APPENDIX 



AN ATTEMPT TO REPRESENT DIAGRAMMATICALLY SOME OF 

 THE IDEAS CONNECTED WITH INHERITANCE 



BY 



HERBERT HALL TURNER, D.Sc., LL.D., F.R.S. 



Savilian Professor of Astronomy, Oxford 



i. 'W'NTRODUCTORY. The perusal of Dr Archdall Reid's Prin- 

 t ciples of Heredity -, and of the present work, suggest that there is a 

 -^- closer resemblance between biological and geometrical reasoning 

 than might be supposed. Starting from certain axioms in geo- 

 metry, a considerable superstructure is erected by following necessary laws 

 of thought. In biology, there are no axioms of the same kind ; but there 

 are some fundamental truths which may to some extent take their place ; 

 as, for instance, that children resemble their parents. The precision of an 

 axiom is absent : so is the self-evidence : but the universality of the truth 

 and its universal acceptance, when once the limits of application are 

 understood, are comparable with those of a geometrical axiom. Every 

 one knows that the offspring of an elephant will be an elephant, of a dog 

 a dog, of a butterfly a butterfly similarly marked. The resemblance 

 between parent and child only extends to broad features and breaks down 

 at details, and hence the necessity for specifying limits of application. 

 But there is no difficulty about this unless we try to be too precise. We 

 know with equal confidence that children differ from their parents ; 

 i.e. that no two beings are ever precisely alike ; each of these two appar- 

 ently contradictory propositions is undeniably true within its own limits 

 of application : and though these limits cannot be precisely defined, they 

 are well understood. 



2. Now, Dr Archdall Reid has shown that we may build upon such 

 truths as these in a manner not very different from that in which 

 geometers build upon their fundamental truths. For instance, he deduces 

 Recapitulation from the two principles just quoted, and little more; he 

 insists that we need not have derived it from independent observation, 

 but could have deduced it (as a necessity of thought) from other principles 

 already known and more familiar. 



3. To a mathematician such a view is fascinating, and his impulse is 

 immediately to seek mathematical analogies or diagrammatic representa- 

 tions, which help him to picture the process of thought. Thus, he may 

 think of the resemblance between the growth of a child and that of its 

 parent as represented by two similar tracks let us say the tracks of the 

 front and hind wheel of a bicycle. They are nearly, but not quite, the 

 same. If a third, fourth, fifth wheel followed in similar sequence, we 



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