APPLICATION OF VORTEX CONSTRUCTION. 47 



2. Arrangement B. 



As previously indicated, the arrangement of superposed whorls in 

 a circular- vortex system can only be regarded as a special case of the 

 more general asymmetrical form of a spiral vortex. In this latter 

 system, therefore, the primordia take the arrangement of " super- 

 posed cycles." 



The circles become log. spirals, and the radii also portions of log. 

 spirals intersecting the former orthogonally. 



As the spiral approaches a circle, the difference between the two 

 constructions will be scarcely observable to the eye, if a portion 

 only of the coil is seen; while even when the deflection of the 

 main spiral is considerable, as in fig. 20, where the width of a 

 member is gained in one quarter of a complete revolution, the 

 deflection of the " orthostichy " lines is almost imperceptible to the 

 eye when the construction lines are omitted. This figure thus 

 illustrates very forcibly the standpoint that lines which appear per- 

 fectly straight to the eye may still be very definitely spiral, and 

 the orthostichies of Schimper and Braun may have no real basis. 

 On the other hand, a glance at the construction of such a typical 

 phyllotaxis system as that of a capitulum of Helianthics is sufficient 

 to show that this type of spiral construction does not obtain in the 

 plant. Nor will any amount of mutual pressure in the primordia 

 produce any change in the system beyond squeezing the spheres 

 into cubes, since they are by construction orthogonally arranged ; 

 although it is conceivable that additional external pressures might 

 produce secondary hexagonal packing. 



Since, then, such a spiral construction will not meet the require- 

 ments of normal phyllotaxis, an alternative method of orthogonal 

 arrangement may be considered. 



3. Concentration Systems. 



That the primordia at the apex of a growing stem were " con- 

 densed " into a confined space, in order that they might be more 



