1907.] Longitudinal Symmetry in Phanerogamia. 307 



case of displacements of branches above their leaf -axils in Boraginacece. In 

 this connection, the curve was constructed by recording as successive ordinates 

 the heights of the successive branches above their subtending leaves. The 

 resultant displacement curve of the branches is of startling regularity, and 

 conforms in type with the displacement sub-curve of the leaves on the 

 chenopodiaceous main stem. 



One significant point is that these old-established fixed (hereditary) dis- 

 placements in Chenopodiacese and Boraginacese follow the same rule in respect 

 to their distribution and relative dimensions as that formulated by De Vries 

 in respect to anomalies and monstrosities. 



The Boraginacese are shown to be probably opposite-leaved in design, though 

 alternate-leaved by displacement, and are thus brought into closer connection 

 with the Labiatse. 



In the advanced case of Solarium Dulcamara, the graphic method showed 

 for the first time that the familiar displacements of leaves high up the axis 

 are anticipated lower down by similar ones. 



Investigations of slighter or more fluctuating leaf-displacements in Lysimachia 

 vulgaris, Veronica virginiana, and (Enothera, showed that where the phyllo- 

 taxis is sometimes cyclic, and at other times acyclic, on the same axis, 

 individual, or species, the internode curve becomes irregular when any of the 

 leaves are alternate or sub-opposite. This irregular curve could be analysed 

 into consistent sub-curves when the displacements were slight. But in some 

 instances of more considerable displacements I failed to accomplish this 

 analysis, partly because the number of leaves originally associated with a 

 node is apt to vary at different 'points of the same axis. The irregularity of 

 the curve is due to two causes : (1) the method of measurement rigidly 

 adopted, namely, from one leaf to the next one, may obviously lead to a 

 merely seeming diminution in length of an internode ; (2) but, beyond this, 

 the displacement of a leaf causes a true (relative) abbreviation of the inter- 

 node up which it takes place. The irregularity of the internode curve in 

 these cases, and in others investigated, is of import in indicating that the 

 construction of an internode curve of merely one specimen (living or fossil) 

 may suffice to show that the phyllotaxis in the family varies from acyclic to 

 cyclic, just as similar treatment of one axis of a herb (living or fossil) may 

 show at once whether the axis be a main one or a branch and, if the latter, it 

 may give some information as to its insertion on the mother axis. 



Incidentally, observations were made on the double-leaves of Lysimachia 

 vulgaris and Bhinanthus, and on the increase and decrease in the number of 

 leaves at a node in these plants. The morphological significance of the 

 observed facts is discussed. Of particular interest and novelty was one case 



