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A 5M
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UNITED STATES DEPARTMENT OF AGRICULTURE
ARS 42-159
Agricultural Research Service JULY 1969
NYCTITROPIC MOVEMENT AS A FALSE WILT SYMPTOM OF COTTON
Albert C. Trouse. Jr.1
Under field situations cotton leaves
frequently exhibit a drooping move-
ment during the late afternoon. This
phenomenon' is sometimes diagnosed
(1) as wilt resulting from insufficient
soil moisture or (2) as wilt result-
ing from an excessively warm day or
(3) as wilt resulting from inadequate
root activity. Since the same drooping
action of leaves also occurs in aeon-
trolled environment chamber in a
normal, healthy cotton plant, a study
was made to determine the cause of
this drooping leaf condition in cotton.
cv:.:.. > • -
Although modern literature does not
mention another possible cause of
drooping leaves on the cotton plant,
Charles Darwin (3J reported about
85 years ago that some cottons exhibit
a nyctitropic (or night drooping) move-
ment on their cotyledons and leaves.2
If the observed phenomenon is a
nyctitropic movement, it will be nec-
essary to determine whether extend-
ing exposure of daytime conditions to
test plants would be harmful to their
normal development.
REVIEW OF THE LITERATURE
Nyctitropic movements in plants
are not a recent observation. Bunning
(2, Ch. 2) states that Androsthenes
noticed diurnal leaf movements (nycti-
tropism) in Papilionacae while with
Alexander the Great about 2,300 years
ago. Throughout history many eminent
scientists and naturalists were at-
tracted to this phenomenon (2, 3, 6, 7).
Although these light controlled
movements, called nyctitropic move-
ments, have long been observed in
some plants, most earlier reports
failed to mention any important crops,
except for some members of the
Leguminosae, exhibiting this phe-
nomenon. Darwin (3), however, listed
a variety of Nankin cotton, which he
^-Soil scientist, U.S. Department of Agriculture, Agri-
cultural Research Service, National Tillage Machinery
Laboratory, Auburn, Ala.
identified as Gos sypium arboreum,
among 55 seedling plants in which
cotyledons exhibited diurnal move-
ment. In this same list, he noted that
Gos sypium herbaceum, an unknown
cotton species from Naples (Italy),
a cotton species from Alabama (U.S. ),
and a sea-island cotton had cotyledons
that did not exhibit diurnal movement
when grown in the middle of winter.
Darwin further stated that leaves of
many genera of plant "...must be well
illuminated during the day in order
that they may at night assume a ver-
tical position." He described these
movements in detail and plotted the
angle of movement. In 37 genera he
noted that leaves or leaflets rose to
p
Underscored numbers in parentheses refer to Liter-
ature Cited, p. ll.
1
a vertical position at night and in 32,
that the leaves or leaflets sank to
a vertical position. He noted that the
leaves of Nankin cotton exhibited 90
degree nyctitropic movement; how-
ever, cottons he describes as Gos-
sypium maritimum and Gos sypium
brazilense only occasionally showed
"sleep symptoms" in a poorly lighted
hothouse.
MATERIALS AND METHODS
With control of lighting, tempera-
ture, humidity, and gaseous exchange
now obtainable within environmental
chambers, the causes of nyctitropic
movement in plants can be defined
more precisely than was formerly
possible. Photographic techniques can
monitor the movements of an entire
plant in response to a particular en-
vironment with minimum disturbance.
Lights flashing on for 2- second inter-
vals each 45 seconds to photograph the
plant did not appear to affect the nycti-
tropic activity of cotton. Therefore,
an isolated cotton plant, growing under
controlled situations in an environ-
mental chamber was photographed on
movie film using a 45- second delay
between each exposed frame. The film
was shown on a screen where the posi-
tion of the leaves was marked and
measurements of movement recorded.
The dominant test plants utilized in
all studies were cotton varieties known
as "Auburn 56" and the double haploid
(M-8) of "Deltapine 14." Both these
cottons are classified as Gos sypium
hir sutum, although many other local
varieties also were observed.
The first studies involved increas-
ing the supply of soil moisture in
an attempt to eliminate wilt due to
moisture stress from later observa-
tions. This was done by first increas-
ing the size of the container about
10 times the volume thought to be ade-
quate and increasing the waterings
from once to three times a day. Cot-
ton was also grown in 5-gallon con-
tainers of nutrient solution with forced
aeration to assure an adequate supply
of moisture and oxygen.
