RADIAL SHOOTS. MECHANICAL HYPOTHESIS OF LEAF-POSITION 81 

 on the other hand the relative size of the organs decreases in the way supposed, 



n 



a four-membered whorl will give a spiral arrangement with the divergence -, a five- 



2 



membered one will result in a spiral with a divergence of - , and generally upon 



2 



whorls with n members a spiral with the divergence will follow. In the 



2n+i 



Aroideae the changes in size are commonly found, but irregularly, so that, as there 

 are many transitions, spirals of other series appear. 



The Aroideae may serve also to illustrate a further cause of change of position, 

 namely, the abrupt diminution in size of organs. The amplexicaul spathe is followed, 

 as is well known, without interruption by the relatively small flowers. The spathe 

 being commonly obliquely inserted, the first flowers which shoot out close above 

 its base are unable to form a complete whorl or the whole cycle of a spiral, 

 consequently the regular positions are observed only at some height above the base. 

 The great variety of systems which is found in the spadices of the Aroideae is easily 

 understood through the mechanical hypothesis of leaf-position. The small individual 

 deviations in respect of the insertion of the spathe and the size of the primordia of 

 the flowers must necessarily lead to the most different relationships of position. 



Let us now turn to the peculiarities exhibited by the position of leaves in 

 relation to the branching of the stem. 



In the rare cases of dichotomous branching, as they are seen in Lycopodieae, the 

 primordia of the leaves on the branch after forking are linked on without interruption 

 to those of the undivided branch. If the angle of the successive dichotomies is 

 somewhat acute so that the branches at first touch one another, there can be no 

 leaf-formation at this place, and in consequence gaps arise here, which may give 

 occasion to a variety of changes of the arrangement which was previously followed. 

 The connexion however always conforms with the rules of the juxtaposition. 



With regard to the more common case of axillary branching, it is evident that the 

 apex of a bud wedged in between a mother-shoot and an axillant leaf experiences less 

 pressure in the lateral direction than in the median ; the first two leaves of the axillary 

 shoot are therefore most usually lateral, and only the succeeding leaves are median, 

 or more or less oblique. If the phyllotaxy is spiral the third leaf has an alternative 

 position. It may shoot out upon that side of the axillary bud which is next the stem, 

 or upon that which is next the axillant leaf, and then there may be displacement towards 

 the right or towards the left of the median. The inequality of pressure to which 

 the bud is in general subjected upon its anterior and posterior sides is partly 

 a consequence of the dissimilarity of the organs which exercise the pressure, partly 

 of the direction of growth of the bud itself, and this is determined by its morphological 

 nature. According to circumstances then that amount of diminution of pressure which 

 is a condition in the formation of lateral shoots takes place in one plant first of all 

 upon the anterior side, that is between the bud and the axillant leaf, whilst in another 

 plant it takes place first of all on the posterior side, that is between the bud and the 

 mother-axis; and it is possible that in the same plant sometimes the one side, 

 sometimes the other is the more favoured. As we cannot of course measure 



GOEBEf. G 



