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production of leaves and of branches, for it was demonstrated 

 that the sepals and petals are only leaves and the flower a 

 shortened branch. 



Since the leaves are arranged either opposite or in a spiral, 

 these two types may also be admitted in the process of the 

 formation of the flower, namely that of whorls and of spirals. 

 The latter case is the most frequent, and it is proved by an 

 examination of the doctrine of the position of leaves that na- 

 ture acts after the same laws in the formation of the flower. 

 Now since the flower is a shortened branch, the leaves united 

 to form a whorl cannot always stand next one another so as 

 to be in contact in their regular succession ; for were this the 

 case with a whorl of five members, each leaf would only be at 

 a distance from the next of one-fifth part of the circle, while 

 they are in reality two-fifths or three-fifths of the circle from 

 one another. The arrangement of the sepals and petals is ge- 

 nerally distinguished by their imbrication, those leaves being 

 superposed which first separated from the stem, exactly as in 

 the leaf-bud. We have already seen that the members in the 

 successive verticils of the flower alternate, and this may be 

 explained by the supposition that a different proportion is in 

 action between the different whorls ; a proportion, which is 

 one half greater than that which prevails between the mem- 

 bers of the same period. 



When the number of the members in the whorls does not 

 remain constant through the whole flower, we may suppose 

 two possibilities to explain it ; either a reduction occurs in the 

 members of one or more whorls which agree in proportion 

 with the rest, or the several series of the flower follow differ- 

 ent proportions. In both cases a dissimilarity occurs in the 

 numerical relations, and frequently connected with it an ir- 

 regularity of form also. The latter arises from unequal ex- 

 pansion and elongation. 



Fourth Lecture. Von Martius endeavours to demonstrate 

 in this last lecture the general morphological laws which were 

 developed in the preceding one in their special relations ; those 

 of the flower are first entered upon, and he then treats of the 

 top, the bottom, the front, the back, the left and the right of a 

 plant : the gradual passage of the carpel into fruit is treated 

 of more at length, butjhis I can merely indicate. 



H 