The next studies attempted to regu-
late the ratio of the transpiring sur-
faces to the size of the root system.
Young plants, 3 weeks old, with a very
small leaf surface area were observed
as well as large plants, 3 months old,
with large, well- distributed root sys-
tems. One older plant, in a very large
container (6 feet deep), had 50 per-
cent of its leaves removed to reduce
transpiration, after its root system
was fully developed.
Another variable related to mois-
ture control is that of the atmospheric
relative humidity surrounding the
plant. In a third study the relative
humidity varied from 80 to more than
95 percent in an attempt to reduce
the vapor pressure deficit between
the plant and the atmosphere.
Since the drooping leaf movement
could not be eliminated by any mois-
ture control, the relative humidity of
the chamber for all later observa-
tions was maintained over 95 percent
and 1-cubic-foot containers with a
well- fertilized loam soil were used.
The plants were watered twice daily
to assure against wilt due to a lack
of moisture or low relative humidity.
Next, the effect of temperature on
nyctitropic movement was observed.
The temperature was held constant
during both the light and dark periods
at 26.7°, 29.4°, or 32.2° C., and in
other observations the temperature
was programed to vary similarly with
a typical July- August day at Auburn,
Ala. Using the programed discs, the
night temperature was held at 23.9°
for 8 1/2 hours and starting at sun-
rise raised for 6 1/2 hours to 29.4 ,
32.2°, or 35.0°, kept at the peak tem-
perature for 4 hours, then gradu-
ally reduced to 23.9° during the
next 5-hour period. Although several
2
additional variations were made, the
most severe treatment was a 35.0°
temperature for a 6-hour period with
an 18-hour "light" period.
In another study the timing of the
period was varied with respect to the
actual time. The 14-hour daylight pe-
riod (approximately typical of the local
mean July- August day) was adjusted
to have a 5:30 a.m. central standard
time "sunrise" and a 7:30 p.m. "sun-
set"; a 9:30 a.m. sunrise and an
11:30 p.m. sunset; a 4:30 p.m. sun-
rise and a 6:30 a.m. sunset; and a
10:00 p.m. sunrise and a 12 o'clock
noon sunset. The length of the day
(light period) was also adjusted from
11 to 18 hours. Attempts with a no-
light period (except for 2 seconds of
light as each frame of the movie was
exposed) was unacceptable, because
as the rhythm of the previous cycle
was dissipating, the plant was unable
to produce foods and became physio-
logically starved. To complete the
light study, light intensities of ap-
proximately 1,000, 2,000, and 2,700
foot-candles were tested in the con-
trolled environment chamber, and
a peak intensity of 8,300 foot-candles
was reached in field studies. The field
studies were conducted to support and
extend some of the studies conducted
in controlled environment chambers.
The test plant was allowed 3 to 5
days to become adjusted to the new
environment situations before obser-
vations started, except those in the
studies on container size and mois-
ture-treatment variations which re-
quired longer periods of adjustments.
In field observations before filming
began, all cotton plants for more than
a 6-foot radius around the plant to be
photographed were removed and a dike
was built up about 3 feet from this
plant. To insure an adequate supply
of water for this plant, about 20 gal-
lons of water was added weekly for
5 weeks to the dike, in addition to
the normal rainfall. All test runs
were photographed for approximately
2 1/2 days. Although many runs were
replicated, not all observations were
repeated under completely identical
situations.
RESULTS AND DISCUSSIONS
The dominant species background
of the cotton grown in Alabama ap-
pears to be Gos sypium hirsutum,
although characteristics of other spe-
cies may have been introduced into
some of the commercial seed now
grown throughout the area. In con-
trolled environment studies, Auburn
56, Coker 100A, Coker 413, Deltapine
Smooth Leaf, a double haploid (M-8)
of Deltapine 14, Dixie King II, Caro-
lina Queen, Stoneville 7 A, Stone ville
213, McNair 1 032, and okra-leaf vari-
ent of Auburn 56 were the varieties
used. All of these varieties exhibited
nyctitropic movement under the test
conditions, as did test plants of a wild
hirsutum from Mexico, a wild Gos-
sypium barbadense from Galapagos
Island, Gos sypium herbaceum (v. ini-
dicum) from India, and a diploid, Gos-
sypium arboreum, from Asia. Fig-
ure 1, B shows a young cotton plant
(Auburn 56) in the drooped leaf con-
dition, and A shows the same plant
fully recovered while undergoing nyc-
titropism.
