»889-] Proceedings of Scientific Societies. $47 
It is obvious that the form of leaves must be the resultant of 
rates of growth in various directions. That a simple leaf with 
a single midrib will assume such a mature form as will express 
the equilibrium of the growing impulse along two axes, a lon- 
gitudinal and a lateral one, and that as this ratio varies in 
favor of the first or the second, the leaf becomes ovate, circular, 
broadly elliptical, etc., or lanceolate, linear and elongated. 
And secondarily, in the case of the simple leaf, the point of 
intersection of the axis will modify the final form. If the lat- 
eral axis is developed at an early stage in the elongation of 
the midrib we have ovate leaves, if at a point half way along 
its length elliptical, if at the distal extremity obovate. And 
in leaves of a complex structure, whether palmate, pinnate or 
numerously veined with woody and rigid vascular fibres, we 
can resolve the entire form into a group of simple forms, where- 
in we may study the related rates of development in lamina- 
tion (formation of parenchyma), and in vasculation (formation 
of ribs, veins, etc.). In other words, the rapid movement for- 
ward of rib cells would appear to interfere with or prevent the 
making of the leaf lamina, and their slow movement to assist 
it. In a leaf with several ribs, the slow progress of the rib- 
making permits the coalescence of the marginal tissues, and 
forms polygonal and crenate circular leaves, and also tends to 
introduce bifurcation and deliquesence of the original fibre 
bundles. In one, where the extension of the ribs is rapid, 
this coalescence is checked, and the leaf is sinuate, lobed, ir- 
regular and pinnatified. 
It is thus apparent that a determination of the actuai rate of 
growth in leaves may throw some light or be useful in assisting 
speculation as to the origin of leaf forms. And it is also ap- 
parent that there might be a condition of things exactly the 
reverse of our supposition given above, and yet produce the 
same result. That is, a linear leaf might be a, so to say, 
slowly made leaf as well as a quickly made leaf, if the move- 
ments of its parts maintain a ratio which gives extension in 
length and not in breadth. And in many cases of turgid and 
dense tissues in leaves this is probably so. 
However the measurement of a number of leaf growths in- 
cluding those of Morning-glory, Musk-melon, Water-melon, 
Maples, Magnolia, Beach, Japanese Quince, Five Finger, etc., 
made this year on Staten Island, do seem to show that the 
elongated leaves grow much the more rapidly, that the palmate 
and pinnate leaves stand next in order, and the circular and 
