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

The inxt point is especially important. The parts found w i. r(rd h'l/x are those parts which are in the normal leg peripheral t<> Ilif fiuint from which the extra legs arise, and, as a rule no more. Though in extra legs parts may be deficient or malformed, st mi-hires which in the normal leg are central to the point of origin of the extra legs are not repeated in them1. For instance, if the extra legs spring from the trochanter they do not contain parts of the coxa, if from the second tarsal joint, the first tarsal joint is not represented in them, and so on.

Extra legs may arise from any joint of the normal leg, and are not much commoner in the peripheral parts than in the central ones, but there is a slight preponderance of cases beginning from the apex of the tibia. It is rather remarkable that cases of extensive repetition are not much less rare than others, the contrary being for the most part true of the limbs of vertebrates. It does not appear that extra legs arise more commonly from either of the three normal pairs in particular.

Supernumerary legs of double structure are sometimes found as two limbs separate from each other nearly or quite from the point of origin, but in the majority of cases their central parts may be so compounded together that they seem to form but one limb, and the essentially double character of the limb is not then conspicuous except in the periphery. For example it frequently happens that the femora of two extra legs are so compounded together that they seem to have only a single femur in common,

1 Tarticular attention is therefore called to one case of extra antenna, which actually contain parts normally central to the point of origin. (See No. 804.) and careless observers have often thus declared them to be two legs with one femur. Similarly the two tibia? or the two tarsi may be more or less compounded. In the case of Silpha nigrita (No. 7G9), the two extra legs which arose from a femur were compounded throughout their length, having a compound tibia and tarsus (see Fig. 167). Even in cases when the two extra legs appear to arise separately it will generally be found that they articulate with a double compound piece of tissue which is supernumerary and is fitted into the joint from which they appear to arise. This is especially common in cases of two extra tarsi, which seem to spring directly from a normal tibia. As a matter of fact in all such cases these extra tarsi articulate with a supernumerary piece of tissue, as it were let into, and compounded with, the apex of the normal tibia. These bodies are themselves double structures, composed of parts of two tibiae. In determining the morphology of the limbs they are of great importance, but unfortunately they are not generally mentioned by those who describe such formations. But though extra parts are generally present in the leg centrally to the point from which the extra legs actually diverge, it should be expressly stated that if this point is in the periphery of the leg, the central joints are normal : if for example, there are two extra tarsi, there may be parts of two extra tibial apices, but the base of the tibia, the femur, &c. are single and normal.

To appreciate what follows it is necessary to have a distinct conception of the normal structure of an insect's leg, and to understand the use of the terms applied to the morphological surfaces. If the leg of a beetle, say a Carabus, is extended and set at right angles to the body, the four surfaces which it presents are respectively dorsal, ventral, anterior and posterior. In the femur, tibia and tarsu< the dorsal is the extensor, and the ventral is the flexor surface. The anterior surface is seen from in front and the posterior from behind. (The terms 'internal' and 'external' are to be avoided as they denote different surfaces in the different pairs.) Difficulty as to the use of terms arises from the fact that as the beetle walks or is set in collections, the legs are not at right angles to the body but are rotated on the coxae, so that the plantar surface of the first pair of legs is turned forwards, but the plantar surfaces of the second and third ]>.-m- are turned backwards1.

1 Attention is directed to the fact that in a beetle there is a complement :u > relation not only between the legs of the right and left sides but also imperfectly between the legs of the first pair and those of the second and third pairs which air in some respects images of the first leg of their own side. For iiistnnc. , in < '< r.imlii.c (see Fig. 160) the trochanter of the fore leg is kept in place by a process of the coxa which goes down behind it, but the corresponding process in the -eeoml :md tliii.l legs is in front of each trochanter. Again in Melolontha etc. the tibial serrations of

Extra legs may arise from any one of the morphological surfaces, but m»re often their origin is in a position intermediate between them, e.^., antero-ventral, or postero-dorsal. The next question i- ihat of the determination of parts which are extra from the parts which are normal. Two extra legs spring fn.m a normal leg. The appearance is often that of a leg single proximally, but triple peripherally. All three limbs are often .Dually developed and at first sight it might well be supposed ihat t'he three collectively represent the single leg of ill-- ii»niial.

In many cases of Meristic Variation I have contended that the facts are only intelligible on the view that there has been such collective representation. But in these Secondary Symmetries this MI pj H .-it mn is [('always] inadmissible. On closer examination it is generally more or less easy to see that the three legs do not arise in the same way, but that one arises as usual while the other tw<> are., as it were, ingrafted upon it. It is thus possible in all but a very few cases to determine the normal leg from the others by tracing the surfaces from apex to base, when it will be found that some surface of the normal is continuous throughout the appendage while those of the extra legs end abruptly at some part of the normal leg.

