chap, xxv.] CONCLUDING REFLEXIONS. 571 



use ; but the pursuit of this search as an aim in itself has led to 

 confusion, and has tended to conceal the fact that there are pheno- 

 mena to which the strict conception of individual Homology is not 

 applicable. 



This exaggerated estimate of the fixity of the relationship of 

 Homology has delayed recognition of the Discontinuity of Meristic 

 Variation, and has fostered the view that numerical Variation 

 must be a gradual process. 



This view the evidence shews to be wrong, as it was also im- 

 probable. 



Brief allusion may be made to three separate points of minor im- 

 importance. 



It is perhaps true that, on the whole, series containing large num- 

 bers of undifferentiated parts more often shew Meristic Variation than 

 series made up of a few parts much differentiated, but throughout the 

 evidence a good many of the latter class are nevertheless to be seen. 



Reference may be made to a point that might with advantage be 

 examined at length. The fact that Meristic Variation may take place 

 suddenly leads to a deduction of some importance bearing on the expect- 

 ation that the history of development is a representation of the course of 

 Descent. In so far as Descent may occur discontinuously it will, I 

 think, hardly be expected that an indication of the previous term will 

 appear in the ontogeny. For example, if the four-rayed Tetracrinus 

 may suddenly vary to both a five-rayed and also to a three-rayed form 

 (see p. 437) it is scarcely likely that either of these should go through 

 a definitely four-rayed stage ; and if the origin of the four-rayed form 

 itself from the five-rayed form came similarly as a sudden change, it 

 would not be expected that a five-rayed stage would be found in its 

 ontogeny. Similarly, if a flower with five regular segments arise as a 

 sport from a flower with four, it would not, I suppose, be expected that 

 the fifth segment would arise in the bud later than the other four. I 

 suggest these examples from Radial Series, as in them the question is 

 simpler, but similar reasoning may be applied to many cases of Linear 

 Series also. 



It will be noted that the attempt to apply to numerical variations 

 the conception of Variation as an oscillation about one mean is not 

 easy, difficulty arising especially in regard to the choice of a unit for 

 the estimation of divergence. In few cases can facts be collected in 

 quantity sufficient even to sketch the outline of such an investigation ; 

 but, to judge from the scanty indications available, it seems that in 

 cases of numerical change variations to numbers greater than the 

 normal number, and to numbers less than it are not generally of equal 

 frequency. Probably no one would expect that they should be so. 



As was stated in the Introduction, we are concerned here with 

 the manner of origin of variations, not with the manner of their 

 perpetuation. The latter forms properly a distinct subject. We 

 may note however, in passing, how little do the few known facts 

 bearing on this part of the problem accord with those ready-made 