Regardless of the reduction in
transpiration requirements of the en-
vironment and the plant, increase in
size of root system in soil- moisture
content (with aeration), nyctitropic
movement still persisted in the test
plants. Apparently the drooping leaves
in field-grown cotton is a character-
istic of the plant and not related to
moisture deficiency. On the other
hand, early drooping of leaves of cot-
ton, frequently noted in fields, can be
caused by moisture stress.
The economic significance of the
nyctitropic movement of important
3
Figure 1. — Nyctitropic movement of cotton, Range of diurnal leaf
movement of young cotton: A, Leaf arrangement at 9:30 a.m.
when the leaves are fully erect; B, leaf arrangement 12 hours
later when "leaf droop" is complete.
Figure 2. — Nyctitropic movement of cotton: A, Typical exposure surface
of leaves of a young cotton plant visible to a vertical light source when
the leaves are fully erect; B, exposure surface of leaves of the same
plant visible to a vertical light source when the leaves are in the com-
plete droop position. (Note that the exposure of ventral side of the leaves
accounts for about 30 percent of the total exposure surface in the droop
position.)
crops has not been investigated. It is
certainly true that the leaves on one
side of a plant with 90-degree leaf
movement during nyctitropism tend
to remain somewhat perpendicular to
the rays of a rising sun, and those on
the other side of a plant tend to main-
tain a near perpendicular alinement
to the setting sun. In the chamber
where overhead lights are stationary,
the "capture" of the sunlight by a plant
undergoing nyctitropic movement
would not be as efficient. Figure 2
shows the exposed leaf area of a
typical young cotton plant, visible to
a perpendicular light source: A(fully
erect) shows an exposure surface
which is usually more than 350 per-
cent greater than 13 (complete droop)
and, if exposure of only the dorsal
4
sides of leaves is compared, the ex-
posure surface is usually increased
to about 500 percent.
Associated with exposure surface
of the leaves is the angle of incidence
of the light upon the leaves. With per-
manently mounted overhead lights, the
angle of incidence increases from
near zero in the erect position to a
maximum of 90 degrees as the com-
plete droop position is reached. Leaf
canopy inclination may be important,
since the intensity of light, as meas-
ured in foot-candles by a horizontally
placed photoelectric cell, can increase
from 10 foot-candles 30 minutes be-
fore sunrise to 110 foot-candles at
sunrise, to 260 foot-candles 15 min-
utes later, to 400 foot- candles 45 min-
utes after sunrise, while the photo-
electric cell held perpendicular to
the sun's rays can read 2,000 foot-
candles 15 minutes after sunrise and
4,800 foot- candles 45 minutes after
sunrise.
On a clear summer day at Auburn
about 2 hours was required for the
intensity to reach 4,000 foot- candles .
A peak intensity of about 7,000 foot-
candles using horizontal instruments
was not obtained until 6 hours after
sunrise, while instruments held per-
pendicular to the sun's rays measured
over 7,000 foot-candles for 7 hours
throughout the middle of the day.
The light intensity reduction during
the afternoon hours was somewhat
similar to the morning increase on
clear days. During cooler days when
much less moisture is inthe air, per-
pendicular readings exceeded 12,000
foot- candles most of the day.
Should a plant that undergoes nycti-
tropic movement and maintains its
leaves somewhat perpendicular to
the light source have the capability of
utilizing the sun's energy more effi-
ciently, it would be important in a
plant- breeding program.
During these studies, we noticed
that the opening and closing of stomata
of the lower leaf surface of cotton
coincided with the nyctitropic move-
ment of the leaves very closely. The
Agricultural Research Service is
studying stomata relations to nycti-
tropism. If the drooping leaf seriously
reduces transpiration, could not this
mechanism then reduce the water
requirement of the plant?