Nearly always besides, as has been mentioned, the extra legs are more or less compounded together at their point of origin even if separate peripherally. In a few very exceptional cases it happens that one of the extra appendages is compounded with the nnnnal and not with the other extra appendage. A remarkable rase of this in an antenna may be seen in Melolontha, No. *()(), ami in a leg in Platycents camboides, (q.v.) We have now to consider the positions of the paired extra legs in regard to the normal leg and in regard to each other. At first sight their dispositions seem entirely erratic ; but though it is true that scarcely two are quite identical in structure, yet their divers structures mav for the most part be reduced to a system.

This system, though far from including every case, still includes a large proportion and even the remainder do not much depart from it except in very few instances. The comprehension of the general system will also greatly help to make the aberrant cases appreciated with comparatively few words. For simplicity therefore, the considerati..n of exceptional cases will be deferred and the principles stated iii a general form. It will be remembered that we are as \et concerned only with doi/h/e extra legs.

When extra appendages, arising from a normal appendage, are thoroughly relaxed and extended, the following rules will be the first legs curve backwards, but those of the other legs curve forwards. This i ircumstance is mentioned lest it mi^'lit In- thought to have boon neglected in what follows, but this complementary relation has nothing to do with that which will be shewn to exist between the extra legs. found to hold good with certain exceptions to be hereafter specified.

two extra appendages are in one plane : of the two extra appendages one is therefore nearer to the axis of the normal appendage and the other is remoter from it. and position formed as the image of the normal appendage in a 'plane mirror placed between the normal appendage and the nearer one, at right angles to the plane of the three axes; and the remoter appendage is the image of the nearer in a plane mirror similarly placed between the two extra appendages. Transverse sections of the three appendages taken at homologous points are thus images of each other in parallel mirrors.

As the full significance of these principles may not be at once seen it may be well to add a few words of general description. The relation of images between the extra legs is easy to understand. They are a complementary pair, a right and a left. This might indeed be predicted by any one who had considered the matter. The other principles, which concern the relations of the extra legs to the normal leg, are more novel. For first it appears not that either of the extra legs indifferently may be adjacent to the normal, but that of the extra pair the adjacent leg is that which is formed as a leg of the other side of the body. If therefore the normal leg bearing the extra legs be a right leg, the nearer of the extra legs is a left and the remoter a right. This principle holds in every case of double extra appendages of which I have any accurate knowledge, where the structure of the parts is such that right limbs can be distinguished from left.

But perhaps of greatest interest is the fact that the inclination of the surfaces of each extra leg to those of its fellow and to those of the normal are determined with an approach to uniformity in the manner described. These principles of arrangement may be made clear by a simple mechanical device (Fig. 153). A horizontal circular disc of wood has an upright rod fixed in its centre. This rod passes through one end of a vertical plate of wood which can be turned freely upon it as an axle, so as to stand upon any radius of the horizontal circle. The head of the axle bears a fixed cog-wheel. In the vertical wooden plate are bored two holes into which two rods eacli bearing a similar cog-wheel are dropped, so that each can rotate freely on its own axis. The three cog-wheels are geared into each other. They must have the same diameter and the same number of teeth. Three wax models of legs are fixed on the head of each \\h« •<•! ;i- shewn in Fig. 153. In that figure, E represents the apex of the tibia and tarsus of a normal right leg. The anterior surface is dark, and the posterior is white. The anterior and posterior spurs of the tibia are shewn at A and P. SL and SR represent tlir two supernumerary legs, SL being a left, SR a right. (The}- are supposed t<> aria from the leg R at some proximal point towards which they converge.) 'When the wooden plate is put so that the arrow points to the word "Post, rini •" on the di.-i-. the models will then take the positions they would have if they arose from the posterior surface, all the ventral surfaces coining into one plane. If the arrow In

to "Ventral" tintwo supernumeraries will turn their dorsal surfaces to each i. :ui 1 .-» on. The model SL thus rotates twice oil its own axis for each FlG. 1")H. A mechanical device for shewing the relations that extra legs in Secondary Symmetry bear to each other and to the normal leg from which they arise. The mode! /,' represents a normal right leg. Sf, and SR represent respectively the extra right and extra left legs of the supernumerary pair. A and 1\ the anterior arid posterior spurs of the tibia. In each leg the morphologically anterior surl'aee i- -haded, the posterior being white. R is seen from the ventral aspect and si. and SR are in Position VP.

revolution round R, but the surfaces of the model SR always remain parallel to' those of the model R. In every possible position therefore each model is the image of its hbour in a mirror tangential to the circle of revolution. In the figure the models ha\e tin jMi-iiion they should have if arising postero-ventrally. Here the plantar surface of SL is at right angles to the plantar surfaces of the other two legs. Since at each radius the relative position of the legs differs, it is jms.sible to define these positions l>y naming the radius. This will be dene as shewn in Fig. 154. In this diagram imaginary sections of the legs are shewn in the various positions they would assume at various radii. The central thick outline shews a section of the normal leg, a lunger process distinguishing the anterior surface from the posterior. 'I'll.' radii andrawn to various points D, A, V, P, representing the dorsal, anterior, ventral and posterior positions respectively. In- termediate positions may be marked by combinations, DA, VVP, &C., using (he system employed in boxing the Compass.

