THE HIGHER CRYPTOGAMIA. 



233 



tinctly marked upon the latter in the form of slightly pro- 

 tuberant ridges, and admit of the most accurate measure- 

 ments. Each of the following is the mean of at least five 

 measurements which did not differ from one another by 

 more than half a micro-millimeter.* 



Measurements of the apical cells of Ferns having the -^frond- 

 arrangement. 



— 



Base. 



Side. 



Belation of 

 the two. 









M.M.M. 



M.M.M. 





Aspidium filix-maS) 



Spiral 



right . 



33.6476 



47.1618 



1 : 1.401 





3 55 



33 



33 • 



39.912 



56.542 



1 : 1.416 





3 99 



3? 



33 • 



43.3104 



61.0986 



1 : 1.401 





9 99 



33 



53 • 



45.2312 



63.7098 



1 : 1.408 





9 55 



55 



53 • 



46.564 



66.52 



1 : 1.41 





9 99 



55 



33 



49.89 



70.6773 



1 : 1.416 









55 * 



51.8504 



73.6386 



1 : 1.42 





1 99 



55 



33 * 



52.859 



75.0198 



1 : 1.419 





3 33 



33 



53 



55.7116 



78.593 



1 : 1.41 







55 



33 



55.7116 



79.5336 



1 : 1.427 





3 99 



3 99 



99 

 53 



33 



55.9874 

 56.542 



78.593 



79.824 



1 : 1.403 

 1:1.411 





, spi?iulosum „ 



left '. 



36.6076 



51.3022 



1 : 1.401 





y 99 



35 



5» 



40.1194 



56.4582 



1 : 1.406 





3 99 



35 



right . 



43.0526 



60.3246 



1 : 1.401 





» 33 



53 



»> 



43.0526 



44.0838 



60.8408 

 61.7421 



1 : 1.413 

 1:1.4 





3 33 



35 



left \ 



52.0756 



73.2152 



1 : 1.407 





5 99 



J3 



right . 



52.6778 



74.5487 



1 : 1.401 





3 33 



55 



35 ■ 



52.9536 



75.5692 



1 : 1.428 



Aspl. filix-fem. 



35 



S3 • 



33.26 



46.564 



1:1.4 









]V 



Lean . . 



1 : 1.4094 



This proportion of the base to the sides is that of an 

 equilateral triangle with an apical angle of 69° 13' 5 3- 3", 

 and whose angles at the base are 41° 32' 13-4"; angles 

 which very nearly approximate to those of a triangle which 

 is bounded by the chords of two arcs of 138° 27' 41-53' — 

 (two successive steps of the smaller divergence of the ^ frond- 

 arrangement) — and by the line uniting the free terminal 

 points of these chords, which line is the chord of an arc 

 of 83° 4' 36 •94", being the difference between the larger 

 and the smaller divergence of the ^ arrangement. The 

 apical angle of such a triangle is 41° 32' 18'47"; each of 



* 1 m.m.m. = 9 - 0001 millim. 