The mechanism causing the loss of
erectness in the leaves undergoing
nyctitropism is beyond the scope of
the study reported here, but Blackman
and Paine (1) apparently believed that
there is an outward movement of
water from the cells to the intercel-
lular space within the leaves. They
recorded an increase in the perme-
ability of the cytoplasmic membranes
and a decrease in the osmotically
active contents of these cells during
nyctitropic movements in Mimosa
pudica. Teorell (9J supplemented this
observation when he reported that
rhythmic changes can occur in mem-
brane potentials, membrane resist-
ance and water flow through artificial
membranes under the proper stimuli,
as well as in the Nitella algal cell.
Many other scientists have detected
cyclic fluctuations in functioning ca-
pabilities that coincide with nycti-
tropic movements, and often when
nyctitropic movement ceases, these
fluctuations cease. Huck, Hageman,
and Hanson (5.) noted diurnal changes
in root respiration occurring in corn
and soybeans growing in alternating
exposures of light and dark that are
missing in plants grown in continuous
light. The same situation occurred
in excised roots of plants grown
under alternating light- dark condi-
tions .
Grossenbacher (4) reported diurnal
fluctuations in root pressure of de-
capitated 5-week old Helianthus. Bun-
ning (2, Ch. 9 ) states that even enzymes
localized in the plastids exhibit endo-
diurnal fluctuations in their activity
and that diurnal changes in photosyn-
thetic capacity have been observed.
He further states that the ability to
form chlorophyll fluctuates diurnally.
The volume of nuclei of guard cells of
5
Allium cepa has been reported (2,
Ch. 9) as varying from a low of
1,500 fi about midday to a high of
6,000/x during hours of darkness. Bun-
ning (2, Ch. 9) mentions that many
plants and animals have a circadian
rhythm of cell division. Regulating
the rate of cell division may be an
important factor in obtaining the most
desirable growth or development of
agricultural crops.
The extent of leaf movement during
nyctitropism in commercial cottons
grown in Alabama can exceed 90 de-
grees, especially in the younger top
leaves that do not have any physical
interference from other leaves or
branches. Older, lower leaves do not
exhibit this degree of movement.
Each leaf on a particular plant does
not initiate droop or recovery at the
same instant and the cessation of the
motion is not uniform. The data pre-
sented in table 1 are typical of the
extreme range of variations in angle
of leaf droop for a 2-month- old cotton
plant under an 1 8-hour-light, 6-hour-
dark cycle. The leaves selected did
not move through the same arc (arcs
vary from 34° to 95°) nor did they
reach their peak or minimum values
at the same hour; the elapsed time
from a peak to a minimum value
varied from 6 to 1 1 hours, and this
time is not related to the width of the
arc obtained. Most leaves on a par-
ticular plant are intermediate of the
extremes in table 1.
These findings agree with those of
Pfeffer in 1907 according to Biinning
(2, Ch. 15) in which Pfeffer observed
that single leaves of a plant can oscil-
late independently of each other if
they had been exposed to light-dark
cycles with different phases. Cer-
tainly, a plant exposed to overhead
lighting will have some shaded leaves
or parts of some that are shaded.
This, then, indicates a possibility
that a plant may not have a central
"nervous system" that controls the
nyctitropic response for the entire
plant.
Within a temperature variation of
23.9° to 35.0° C., leaf response of
cotton did not vary noticeably under
any particular circadian light-dark
cycle tested. Sweeney (7) found that
when nyctitropic movement measure-
ments made at different temperatures
were compared, the value for the
length of cyclic treatment did not
depend on the ambient temperature;
in fact, the movement was almost
completely independent of tempera-
ture.
Sweeney (7) further reported that
circadian rhythms in most plants
were -also remarkably stable to light
intensity and to most chemical fac-
tors. The study reported here did
not include comparison of chemical
factors, although the light intensity
variations observed concurred with
Sweeney's results. Nyctitropism
in cotton appeared similar with il-
lumination intensity up to 8,300 foot-
candles.
Sweeney (2) stated that wavelengths
of light that are effective in circadian
rhythms differ from organism to or-
ganism as well as the pigments re-
sponsible for active light absorption.
In some plants all colors of visible
light are said to begin the rhythms.
Both incandescent and fluorescent
lights were used as the light source
for the controlled environment cham-
ber in these studies. No study was
made involving the wavelengths of
light that are effective in nyctitropic
movements of cotton.