<>n several of the radii ideal sections of the extra lei's are shewn in i liin lines, the shaded one being the nearer and the plain one the remoter. .!/' ;uul M~ >he\v the planes of the imaginary mirrors. The manner in which the pair of extra limbs are compounded with each other in their proximal parts, and with the normal limb at their point of origin is most extraordinary. It does not appear that the surfaces compound together along any very definite line or that the

FIG. 154. Diagrams of the relations of extra legs in Secondary Symmetry at various positions relatively to the normal leg from which they arise. The legs are represented in transverse section, the morphologically anterior -i.ltof each being indicated by the longer spur. The section of the normal l>r. in which the radii converge, is shewn with a thick black line. The section of the nearer extra leg in Diagram 1 is shaded, while the rcninti'r is blank. The radii shew them in various positions, anterior, posterior, dorsal, ventral. &c. ivlati\>-ly tithe normal leg.

J/1, the plane of reflexion between the nearer extra limb and the normal. M-, plane of reflexion between the nearer and the remoter extra liiiilis. Diagram II is constructed in the same way to illustrate special cases ..f extia legs arising anteriorly or posteriorly. If the two extra legs diverge from eaeh other centrally to the tibial apex each tibial apex is then complete, as on radiu- A <>f Diagram I. In Diagram II are shewn two degrees of composition of the t\v. • tibial apices, illustrating how, in cases of complete composition, the extra partma\ consist wholly of two morphologically posterior or anterior >urfae.-> arrordnii: a- they arise posteriorly or anteriorly to the normal leg. (See for instance N<>.-. 750 and 764.)

line of division between the several limbs is determined by tinnormal structure of the limbs. The homologous parts seem to be compound-.! at any point, almost as an objrrt partly iimnrrsr.l in mi-miry com pounds with its image along the line to which it is imtii.T-.'d. w ever that line may be. tlii- -.in,, curious re-ult- i'n]].i\v. For instance, if two extra liinl.- arise anteriorly and anseparate at their tibial apices, they bear four -purs as shewn at radius A in the upper diagram of Fig. 1 •> 1. I '.ut it' tiptwo anfully compounded at the tibial apices in the anterior po-itioii tinronipMiiinlcil limb will only have two spurs, both being -haped ae anterior -pur- (as shewn in the lower diagram) and conversely for tinposterior position (see No. 7'i4). The parts, in fact, winre the pair may be supposed to interpeiiet rate ,, lotted in the diagrams) are not represented.

Tho-e u ho ha\e described these phenomena have in consequence often made the following error. Observing a limb giving ofi' a morphologically double limb with a common proximal part subsequently separating into it- t \\ o components, they speak of this as a "primary and -econdary dichotomy When the facts are understood it is clear that there j- nit dichotomy between the extra legs and the normal, for the parts are not ci|iii\alent and the normal is undivided.

Such are tinprinciples followed. It would not be true to ..... •/•/ tlnif iln'sf rules wre followed with mathematical />recixi»/i, hut in tinni'i/ii tin-;/ Lnlii ,/, ,:n/. Special attention will be given to cases departing from them. but the number of such cases is -mall. The cases of slight deviation from the schematic positions are bcsid,-, mostly those of extra limbs in the Positions A and P, and generally the deviation in them takes the same form, causing tinventral sin-faces of the extra parts to be inclined to each other downwards at an obtuse angle instead of forming one plane.

In all cased possible I have examined the specimens myself, and I am tinder obligation to numerous persons who have ver\ generously given me facilities tor doing so. Amongst others 1 am thus greatly indebted to M. H. Gadeau de Kerville, Dr G. Krait/. and Dr L. von Heyden f>r the loan of many valuable insects, and also bo Messrs IVnnetier, (Hard, Dale, Mason, West- n-ood. YVaterhoiise, .laiison, Harrington, I'.leuse, Me. In this part of the work I am under especial obligation to Dr D. Sharp, for \\ithoiit his i ..... pei-ation it would not have been possible for me to have undertaken the manipulations needed. He has most kindly given up his time to the subject, and in the case of almost every one of the specimens examined al Cambridge I have had tinbenefit of his help and advice.

