CHAP, xx.] SECONDARY SYMMETRY: PRELIMINARY. 475 



mutilated or so amorphous that the morphological relations of the 

 surfaces cannot be determined. 



Over and above these there remain a very few cases of 

 Repetition of parts of appendages where the arrangement is cer- 

 tainly not in Secondary Symmetry, but is of a wholly different 

 natuie, exemplifying in Arthropods that duplicity of limbs already 

 seen in the human double-hands (p. 331) and in the double-feet of 

 Artiodactyles (p. 378). Genuine cases of this kind are excessively 

 rare ; but owing to hasty examination great numbers of cases have 

 been described as instances of duplicity, though in reality the 

 supernumerary parts in them can be shewn to be of paired struc- 

 ture. To emphasize the distinctness of these cases they will be 

 made the subject of a separate consideration. Logically they should 

 of course be treated before the Secondary Symmetries ; but their 

 essential features may be understood so much more readily if the 

 latter are taken first that I have decided to change the natural 

 order. 



In continuation of the evidence as to Secondary Symmetry in 

 Arthropods will be given a brief notice of similar phenomena in 

 vertebrates. This evidence is comparatively well known and 

 accessible and I shall attempt no detailed account of it, referring to 

 the facts chiefly with the object of shewing how the principles 

 found in Arthropods bear on the vertebrate cases. 



It will then be necessary to consider how repetitions in Second- 

 ary Symmetry are related to other phenomena of Repetition. 

 Lastly something must be said with regard to the bearing of these 

 facts on the general problems of Natural History. 



Preliminary account of paired Extra Appendages in 

 Secondary Symmetry (Insects). 



Supernumerary appendages in Insects are not very un- 

 common, perhaps 120 cases of this kind being recorded 1 . Nearly 

 all known examples are in beetles, but this may be due to the 

 greater attention paid to the appendages in that order. They 

 do not seem to appear more often in one family than in another, 

 but perhaps the rarity of instances in Curculionidae is worth 

 noting. They are found in both sexes, in all parts of the world, 

 and in species of most diverse habits. 



Supernumerary parts may be antennae, palpi or legs. (Extra 

 wings are probably in some respects distinct. They have al- 

 ready been considered. See p. 281.) Extra appendages may 

 be either outgrowths from the body in the neighbourhood of 

 the part repeated, or, as in the great majority of cases, they 

 occur as outgrowths from an appendage, extra legs growing from 

 normal legs, extra antenna? frum antennas, &c. In every case 

 there are two essentials to be determined : first the constitution 



1 Not including some 110 cases of alleged duplicity of appendages given later. 



