155 



re h,i\v <li-M ii>snl in the above. Exactly as the growth of a crystal IIP- 

 irdium is only bounded by secondary circumstuiuvx existing in 

 mother-liquid or its immediate environment, while ttorn a 

 icoretical point of view, it is also an endlessly extended system 



ularly arranged units. 



In tins connection some considerations may be inserted In p 

 iiMg the ivmarkable views about phyllotaxis, i.e. about the 

 ly of arrangement of leaves in plants. As we shall see, these phe- 

 >mrna are in many points very analogous to those dealt with in 

 le preceding paragraphs. Closely related to them are the pecu- 

 itios observed in the arrangement of buds, of scales, and of the 

 lifferent parts of muscles etc., as observed in oceanic conchifers. 

 I 'lu 1 fact that the leaves of plants are arranged in spiral series 

 ibout their axis, has long been observed and recognised by botanists, 

 ic spiral-theory of phyllotaxis has since the days of Goethe and 

 Sonnet *) often been a subject of investigation and speculation, 

 id for a considerable time it has been an object of botanical interest, 

 ice its development by Schimper and Braun 2 ) and by A. and 

 . Bravais 3 ). 



Its fundamental conception is that the arrangement of such leaves 

 ;curs in series which form alternating rows when viewed in a hori- 

 mtal or vertical direction. Thus proceeding along such a spiral 

 ic, we shall meet a definite number of leaves ("members" of the 

 sries), until after one or more revolutions a leaf is reached, which 

 lands exactly vertically above the first one. The members included 

 such a series form together a cycle ; the row of vertically superposed 

 ives are called orthostichies, while the parallel spirals are named 

 *>arastichies. The cycle is indicated by a numeral symbol in the 

 )rm of a fraction, like : \, -J-, ^, etc., the numerator of which indicates 

 le number of turns of the spiral in each cycle, while its denominator 

 idicates the number of members inserted in each cycle. As an 

 stance of this, we have in fig. 125 reproduced the plane projection 

 such a spiral arrangement on a conical surface, in which five mem- 

 are included in a cycle of two revolutions (). The orthostichies 

 (e. g., 2-7-12) are projected as the radii of the system of circles, while 



1) Ch. Bonnet, Recherches sur 1'Usage des Feuilles dans les Plantes, Goettinge 

 et Leyde, (1754). p. 159. 



'-9 K. F. Schimper and A. Braun, Flora, 2. (1835); A. Braun, Nova Acta 

 Acad. Carol. Leopold. Nat. Curios., Halle, 15. 1. p. 195. (1.831). 



3) A. and L. Bravais, Ann. des Sciences naturelles (2) 7. p. 42, 67. (1837). 