Of cases not seen by me few are described in detail sufficient to warrant a state ..... nt as to the planes in which the parts stood, but sometimes the figures give indications of this. Some of the accounts are ipiite worthless, merely recording that such an insect had two extra legs: in such cases I have thought it enough to give the reference and the name «»f the insect for statistical purposes. |;ut every case known to me is here recorded: tin-re has been no rejection of cases.

The cases \\ill be taken in order of the Positions, beginning with the Position V and taking the other radii in order round against the hands of a watch. *736. Carabus scheidleri $ : pair of extra legs having ;l ,-nnmion femoral portion arising from the trochanter of the right fore leg (Fig. 155). This case is of diagrammatic simplicity. The troch- FIG. 155. Carabus scheidleri, No. 736. The normal right fore leg, R, an extra pair of legs, SL and Sit', arising frorn the ventral -uituo nt' tin coxa, (.'. Seen from in front. (The property of Dr Kraatz.)

anter bears a normal leg (R) articulating as usual. Immediately ventral to this articulation there is a second articulation \\\>«\i a small elevation. This bears a double femur made up nf partof a pair of femora compounded by their dnr-al lmrd<T- Tindouble femur has thus two structurally ventral surface- to each other. The apex presents two articular surfaces in the same plane as that of the normal leg, each bearing a tibia, both tibiaflexing in the same vertical plane.

Since the double femur of the extra legs stands vertically downwards at right angles to the normal femur, it will lie seen that both the extra tibia? hVx H Awards, but «me nf them is a left leg (SL), bending to meet the iiunnal leg. while the ntln-r is a right (SR'), bending towards the ventral surface nf the bndy. The tibia of the left extra leg is a little shorter ih:m that <f the normal, and the tibia of the right extra leg is a little l.m^er than it. All three tarsi are thinner than a normal tarsus: and the claws are a good deal reduced in tincase l»«.th <>f tinimnn;d and the right extra leg, while in the left extra leg they are aWnt altogether. This is an example of a pair nf .-xtra le-s an-m-

7:}7. Carabus marginalis : penultimate joint of left hind tarsus is enlarged .-mil pre-eiittwo articular surfaces, a proximal one on the \enir.-d -urfac... and another at tinapex. The latter bears the normal last joint with it-cla\\-. 1'Yom the proximal art i.-ular surface arises a thick joint .shorter than the normal last joint, hearing at its apex ttm li,i'n* of (-la\\ - Bel l-a.-k to bark, as in the Position V. .Specimen reclescril.ed from KI;A ATX. <;.. l>> "t. ''lit. Zt., 1880, xxiv. p. 344, PI. n. tig. -'.'.

7:;^ Carabus granulatus ,-/. l.-t't posterior tibia bearing an amor phous rudiment nt' two extra tarsi arising from the ventral surface of its apex. Tinap.-\ of the tiljia is produced at the dorsal border to tonn an irregular process which bears a tarsus of normal form but reduced si/e and immediately ventral to this tarsus is a pair of til>i;d -pur.-. N'eiitral t.. the-c spurs is another deformed pair of spurs and IH-|OW them aLcain is a deformed ,'5-jointecl rudiment which probably i -,.|,i -,. -ents two tarsi. Ventral to the rudiment of the extra tarsi is a third deformed pair of -purs. It was not possible to recognize the .surfaceof the tarsal rudiment, but the presence of two extra pairs of spurs indicates plainly that the extra parts are morphologically of double structure: and as the spurs indicate the morphologically ventral surfaces, it follows that the surfaces adjacent in the extra tarsi are ilm-sitl. This specimen was originally described by Dr L. Vox HEYDEX, who was so good as to lend it to me for examination, see Deut. enf. Zi.,

739. Prionus coriarius (Longicorn): three legs in region of right posterior leg. The proximal relations not quite clear and hence it is not easy to di-tin-ui-h the normal. Presumably it was the most dorsal. This leg was of normal form but of reduced size and it wanted the claw-joint. Internal to it, arising by a double coxa, trochanter and f.-mur, were the other two le--. The remoter was a normal right, but the nearer was a left leg of reduced size, slightly crooked and lacking three apical tarsal joints. The compound femur was just as in No. "•"><'>. The normal leg must either have been the most dorsal or the most ventral. If the former, th" extra parts are in the Position V; if the latter, they are in the Position 1), but in this event the normal would be compounded with one of the extra legs. [Kedescribed from description and figure gi\ en liy KI;\I 8E, Sitzb. inif. Fr. Bert., 1888, p. 14">. //'//.]