of the moan length of the joint concerned. the dift'ei.-nt pairs of legs may -.em to point to the existence of some control other than the Dimple . -l,ane,s of fortuitous injury. As regards the latter point it is not unlikely thai ill. legs of the third pair, being longer and less protected, may lie more often mutilate. 1 than the otln

It is thus seen that the percentage variation of the ratios of the several joints to the total length is very little greater in the case of the abnormal than it is in the normal tarsus. As regards the longer joints these results are probably a trustworthy indication of the amount of Variation, but in the case of the shorter joints the errors of observation must no doubt be so great in proportion to the smallness of the lengths to be measured that no reliance should be placed on results obtained from them.

As evidence that in spite of the small number of instances examined the general result is satisfactory it may be mentioned that the mean obtained as the value of -^~ agrees fairly well in each case both with the value of M, the middlemost value, and also with the arithmetic mean given above. It may therefore be taken that the curve is regular and the series nearly uniform. The correlations between the lengths of the joints and that of the whole tarsus have also been, examined by Mr Brindley using the method proposed by GALTON I.e., the results closely agreeing with those obtained by the ordinary method here described1.

If the 4-jointed tarsus be a congenital variation the significance of the fact that the abnormality is in its constancy to its normal hardly less true than the type-form must be apparent 1 It is hoped that a fuller account of this subject will be given separately. I am indebted to Mr F. Galton for advice kindly given when this investigation was begun, and Mr Alfred Barker has most obligingly given much help in connexion with it. to all. Yet eveE if, as now seems likely, the 4-jointed tarsus I..- not a congenital variation but is rather a result of regeneration, there i-; .-till difficulty in reconciling the now established t'ai-t that tli'' till-in of the regenerated part, though different from tinnormal, i> >carce]y less constant, with any hypothesis that th«- constancy i.t' tinnormal is dependent upon Selection.

If it were true that the smallness of the mean variation of the ratio , which is ultimately the measure of the constancy and truth to type of the 5 -jointed tarsus, is really due to Selection and t«>i hicomparative prosperity of specimens whose tarsal proportions departed little from the normal, to what may we ascribe the smallness of the mean variation of the ratio -j- ? Are we bo suppose that the accuracy of the proportions of the regenerated tarsus is due to the Natural Selection of individuals which in tin ir tarsi conformed to this one pattern ?

\\V antold that the struggle for existence determines every detail of sculpture or proportions with such precision that individuals which fall short in the least respect are at a disadvantage so great as to be capable of being felt in the struggle, and so decided as to lead to definite and sensible effects in Evolution. It' this is so, should we not expect that individuals which had sut'ti'ivd such a comparatively serious disadvantage as the loss of a leg or of a tarsus, would be in a plight so hopeless that even though some of them may survive, renew the limb and even breed, yet, as a class, by reason of their mutilation they musl rank with the unfit? Nevertheless we find not only that there is a mechanism for renewing the limb, but that the renewal is performed in a highly peculiar way ; that in fact the structure newly produced differs from the normal just as species differs from species, and is scarcely less true and constant in its proportions than the normal itself.

Now it' this exactness in the proportions of the renewed limb is due to Selection, it must be due to Selection working among the mutilated alone; and of them only among such as reni'wed the limb; and of them only among such as bred. Moreover if the accuracy of the form of the renewed tarsus is due to Selection working on fortuitous variations in the method of renewal, and not to any natural detiniteness of the variations, the number of selections postulated is already enormous. But this \a.-t nunilier <>f selections must by hypothesis have all been made from amongst the mutilated — a group of individuals that would be suppose -i I to be at a hopeless disadvantage1.

1 The same dilemma is presented in nil cases win-re a special mechanism or device exists (and must lie supposed to have beeu evolved) only in connexion with Deration. An in tain-,- i- to he seen in the Loh-tei 's antenna. As is well known [In- antennai y tilainriit of the Lobster when lost is rein-wed not as a str<ii<iltt out- One or more of the hypotheses are thus clearly at fault. A natural, and I believe a true comment will occur to every one : that probably the injured insects are not at any serious disadvantage, and that these mutilations perhaps make very little difference to their chances. But can we admit that the loss of a leg matters little, and still suppose that the definiteness and accuracy of the exact proportions of the tarsal joints makes any serious difference ?

