On the Mechanical Properties of the Vitelline Membrane of the Frog Egg

Abstract

Cole’s method is employed to measure the internal pressure in body cavity eggs of Rana temporaria. In the interpretation of the results the effect of bending resistance is considered.
The internal pressure in the undeformed egg in isotonic solution, at 25 °C, is 30 dyn/ cm2, corresponding to a stress resultant, or tension, in the vitelline membrane of 1-5 dyn/cm. In hypotonic solutions substantial increases in the pressure have been recorded.
When the pressure is studied as a function of temperature an anomalous high pressure is found at 16 °C for all the different incubation media employed.
A new method is applied to determine Young’s modulus of the membrane. The result obtained is 3·7 x 105 dyn/cm2 at 23° C.

Full text

J. Exp.
Biol.
(1974). 60. 807-820
With 16
text-figures
Printed in Great Britain
ON THE MECHANICAL PROPERTIES OF THE
VITELLINE MEMBRANE OF THE FROG EGG
BY
KJELL HANSSON MILD,»t S0REN LOVTRUPf
AND
TOMMY BERGFORSf
*Department of Theoretical Physics and ^Department of Zoophysiology,
University of
Umed,
S-901 87
Umed,
Sweden
(Received 19 October 1973)
INTRODUCTION
The mechanical properties of the cortex of the echinoid egg have for a long time
been the subject of investigation. In the early studies the sessile drop method was
employed (Vies, 1926; Harvey
&
Fankhauser, 1933) and in the interpretation of the
results obtained the assumption was made that, corresponding to an interfacial tension,
the membrane tension is constant and independent of the state of strain. Cole (1932)
devised a method in which the egg was compressed with a known force between two
parallel plates and the tension
was
calculated from the degree of compression. He found
evidence for an elastic tension in the cortex of sea-urchin
eggs.
In the undeformed state
the internal pressure is 40 dyn/cma. This early work has been reviewed by Harvey &
Danielli (1938).
The experiments of Cole were repeated by Hiramoto (1963), who reported the
prevalence of an elastic tension, and by Yoneda (1964,1972), who came to the opposite
result. Mitchison
&
Swann (1954a,
b)
criticized Cole's method for neglecting bending
resistance. Introducing a new device, the cell elastimeter, they found that the cortex is
thick enough to resist bending and that there is probably no internal pressure in the
normal sea-urchin egg. Hence, for mechanical purposes the unfertilized egg can be
compared to a hollow sphere filled with fluid and surrounded by a solid elastic wall
(Mitchison
&
Swann, 19546).
In the present study Cole's method has been adopted for measurements on the body-
cavity egg of Rana
temporaria.
In this object the mechanical strength of the ' cortex' is
primarily provided by the vitelline membrane, and it is thus the properties of
the
latter
which have been determined. In this structure the ratio R/h between egg radius and
thickness of the cortex is such that bending resistance can be neglected. The circum-
stance that the vitelline membrane plays an important, though not indispensable, role
for the early development in many amphibian species may serve to justify the present
study.
The pressure changes induced by incubation in hypotonic Ringer solutions of dif-
ferent concentrations have been studied as well as the effect of temperature on this
parameter.
J2-2

