THE LEAF-TRACE IN SOME PINNATE LEAVES. 
7 
reinforcement of the adaxial strand below each pinna. Reinforcement of the adaxial 
strand may take place just after a pinna-trace has been nipped off, and again just 
before the next pinna-trace leaves the adaxial strand. Such a double reinforcement 
has been found only in this heavily-pinnate leaf. 
The abaxial side of the leaf-trace makes its appearance in a relatively long leaf, 
becomes more prominent the longer the leaf in which it occurs, and is ultimately 
developed as a system of separate vascular strands. In leaf-traces with the abaxial 
system of strands, that system is commonly used to reinforce the adaxial strand 
before the pinna-traces depart from its margins. Where the pinnae are large and 
closely set on the rachis, a double reinforcement of the adaxial strand from the 
abaxial system may occur. 
In P. decurrens (text-fig. If) we have another use of the abaxial system in 
connection with the formation of the pinna-traces. Here the marginally-derived 
strand moving from the leaf-trace into a pinna is joined by another or by other two 
which come from the abaxial series- of strands. The abaxial system is in this species 
employed directly to give vascular tissue to the pinnae ; in the other species of 
Polypodium it is employed to reinforce the strand which supplies the pinnae with 
a vascular system and thus indirectly contributes to the supply of the pinnae. In 
P. decurrens the abaxial ends of the adaxial strand are also affected during the 
process of departure of the pinna-trace. These ends give off small strands which 
unite with the strands linking the adaxial strand to the abaxial curve series (cf 
text-fig. 1 f). Each of these fused strands then gives off its outward tip to the pinna, 
this tip fusing with a small strand, derived from the corner strand of the abaxial 
curve series, to form the abaxial system of the pinna-trace. 
It is worth noting here — the full discussion of the process will be found below — 
that the abaxial system of the leaf-trace is used directly to supply the pinna in this 
species only among the ten Brazilian species examined, and that in this species the 
individual pinnae are larger than in any of the others. 
Species of Polypodium from the Andes of Colombia. 
The general conclusions which have been drawn from the Brazilian species 
regarding the relation between the length of a leaf and the size of its ninnse on the 
one hand, and the degree of development of the abaxial portion of the leaf-trace on 
the other, find an interesting confirmation in the account recently published by 
Borkowski (’14) of the anatomy of some Ferns from the Colombian Andes. The 
leaf- trace of P. crassifolium, Linn. ( loc . cit. , Taf. 1, fig. 14) shows the greatest 
development of the abaxial series of Strands among the four species of Polypodium 
of which the leaf-traces are figured. And it has the longest leaf of all and the 
largest pinnae. The leaf of P. angustifolium, Sw., is shorter and has smaller pinnae ; 
the abaxial development of its leaf-trace (ibid., fig. 12) is less. P. Mayoris, Rosen- 
stock, has as long a leaf as P. angustifolium, but it has small pinnae. In the 