The hypothesis, therefore, that the smallness of the mean variation in the proportional lengths of the tarsal joints of the 4-jointed tarsus has been gradually achieved by Selection is untenable, whether that 4-jointed tarsus be a product of regeneration or a congenital variation. But if the accuracy with which the abnormal conforms to its type be not due to a gradual Selection, with what propriety can we refer the similar accuracy of the normal to this directing cause ?

The number of radial joints above the basals up to the division of the rays in Crinoids is usually constant in the genera. In Antedon and Actinometra there are normally three such joints, the third radial being the axillary, and none of these bear pinnules. Both increase and decrease in the number of radials has been observed, but variations from this number are rare, more so than variations in the number of rays. CARPENTER, P. EL, Chall. Rep., xxvi. Pt. LX. p. 27.

626. Antedon alternata: specimen having in one ray four radials, none bearing pinnules or united by syzygy. ibid., PI. xxxii.^. 6. 628. Antedon remota, A. incerta, Actinometra parvicirra (Fig. 126); one specimen of each of these species had one ray with only two radials. CARPENTER, I.e., PL xxix. fig. 6; PI. xvin. fig. 4; PL LXI. fig. 1. FIG. 126. Actinometra parvicirra, No. 628. Specimen having only two radials in the ray marked x. (From P. H. CARPENTER.)

growth, as the other appendages are, but when formed again it is coiled up in a tight conical spiral which cannot be extended at all, but is kept firmly in place by the shortness of the skin on the inner curvature. (For figure see HOWES, Jour. Anat. Phys., xvi. p. 47.) During the process of regeneration the antenna is very soft, and were it extended it would from its great length be much exposed to injury. At the next moult after renewal the new antenna is drawn out as a straight filament like the normal, and its skin then hardens with that of the rest of the body. This strange manner of growth occurs only on regeneration. It is hard to believe both

Metncrinitg. Some species have normally 5, others normally 8 radials. If there are 5, the 2nd and 3rd anunit>-<l by syzygy and bear pinnules; but if there are 8, both 2nd and 3rd, and the oth and Oth are thus united and bear pinnules. In I'licntiirrinii* the number of radials is two, and this is also the case in one or two fossil Comatula-. I'l'iitni-rinug has normally three radials lik«- Anti-don. 629. Fentacrlnua mulleri: specimen having in one ray Jour radials, the 2nd and 3rd uniti'il hij mj:ii<jij, though bearing no pinnules. CARPENTER, I.e.; and Chall. Rep.

(1) that the number of individuals that have lost antennae — a serious injury one may judge — and have renewed them, and have bred, can have been enough to lead to tli. . -i;il)lishment by Selection of a distinct and highly special device to be invoked solely on the occasion of mutilation of an antenna ; and also (2) that the 1> t.-t iletidl of normal form is of such consequence as to be rigorously maintained by Selection. LITTLE need be said in preface to the facts of Meristic Variation in Radial Series. In them phenomena analogous to those of the Variation in Linear Series are seen in their simplest form. Just as in Linear Series the number of members may be changed by a reconstitution of the whole series so that it is impossible to point to any one member as the one lost or added, so may it be in the Meristic Variation of Radial Series: and again as in Linear Series, single members of the series may divide. Be- tween these there is no clear line of distinction.

Next, as in Linear Series, Variation, whether Meristic or Substantive, may take place either in single segments (quadrants, sixths, &c.), or simultaneously in all the segments of the body. For instance, a single eye may be divided into two, or there may be duplicity simultaneously occurring in all the eyes of the disc (see No. 634) and so on. These phenomena are here illustrated by facts as to the Meristic Variation of Hydromedusae and of Aurelia. The latter is exceptionally variable and in its changes exhibits important features.

Together with these facts as to Variation in Major Symmetries is given an instance of similar Variation in the pedicellariae of an Echinid, and it will be seen that in this case of a Minor Symmetry the change is perfect and altogether comparable with those found in Major Symmetries of similar geometrical configuration. The best field for the study of the variations of Radial Series is of course to be found in plants ; and in the Meristic Variations of radially symmetrical flowers precisely similar phenomena may be easily seen.