808 K. HANSSON MILD, S. LOVTRUP AND T. BERGFORS
MATERIAL
AND
METHODS
The biological material was body-cavity eggs from Rana
temporaria.
Mature frogs
were purchased from commercial dealers in Western Germany and the frogs were kept
under moist conditions at
5
°C until
used.
The eggs were surgically removed from the
body cavity after artificial ovulation induced by the method described by Rugh (1952).
According to the method of Cole (1932) the internal pressure of an egg may be
estimated by compressing the egg slightly between two parallel plates with a known
force F. From the contact area A between the plates and the egg the pressure p can be
calculated fromP = F/A. (1)
This equation is valid only if the bending of the membrane can be neglected. It is
shown by Hansson Mild & Kalnins (1974) from theoretical considerations that this
assumption holds for amphibian eggs.
The applied force was measured
by
the automatic diver balance (Bergfors, Hansson
Mild & Lflvtrup, 1970; Levtrup, 1973). The basic principle of this method is as
follows. A plastic diver with density less than the surrounding medium is prevented
from rising to the surface by an electromagnetic force acting on a small piece of iron
placed in the bottom of the diver. The current through the coil to the electromagnet is
proportional to the force holding the diver in place. If an object is placed on the diver
less force will be needed to hold the diver, and if the diver has been calibrated with
known weights, measurements of the current through the coil will give the reduced
weight (i.e. weight minus buoyancy) of the submerged object placed on the diver.
The diver employed in this study
is
shown in Fig.
1.
The diver body
is
made of poly-
propylene, except for the top where a piece of Plexiglass is inserted to accommodate
the egg. The reason for this construction is that the contact-area between the egg and
the diver must be very smooth, a requirement which is satisfied by Plexiglass but not
by polypropylene.
To ensure that the diver remains vertical when pressure is applied from above it is
necessary that the centre of gravity
is
situated as far down as possible. For this reason
the diver has been designed with a broad collar at the upper end enclosing an air
pocket, the size of which influences the loading capacity of the diver.
At the bottom of the diver there
are
inserted, at equal distances from the centre of the
diver, two pieces of soft iron with
a
length of 6-8 mm and a diameter of o-2-0-4 mm- ^
is desirable to have a high length-diameter ratio of the iron pieces because of the
demagnetization effect (Bozorth, 1951; Bergfors et al. 1970). By using two pieces of
iron at equal distances the diver is prevented from rotating during the course of the
experiment. To lower further the centre of gravity
a
piece of platinum is inserted in the
middle at the lower end of the diver.
The
holes,
in which the iron and platinum
pieces
are situated, are
filled
with Araldite;
this is done under vacuum in order to prevent air from being left around the metal
pieces. The device used for this purpose
is
shown in
Fig.
2.
When the
glue
has hardened
the lower end of the diver is polished against a blasted glass plate in order to get the
surface as smooth and plane as possible.
The diver is calibrated by loading with known weights of platinum. The calibration
curve depends, among other things, on the density of the liquid in the cuvette and on

Mechanical properties of
the
viteUme membrane
Plexiglass
809
Polypropylene
Glue
Air space
-Syringe
-Araldite
Needle
Rubber membrane
Iron
Platinum
Araldite
Fig.
1
Fig.
a
Fig.
1.
Section
of a
diver.
The
measurements
are:
length
25 mm,
smallest diameter
3 mm,
largest diameter
8 mm.
Fig.
2.
Apparatus employed
for
filling
the
space around
the
iron
and
platinum pieces with
Araldite.
the distance between the diver and the electromagnet. It is therefore necessary to start
each experimental series with a calibration of the diver. Examples of calibration curves
are shown in Fig. 3 for two different divers. When the load approaches the maximum
capacity of the diver, the curves deviate from a straight line for reasons outlined earlier
(Bergfors et
al.
1970).
After deposition on the diver, the egg is compressed by a Plexiglass rod which is
lowered to touch the egg and which, by means of a micromanipulator, can be moved
further down to get the desired degree of compression (Fig. 4). The current in the
magnet coil is now a measure of the force applied by the rod.
As has been pointed out by various authors, among others Mitchison & Swann
(1954 a,
b)
and Yoneda
(1964),
the critical point in this method
is
to measure the contact
area between the rod and the egg. Several attempts were made to overcome this
difficulty. Thus, we tried to measure the diameter of the contact area from photographs
taken through a microscope, but good accuracy cannot be obtained in this way because
the edge of
the
diver is closer to the camera than is the edge of the contact
zone.
We also

8ioK.
HANSSON
MILD,
S.
LOVTRUP
AND T.
BERGFORS
200
150
100
50
00 10 20 30 40 50
Force (dynes)
Fig.
3. Two typical calibration curves.
-Micrometer screws
Plexiglass rodPlexiglass rod
Photocell house Cuvette Lamp-house Mirror image Diver
Fig.
4. Micromanipulator arrangement with mirror used for compression of the eggs. The
enlarged part shows an egg compressed between rod and diver.
tried to measure the diameter through a transparent rod, but were unable to distinguish
the contact zone from the rest of the egg.
We solved the problem by designing the rod, by which the egg is compressed, in a
special way (Fig. 5). The part of the cylindrical rod which is in contact with the egg is
carefully polished to get a smooth surface. To obtain different degrees of compression a
set of rods with different diameters of the tip were employed.
The rod is placed in a three-dimensional micromanipulator so that it is possible to