Apparently, the effective factor be-
ginning the nyctitropic movement of
cotton leaves is the timing of the cyc-
lic periods of light-dark. Since most
plants and animals on earth evolved
and developed under a circadianlight-
dark cycle, the cyclic period of 24
hours was maintained in all light- dark
applications used in this study. We do
not know how far cotton can vary
from a 24-hour- cycle period, but
such information would have no appli-
cation to field production as we now
know it.
6
TABLE 1. — Variations in movement of selected leaves of a cotton plant 1
Degrees from horizontal of leaf
Time
Leaf A
Leaf B
Leaf C
Leaf D
Leaf E
Dark
10 p.m.
80°
64°
11 p.m.
86°
70°
Midnight
80°
76°
1 a.m.
78°
76°
2 a.m.
73°
76°
3 a.m.
57°
45°
Light
4 a.m.
39°
31°
5 a.m.
14°
10°
6 a.m.
8°
9°
7 a.m.
2 +5°
3°
8 a.m.
+9°
0°
9 a.m.
+8°
0°
10 a.m.
+5°
0°
11 a.m.
+4°
6°
Noon
+2°
9°
1 p.m.
0°
12°
2 p.m.
6°
19°
3 p.m.
15°
18°
4 p.m.
25°
28°
5 p.m.
45°
42°
6 p.m.
53°
48°
7 p.m.
58°
53°
8 p.m.
63°
55°
9 p.m.
70°
57°
Range
P9° to 86°
0° to 76'
64°
OO
o
c/l
00
o
o
o
66°
o
00
i n
69°
63°
58°
65°
60°
58°
60°
60°
53°
33°
58°
54°
18°
49°
50°
17°
26°
38°
15°
14°
34°
15°
14°
34°
6°
15°
30°
6°
16°
27°
0°
18°
25°
0°
29°
24°
0°
33°
29°
0°
o
00
CO
31°
0°
41°
34°
0°
41°
39°
5°
45°
47°
12°
57°
48°
22°
64°
53°
37°
67°
55°
43°
69°
56°
57°
69°
56°
to 70°
14° to 69°
to
o
rt
o
1 For Auburn 56 and double haploid (M-8) cotton varieties.
2 + is movement extended beyond 0°.
Cyclic light- dark periods not only
induce nyctitropic leaf movement of
some plants but affect such proc-
esses as seed germination, growth
and metabolic activity, plant shape,
leaf coloration, leaf fall, flower pro-
duction, fertilization, seed produc-
tion, and dormancy. Sollerger (6)
states that in some plants under
proper stimuli flower, tendril, and
leaf movements, osmosis, water as-
similation, turgor, C02 metabolism,
acidity, phosphatase activity, seed-
ling, root and stem growth, photosen-
sitivity of pigments, and biolumines-
cence have been observed to have
circadian rhythms.
In this study only leaf movements
were correlated with controlled dark-
light cycles. Since normal light pe-
riods during the growth season in
Alabama approached a 14-hour, sun-
rise to sunset, period, the basic ob-
servations used a 14-hour-light and
10-hour-darkness cycle. All cotton
plants observed showed nyctitropic
movement regardless of age. The
okra-leaf varient was incapable of
rising much beyond 45° but the leaves
would droop to approximately 90°.
On almost all the other cottons tested,
the young, unobstructed top leaves
experienced about 90° movements.
Whether the 14-hour-light period
started before 5:30 a.m. or later than
4:30 p.m. central standard time, the
leaves of the plant were obviously in
a beginning state of nyctitropic move-
ment prior to 1 1 hours of light dura-
tion. The droop rate increased during
the hours of darkness, reached a
maximum, then leveled off for a short
period before slowly starting to re-
cover. Recovery was not quite com-
plete when the lights came on, but the
plant continued to recover until fully
erect. The leaves of the plant re-
mained at their most nearly hori-
zontal position (some leaves would
rise to 18° over the horizontal posi-
tion) for about a 6-hour period during
each complete cycle.
When the period of illumination
more nearly approached that of late
fall or early spring, results were
similar. For an 11-hour-light, 13-
hour-dark cycle, recovery appeared
to be complete when the lights were
turned on; drooping leaves became
obvious just before the lights were
turned off. Recovery was not com-
plete until about 1 1/4 hours after
sunrise; the plant appeared to be fully
erect for about 7 hours before the
leaves started their droop. In figure 3
nyctitropism of 2-month-old cotton
was photographed under an 11-hour-
light, 13-hour-dark cycle.
