38 



HORNS OF BEETLES. 



[iNTROD. 



a few generations by a few large and decisive changes, whether of 

 environment or of organism. 



Referring to the curve of Distribution formed in the graphic 

 method of displaying the statistics, during the monomorphic period 

 the curve has one apex corresponding with the greatest frequency 

 of one normal form, but in the dimorphic period the curve has two 

 apices, corresponding with the comparative frequency of the two 

 extremes, and the comparative rarity of the mean form. The 

 terms Continuous or Discontinuous are applicable to the process 

 of transition from the monomorphic to the dimorphic state according 

 as the steps by which this change was effected are small or large. 



The further meanings of Discontinuous Variation will be 

 explained by the help of examples. The first cases refer to Sub- 

 stantive Variation 1 , and we may conveniently begin by examining 

 a case of Variation in a character which is easily measured arith- 

 metically. 



Among beetles belonging to the Lamellicorn family there are 

 numerous genera in which the males may have long horns arising 

 from various parts of the head and thorax 2 . These horns may be 



T.h 



~~^ 



Cf.k 



Fio. 1. Side-views of the Lamellicorn beetle, Xylotrupes gideon. Legs uot 

 represented. I, High male, II, Medium male, III, Low male. 



1 In referring thus to evidence as to Substantive Variation, I find myself in the 

 difficulty mentioned in the Preface. For it is necessary to allude to matters which 

 cannot be properly treated in this first instalment of facts. In order, however, that 

 the one introductory account may serve for all the evidence together, such allusion 

 is inevitable and I can only trust that full evidence as to Substantive Variation may 

 be produced before long. 



- For particulars of this subject with illustrations, see Descent of Mail, 1st ed.. 

 vol. I. pp. 369 372. A detailed account of this and the succeeding example in the 

 case of the Earwig was given by Mr Brindley and myself in P. '/,. S., 1893. 



