230 HOFMEISTER, ON 



two rather more vigorous ones at a little distance higher 

 up (PI. XXVI, fig. 20). Both pairs run along the protu- 

 berant longitudinal ridges of the frond, the former pair 

 behind, the latter in front (PI. XXVII, fig. 7). The vas- 

 cular bundles not unfrequently anastomose in the interior 

 of the stipes. Hence it arises that transverse sections of 

 the latter sometimes exhibit more than five vascular bun- 

 dles. 



The distribution of the vascular bundles within the stem 

 remains essentially the same during the progress of the 

 arrangement of the fronds, except that (as is manifest) the 

 number of loops increases. The first frond of a cycle 

 receives its vascular bundles no longer from the sixth and 

 seventh, but from the ninth and eleventh of the preceding 

 cycle ; the sixth frond from the first and the third, the 

 eighth from the third and fifth of the same cycle, and so 

 on. Or to state it more shortly the vascular bundles 

 which pass from the right to the new fronds follow (when 

 the turn of the spiral is normal, or to the right hand) the 

 3-numeral fronds ; those which pass from the left follow 

 the 5-numeral ones. Eight transverse sections of vascular 

 bundles lie in one plane passing through the stem at right 

 angles to the axis. In mature plants of Aspidium Jilix-mas, 

 there is a periodicity in the development of the frond which 

 is not found in the one-year-old seedling. The growth of 

 the frond in the former is arrested in winter, but not so in 

 the latter. The number of fronds which unfold in spring, 

 and which all grow simultaneously from the end of May 

 till October, is usually thirteen, corresponding with the 

 number of the joints of a segment of the spiral in which 

 the fronds are arranged. A similar state of circumstances 

 is met with also in some other ferns, as in Asplemum filix- 

 femina, where the number of fronds is usually eight or 

 thirteen, and in Aspidium spinulosum and Asplenium TricJio- 

 manes where eight fronds are usually developed contempo- 

 raneously. As in Pteris aqitilina, the rudiments of the 

 fronds are formed two years before their unfolding. In 

 the first year the stipes only is formed, and in the outer- 

 most fronds of the cycle about three or five of the pinnae. 

 In the second year the pinnae of those fronds which are to 



