REJUVENESCENCE IN NATURE. 119 



These most clear and decisive cases belong chiefly to the 

 genus EchinocactuSy in which, in combination with a 

 most crowded arrangement of the leaves, the pulvini of 

 the leaves are blended in vertical lines, so that these pre- 

 sent themselves more clearly than all oblique lines. If, 

 then, in another genus of the Cactaceae (Mamillaria), the 

 usually still more complicated modes of arrangement are 

 less easily and surely distinguishable, because the leaves 

 are not so closely crowded and the pulvini are separately 

 developed, we certainly must not conclude from this that 

 we have here a different irrational mode of arrangement, 

 essentially distinct from the rational arrangement of the 

 Echinocacti. As regards Naumann's method, of ex- 

 amining, measuring, and naming the arrangement of the 

 leaves from the point of view of the vertical lines, it may 

 be added that within a certain domain this has the same 

 practical applicability as the mode of definition and de- 

 nomination founded on the fundamental spiral ; but if we 

 go back to the genetic succession of the leaves, which is 

 indubitably represented in the fundamental spiral, Nau- 

 mann's method appears contrary to nature. While on 

 the one hand it appears to afford a simpler explanation of 

 the verticillate arrangement, on the other hand it is inca- 

 pable of expressing, even in the formula of nomenclature, 

 the actual and essential connection of the verticillate and 

 spiral arrangements as the transitions in the plant demon- 

 strate them, whence it must appear especially useless in 

 the department of anthonomy or construction of diagrams 

 of flowers. Schleiden further makes the objection to the 

 whole study hitherto of the phenomena of the arrange- 

 ment of leaves, that it has kept solely to fully-developed 

 plants, instead of tracing the subject in the history of 

 development, whence all theories are devoid of safe foun- 

 dation (1. c., p. 175, Transl., p. 264); in this he is partly 

 right and partly wrong, for everything has its time. 

 What is requisite in the first place is an actual review of 

 the conditions of arrangement of leaves occurring in the 

 vegetable kingdom, the mode of their occurrence, their 



