74 PROBLEMS OF GENETICS 



in regard to the original appendage. These relations are best 

 explained by the diagram (Fig. n), from which it will be seen 

 that the two supernumerary appendages stand as images of each 

 other; and, of them, that which is adjacent to the normal ap- 

 pendage forms an image of it. Thus if the supernumerary pair 

 arise from a point on the dorsal surface of the normal appendage, 

 the two ventral surfaces of the extra pair will face each other. 

 If they arise on the anterior surface of the normal appendage, 

 their morphologically posterior surfaces will be adjacent, and so on. 



These facts give us a view of the relations of the two halves 

 of a dividing bud very different from that which is to be derived 

 from the exclusive study of normal structures. Ordinary mor- 

 phological conceptions no longer apply. The distribution of the 

 parts shows that the bud or rudiment which becomes the super- 

 numerary pair may break or open out in various ways according 

 to its relations to the normal limb. Its planes of division are 

 decided by its geometrical relations to the normal body. 



Especially curious are some of the cases in which the extra 

 pair are imperfectly formed. The appearance produced is then 

 that of two limbs in various stages of coalescence, though in 

 reality of course they are stages of imperfect separation. The 

 plane of "coalescence" may fall anywhere, and the two appen- 

 dages may thus be compounded with each other much as an 

 object partially immersed in mercury "compounds" with its 

 optical image reflected from the surface. 



Supernumerary paired structures are not usually, if ever, 

 formed when an appendage is simply amputated. Cases oc- 

 casionally are seen which nevertheless seem to be of this nature. 

 Borradaile, 8 for example, described a crab (Cancer pagurus) 

 having in place of the right chela three small chelae arising from 

 a common base, where the appearances suggested that the three 

 reduced limbs replaced a single normal limb. From the details re- 

 ported however it seems still possible that one of the chelae 

 (that lettered F. I in Borradaile's figure) may be the normal 

 one, and the other two an extra pair. The chela which I suspect 

 to be the normal is in several respects deformed as well as being 



8 Borradaile, L. A., Jour. Marine ZooL, 1897, No. 8. 



