458 The American Naturalist. [May 
cap ; Treasurer, Samuel Henshaw ; Recording Secretary, K. 
B. Newel; Corresponding Secretary, Arthur HoUick ; Cur- 
ator, W. T. Davis. 
Decembers, 1888.— Mr. L. ?. Gratacap read the following 
paper upon the " Relation Between the Growth and Form of 
Leaves:" 
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 longitudinal 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 lateral axis is developed at an early stage in the elonga- 
tion 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, pin- 
nate or numerously veined with woody and rigid vascular 
fibres, we can resolve the entire form into a group of simple 
forms, wherein we may study the related rates of development 
in lamination (formation of parenchyma), and in vasculation 
(formation of ribs, veins, etc.). In other words, the rapid 
movement forward of rib cells would appear to interfere with 
or prevent the making of the leaf lamina, and their slow move- 
ment 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 deliquescence of the 
original fibre bundles. In one where the extention of the ribs 
is rapid this coalescence is checked and the leaf is sinuate, 
lobed, irregular and pinnatified. 
It is thus apparent that a determination of the actual rate 
of growth in leaves may throw some light or be useful in assist- 
ing speculation as to the origin of leaf forms And it is also 
apparent 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 movements of 
Its parts maintain a ratio which gives extension in length and 
not m breadth. And in many cases of turgid and dense tis- 
sues in leaves this is probably so. 
However the measurement of a number of leaf growths in- 