Mechanical properties of the vitelline
membrane
811
18
1-4
06
100%
Ringer
2025
rj 0 5 10 15
U Time (min)
Fig. s Fig. 6
Fig. 5. The design of
the
Plexiglass rod used for compression of
the
eggs. The largest diameter
is 15 mm.
Fig. 6. Changes in force recorded for an egg in isotonic solution. The initial increase in the
force reflects the onset of the compression.
position the rod exactly above the centre of the
egg.
At the side of the cuvette
a
mirror is
placed so that the egg can be viewed from two sides at the same time. The egg is then
compressed so that most of the surface of the tip is in contact with the egg. Since the
tip is not much larger than the contact zone the diameter of the latter can be measured
quite accurately. The error in the diameter measurements
was
estimated to be ± 30 /im.
The manipulation was observed through a stereomicroscope with 25 times magnifica-
tion.
The measurements on a single egg usually comprised five or six different degrees
of compression. This could be achieved, with maintained accuracy in the contact
area measurements, by using two or three different
rods.
The pressures were calculated
according to equation (1) and plotted against the forces. By extrapolation the pressure
in the undeformed state was obtained.
RESULTS
In each individual case the recorded force was dependent on the amount of com-
pression, on the rate of the compression and on the incubation medium used. Examples
of force recordings are shown in Figs. 6 and
7.
Immediately after the rod
was
in position
the force reached a maximum value and subsequently there was a rapid fall lasting for
about 20
sec.
After this stage, two things would happen, depending on the incubation
medium. If isotonic solution
(100
% Ringer) was used, the force continued to decrease,
but at a slower rate, for more than
1
h (Fig. 6). In hypotonic solutions the force began

8l2
K.
HANSSON MILD,
S.
LOVTRUP
AND T.
BERGFORS
90
8-8
£
8-6
8-4
7-5% Ringer
20
25
0 5 10 15
Time (min)
Fig.
7. Changes in force recorded for an egg in hypotonic solution.
5 -
e
3
50%
Ringer
0-5 h
100%
Ringer
3-5 h
I
0-5
10 1-5
Force (dyn)
202-5
Fig.
8. Illustration of the extrapolation procedure used to estimate the pressure in the unde-
formed egg. The media employed and the duration of the incubation are indicated for each of
the curves.
to increase
at
a constant rate with no tendency
to
diminish even after
a
couple
of
hours
(Fig.
7)-
In
no
case could
any
change
be
observed
in the
contact area with time. This means
that the changes
in
pressure
are
directly proportional
to the
changes
in
the forces.
The
value
for the
force employed
was the one
recorded about 20
sec
after
the
change
of
the degree
of
compression. This expedient implies
a
minimum influence
on the
result
for the extrapolated pressure of the undeformed
egg
(Fig.
8).
We have
made no attempts
to find
a
theoretical equation
for
these curves. Four different concentrations
of
Ringer
solution were employed, namely
100%
(isotonic), 50%,
25
% and
7-5 %.
The
lowest
concentration corresponds approximately
to
fresh water.

Mechanical properties of
the
vitelline
membrane
813
c
8
o
ft. 1
10-5 °C
12 3 4 5 6 7
Time (h)
Fig. 9. Pressure versus time of incubation for different Ringer solutions at 10-5 °C.
•, 100% Ringer; •, 50
%
Ringer; A, 25
%
Ringer.
6 -
13
°C
3 4 5
Time (h)
Fig. 10. Pressure versus time of incubation for different Ringer solutions at 13 °C.
•, 100% Ringer. •, 50% Ringer; A, as
%
Ringer; 0,75
%
Ringer.
Figs.
9-13 show the extrapolated pressure corresponding to the undeformed
spherical egg as a function of the time of incubation in the specific media and at dif-
ferent temperatures.
At time t = o, i.e. when the
eggs
are removed from the frog and placed in the specific
medium, the extrapolated pressure is found to be about 30 dyn/cma. After 3 h in
7-5 % Ringer at 25 °C the pressure has risen to 500 dyn/cm2.
In Figs. 14-16 the pressure is plotted as a function of the temperature with time as a
parameter. The curves show an anomalous behaviour at 16 °C. The pressure at 16 °C
is
higher than at 19
°C
and this difference increases with time. This phenomena is most
pronounced in 7-5 % Ringer solution.

