THE HIGHER CRYPTOGAMIA. 235 



'in each mode of frond arrangement following upon the 

 | arrangement, such as &, and so forth, the form of the 

 apical surface of the cell of the first degree would be that of 

 an isosceles triangle. Each cell of the second degree might 

 be treated as the primary mother-cell of a frond, to be pro- 

 duced by the further development of the cells derived from 

 the secondary cell. This supposition would however re- 

 quire that the four sided apical surface of each cell of the 

 second degree, should, immediately after its production, be 

 considerably wider on the hinder edge than on the fore 

 edge. The excess of the length of the hinder edge over 

 that of the fore edge would be determined by the difference 

 between the apical angle and one of the side angles of the 

 upper surface of the cell of the first degree. It would 

 necessarily bear the same proportion to the second youngest 

 side of the apical surface of the compound figure formed by 

 the cell of the first degree and the youngest cell of the 

 second degree, as the sine of the apical angle bears to that 

 of one of the side angles. Consequently each cell of the 

 second degree must, immediately after its production, be 

 wider at the hinder end than at the fore end to the following- 

 extent in each respective case, that is to say, in the farrange- 

 ment to the extent of about the whole length of its front 

 wall and of the oldest wall of the apical cell which repre- 

 sents its prolongation, in the I arrangement to the extent 

 of something more than the half (0'5412) of this length, 

 in the T 5 3 arrangement to the extent of about T 7 (0*70081) of 



the same. 



Observation entirely upsets the above supposition. It is 

 true that in older cells of the second degree, especially in 

 those which are already several times divided, the outer side 

 wall normally diverges from the inner one. But the 

 younger the cells of the second degree which are subjected 

 to examination, the more nearly do their side walls approach 

 to parallelism, until at last it is manifest that the earliest 

 septa of the cell of the first degree appear exactly parallel 

 to the oldest side wall of the same cell (PI. XXVII, fig. 1). 

 It is plain from this that in point of fact the supple- 

 mentary expansion and the multiplication of the cells of 

 the second degree proceed step by step from back to front 



