26o 
AMERICAN JOURNAL OF BOTANY 
[Vol. 9 
zero), assuming that the rectiHnear relation shown by the graph in question 
were to hold at this stage of wilting or closing of the hinges. The values 
of K and L for each of the five equations are given in column i of table I , 
and are also brought together below: 
Test No. K L 
1 -3191 2.2272 
2 .2825 1.6262 
3 .2628 1.6338 
4 -3457 2.1740 
5 .1718 1.6021 
After these equation constants had been derived for each test, the water- 
content value was calculated, by means of the constants for the test in 
question, for each apparent-width value given in table i, and the "cal- 
culated" water-content values are shown in column 5 of the table. The 
close agreement between the corresponding values of columns 4 and 5 shows 
how nearly rectilinear the relation between water content and apparent 
pinna width actually was for these tests. The disagreements are generally 
insignificant, and it seems safe to conclude that the linear equation form 
represents a true relation for these pinna samples. While there are con- 
siderable differences between the values for K and between those for L 
in the five tests (these differences being perhaps due to differences in 
physiological state between the several lots of pinna samples, which were 
selected at random), it may be stated that, in a general way, the values of 
the two constants of proportionality for this relation of coconut pinnae 
may be considered as: K, 0.3; L, 2.0. If this statement approximates the 
general truth, then the water content (in grams) for 100 sq. cm. of leaf 
surface (one side) is numerically about equal to 2 plus one third of the 
apparent pinna width (in centimeters) ; y = 2 -\- O.3.T. 
Referring again to the diagram of figure i, the apparent pinna width— 
which seems to be directly related to the foliar water content, as just 
noted — is itself truly proportional to the sine of half of the angle of diver- 
gence between the two pinna wings, the two wings being of like width, 
practically constant after the pinna has ceased to increase in size. This 
half-angle deserves special attention, for it represents the degree of diver- 
gence of either pinna wing from the position that this wing would have if 
it were in contact with the other wing — when the pinna would be com- 
pletely ''closed." As has been mentioned, each wing is provided with its 
own hinge, where it joins the pinna midrib. The half-angle here con- 
sidered is clearly a measure of the turgidity conditions in the hinge cells, 
although the half-angle does not entirely vanish when all turgidity disap- 
pears, the wings not coming into complete contact even when the pinna is 
strongly wilted. 
Since the sine of the half-angle just considered is directly related to the 
apparent pinna width, and since the foliar water content is similarly related 
to this width, it follows that the v/ater content is likewise related to the 
