866 



D'ARCY WENTWORTH THOMPSON ON 



nothing more mysterious in its conformation than, for instance, in that of a forked 

 twig in which one limb of the fork has grown longer than the other. The case of the 

 begonia leaf is of sufficient interest to deserve illustration, and in fig. 9 I have 

 outlined a leaf of the large Begonia dsedalea. On the smaller left-hand side of the 

 leaf I have taken at random three points, a, b, c, and have measured the angles, 

 AOa, etc., which the radii from the hilus of the leaf to these points make with the 

 median axis. On the other side of the leaf I have marked the points a , V , c ', such 



Fig. 9. — Begonia dmdalea. 



that the radii Oa'=Oa, etc. Now if the two sides of the leaf are mathematically 

 similar to one another, it is obvious that the respective angles should be in continued 

 proportion, i.e. as AOa is to AOa', so should AOb be to AOb'. This proves to be 

 very nearly the case. For I have measured the three angles on one side, and one 

 on the other, and have then compared, as follows, the calculated with the observed 

 values of the other two : — 





AOa. 



AOA. 



All-'. 



AOa'. 



AOft'. 



51-1 

 52 



A( )c. 



o 



157 



Observed values . 

 Calculated ,, 

 Observed ,, 



12 



28°-5 



88 



21-5 



20 



