Branner, | 468 [April 18, 
the time the frond originated at C until it reached D. But such is not the 
case, for some allowance must be made for the increase of altitude caused 
by the side CG becoming parallel with the lower part of the stem. Tak- 
ing GC asa radius and describing CI, the distance IE must be deducted 
as this difference in altitude of the point C when it reaches I, and the 
length grown by the whole section is FL or DI. It is true that when CG 
reaches D, CF will be the difference in altitude made by ©, but this is not 
all due to the growth in the length of the fibro-vascular bundles. In 
actual hemisections of palm stems it is noticeable that the curve CD is not 
an even one, but has a shorter radius near the point D. This is due to the 
fact that during the younger stages growth was principally in length, 
while as the part approached maturity, the lengthening was less marked, 
and the lateral growth predominated. This growing in size after prolon- 
gation has ceased is a characteristic of the fibro-vascular bundles in the 
palms. In the phylophore, the lengthening of the bundles is still possible 
to a limited extent, but it will be shown later that the growth in size con- 
tinues even below the phylophore. It will also be seen later that this in- 
crease in the size of the bundles, and consequently in that of the whole 
stem after longitudinal growth has ceased, causes the fronds to droop 
more, 
It has already been observed that the fronds are developed in connection 
with the central bundles in the phylophore. In regard to the origin of 
the bundles it is sufficient at present to say that they originate at the apex 
of the phylophore, and are developed in it, with it, and as a part of it. 
Von Mohl and Mirbel maintain that these bundles grow up into the 
phylophore ; Gaudichaud that they grow downwards from it—from the 
frond bases; Von Martius that they grow both up and down, while I 
maintain that they are perfected in all directions at the same time, though 
the lateral growth continues to a certain extent after the longitudinal 
growth has ceased, and that they can no more be said to grow upwards or 
downwards than can it be said of the bones of the body that they grow 
outwards into the limbs, It is true that the general lengthening of the 
bundles takes place at the superior end, but there is a growth beside this. 
At the first appearance of the fronds at the apex of the phylophore the 
fibro-vascular bundles are already connected with them, and just as in- 
timately as they are in the perfectly developed frond. The internodes at 
this point are very short, but the bundles are the same in number, and 
have exactly the same connections, directions, and relations to each other 
that they have in later life. But in the perfected frond we find them 
larger, longer and harder, and in the perfect stem the internodes are 
longer, the stem and bundles larger, while the whole plant has grown 
both longitudinally and laterally. In view of this general growth, the 
relations of the parts remaining the same, it is clear that growth does 
take place in all directions. In figure IX, p. 471, the upward and down- 
ward growth of a bundle is represented approximately by the line CD, 
This line cannot be upward growth alone, for the point D was once at ©, 