The extreme light duration cycle
was 18-hours light, 6-hours darkness.
In this cycle the nyctitropic move-
ment seemed just as extensive as it
did in the other circadian light stud-
ies. However, this cycle took the
plant more than 4 hours after the
lights were turned on to reach full
recovery. The plant remained fully
erect for about 5 hours, then the
leaves began their droop. The maxi-
mum droop was reached just before
the lights were again turned off, and
the plant remained fully "drooped"
for about 3 hours before starting to
recover.
Figure 4 shows the mean data of
leaf movement for all plant age,
temperature, moisture, and intensity
situations examined at each of the
light- dark duration cycles.. The mean
extent of leaf movement is essentially
identical for all the light-dark cycles.
The variations in time for the erect
and droop positions of the leaves were
small and inconsistent for the age,
temperature, intensity, and moisture
at each light-dark cycle plotted.
Angle of leaf position and timing of
various phases of the nyctitropic
movement in table 1 are for Auburn
56 and the double haploid (M-8) cotton
varieties only. The other cotton varie-
ties observed were not tested thor-
oughly enough to establish leaf angle
or to determine phase timing re-
sponses to temperature and illumina-
tion intensity variations under various
light-dark duration cycles. Should
differences in varieties exist and
have physiological significance, then
an incorporation of the nyctitropic
characteristics of cotton in a breed-
ing program may have merit.
With limited replications of cotton
grown under the 11, 14, and 18 hours
of light, no advantage was seen to
having more than an 11-hour-light
cycle, nor was there any disadvantage
to the 18-hour-light cycle.
8
DROOP COMPLETE RECOVERY INITIATED
Figure 3. — Two hour sequence of nyctitropic movement of cotton under an 11 -hour-light,
13-hour-dark cycle.
9
Figure 4.— Mean movement of
cotton leaves undergoing nycti-
tropism during various light-
dark cycles.
CONCLUSIONS
Cotton varieties grown in Alabama
and some foreign cottons exhibit nycti-
tropic movement of their leaves.
These nyctitropic movements appear
to be independent of temperature from
23.9° to 35.0° C. whether the temper-
ature is held constant or allowed to
vary in a manner similar to the daily
temperature cycle in Auburn, Ala.
The nyctitropic movement appears
to be independent of the age of the
plant although older leaves do not
droop as completely, or recover as
fully, as the younger, topmost leaves
that are free of any physical obstacles
to movement.
Nyctitropism of cotton appears to
depend on cyclic diurnal light- dark
applications. Definite leaf droop ap-
pears to be initiated in all observa-
tions prior to 11 hours of light du-
ration, regardless of supplemental
variations attempted. The timing of
the droop period can be varied some-
what.
Variations in light intensities from
800 to a maximum 8,300 foot-candles
did not appear to affect the move-
ment, nor did variations in wavelength
composition as observed by use of
actual sunlight, fluorescent lights, or
incandescent lights.
Although several days were re-
quired for a plant to adjust to a new
cycle, once this new pattern was es-
tablished, the movement responded
similarly to all light-dark cycles
tested regardless of season or civil
time.
Cessation of the drooping move-
ment of leaves of a cotton plant (re-
sembling wilt) could not be effected
by additional water, greater expanse
of the root system, or decreasing
transpirational losses. Apparently a
nyctitropic movement is active, and
this drooping movement is not wilt.
Extending the light cycle up to
7 hours per day after nyctitropism
was apparent had no detrimental ef-
fects on the cotton plant. Studies re-
quiring vigorous, healthy cotton plants
can be conducted even though the
plant exhibits nyctitropic movement.
10
LITERATURE CITED
(1) Blackman, V. H., and Paine, S. G.
1918. Studies in the permeability
of the pulvinus of Mimosa
udica. Ann. Bot. 32(1):
9-85.
(2) Biinning, Erwin.
1964. The physiological clock.
Endogenous diurnal
rhythms and biological
chronometry. Academic
Press, Inc., New York, N.Y.
(3) Darwin, Charles.
1881. Power of movement in
plants. D. Appleton and Co.,
Bond Street, N.Y.
(4) Grossenba,cher, K. A.
1938. Diurnal fluctuation in root
pressure. Plant Physiol.
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(5) Huck, M. G., Hageman, R. H., and
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