210 HOFMEISTER, ON 



exactly opposite to one another. The position of the first 

 lateral bifurcation on the mid-rib is not constant in any 

 species ; in Pteris aquilina it is more often to the left, in 

 Aspidium jilicc-mas to the right. The principal segments of 

 the fronds, however, taken in relation to their subsequent 

 ramifications, are very regularly antidromal : on the pinna3 

 to the left of the axis of the frond the first segment of the 

 second degree, or the first tooth of the margin, is on the 

 right : on the pinnae to the right of the axis it is on the 

 left. 



Prom the first commencement of the frond its growth 

 in thickness is most vigorous behind. Its mathematical 

 longitudinal axis is not identical with the morphological 

 one i it does not coincide with the surfaces of contact of 

 the masses of cells, produced by the multiplication of the 

 cells of the second degree, which are turned towards the 

 front and back surfaces of the frond. At the time of the 

 commencement of the formation of the blade of the frond, 

 which is produced by the widening of its apex, the cell- 

 multiplication in a longitudinal direction increases on the 

 hinder surface of the frond. It exceeds that which takes 

 place on the front surface and thus leads to the commence- 

 ment of the rolling inwards of the frond (PL XXIX, fig. 1), 

 which is completed by the stretching of the cells of the 

 hinder surface which shortly afterwards takes place. Con- 

 temporaneously with the commencement of the rolling 

 inwards, the axile longitudinal rows of cells separate them- 

 selves by the cessation of transverse division, and become 

 transformed into the simple vascular bundle which traverses 

 the stem and mid-rib of the frond. Pour cells of the 

 adjoining parenchyma are about equal in length to one of 

 the cells of the rudimentary vascular bundle. This latter 

 passes through the morphological longitudinal axis of the 

 young frond, near its front surface. It is concave in a 

 transverse section, open towards the front (PI. XXIX, 

 fig. 14). 



During this development of the frond, the first root also 

 has grown considerably. Its axile rudimentary vascular 

 bundle becomes visible contemporaneously with that of the 

 frond. The two meeting together in their entire breadth 



