17 THE MATHEMATICAL TEST 



to the present Itkomia> it is impossible to assert that the 

 normal forms of the two butterflies were as wide apart 

 at the beginning of that period as they are at present. 

 The mimicry having once set in, might be retained by 

 parallel variations. This, indeed, cannot fail to be the 

 case, if the protection is to be a lasting one ; for when 

 the Itkomia varies in outward appearance, unless the 

 Leptalis varies in the same direction, the resemblance 

 will be lost. This progressive mimicry would be more 

 valuable than an imitation in which no changes occurred, 

 since the enemies of a mimetic species would in time 

 become aware of a fraud which had no variations at its 

 command, as birds are said now-a-days to pounce without 

 hesitation upon caterpillars which very much resemble 

 twigs 1 . Even ' a rough imitation' may be useful in the 

 first instance, and yet when hostile eyes have long been 

 exercised, and have acquired greater and greater sharp- 

 ness, finally nothing less than absolute identity of appear- 

 ance may be thoroughly effective. Thus the perfecting 

 of the resemblance will be no ' mere freak of Nature,' 

 nor shall we be ' landed in the dilemma that the last 

 stages are comparatively useless' in this procedure. 



The array of figures brought forward to prove that the 

 Leptalu could not have made twenty steps of variation 

 in the direction of the Itkomia by chance, would be much 

 to the purpose if any exponent of the theory of Natural 



1 Applying to these caterpillars Mr. A Murray's recent hypothesis 

 for explaining 'mimicry' by hybridization, we should draw the poetical 

 inference that a happy marriage is possible between a butterfly and 

 a rose-bush. 