814
K.
HANSSON
MILD,
S.
LOVTRUP
AND T.
BERGFORS
12 3 4 5
Time (h)
Fig.
II Fig. ia
Fig.
II.
Pressure versus time of incubation for different Ringer solutions at 16 °C. •, 100%
Ringer;
•, 50
%
Ringer; A, 25
%
Ringer; O, 75
%
Ringer.
Fig.
12. Pressure versus time of incubation for different Ringer solutions at 19
"C.
•,
100
%
Ringer;
•, 5°
%
Ringer; A, 25
%
Ringer; O, 75
%
Ringer.
Combining the relations for pressure versus time from Figs. 9-13 with separate
swelling experiments in hypotonic Ringer solution where the radius was measured as
a function of time, Young's modulus, E, for the egg membrane has been calculated
according to the formula derived by Hansson Mild
&
Kalnins (1974),
T 1. D
(2)
where v
is
the Poisson's ratio (assumed to be
0-5),
RQ
is
the radius at t = o,
p
0
the corre-
sponding internal pressure,
Ai?
and
A/>
the changes in these parameters and
h
the thick-
ness of the membrane. The modulus
was
found to be
(3-7
±
I-I)
x io5 dyn/cm2 at
23
°C
(31 experiments). No significant difference could be noticed for the various experi-
mental conditions employed.

Mechanical properties of
the
vitellme
membrane
815
10
'6
x
25 °C
10
0-5
100%
Ringer
101316192225
3 4
Time (h)
Fig. 13
50%
Ringer
10 13 16 19 22
Temperature (°C)
Fig. 14
», 100%
25
Fig. 13. Pressure versus time of incubation for different Ringer solutions at 25 °C.
Ringer; •, 50% Ringer; A, 25 % Ringer; O, 7-5 % Ringer.
Fig. 14. Pressure versus temperature for 100% and 50% Ringer solutions at different times
of incubation. In the case of 100
%
Ringer no change with time is observed.
DISCUSSION
From Fig.
6
it
is
seen that in isotonic solution there
is a
very rapid initial drop in force,
followed by a much slower gradual decrease. In hypotonic solution the initial reaction,
for which we can offer no explanation, is also seen, but here an increase in tension is
observed to begin after about 5 min. This change may presumably be referred to the
swelling of the egg which occurs under our experimental conditions.
A decrease of pressure in isotonic solution has also been observed by Yoneda (1964)
and by Hiramoto (1963), both of whom employed Cole's method on sea-urchin eggs.
They used a constant force for the compression and observed a decrease in the distance
z,
and thus an increase in the contact area. The observations were made at 5 sec,
30 sec and
5
min. From the values reported it appears that the change is most rapid at
the beginning of the experiment, similar to that shown in Fig.
6.
This initial decrease in
force may be referred either to the viscosity of the protoplasm or to the rheological
properties of the egg membrane. Hiramoto (1963), on basis of experiments with eggs in
different stages of development, claims that the latter alternative is most
likely.
No such
experiments have yet been carried out with frog's eggs.

8i6
2 4
x
K.
HANSSON
MILD,
S.
LOVTRUP
AND T.
BERGFORS
7-5%
Ringer
7
6
25%
Ringer
§
lh
1025
13 16 19 22 25 10 13 16 19 22
Temperature ("C) Temperature (°C)
Fig.
is Fig. 16
Fig.
15.
Pressure versus temperature for as
%
Ringer at different times of
incubation.
Fig.
16. Pressure versus temperature for 7'5
%
Ringer at different times of
incubation.
From the measured pressure the stress resultant (i.e. the tension) in the membrane
can be calculated. For a spherical shell the tensions in the two main directions are equal
and given by
*i-tf.
= ^ (3)
(Fliigge, 1967). The mean radius of the egg used in this study
was
about 0-09 cm. This
leads,
at 25 °C, to a tension of 1-5 dyn/cm in 100% Ringer and 45 dyn/cm after 7 h
in 7-5 % Ringer.
Yoneda (1964, 1972), in his studies of the cortical tension in sea-urchin eggs, made
the assumption that the tension is constant and independent of the deformation of and
the direction on the
shell.
When his theory is applied to our experiments, the theoretic-
ally calculated form of the compressed egg clearly deviates from the real form. The
calculated contact radius was in all cases examined considerably lower than the
measured radius. Evidently, this approach must lead to a large overestimation of the
internal pressure.
To obtain a satisfactory theoretical evaluation of the contact radius from the form of a
compressed egg, the theory of thin elastic shells must be employed. As a first approxi-
mation the results presented by Reissner (1949) and by Updike
&
Kalnins (1970, 1972)

Mechanical properties of the vitelline
membrane
817
may be applied. In the latter paper the membrane tensions in the two main directions
are calculated for a situation similar to the experimental arrangement presented here,
and it is seen that the tensions in the two directions are equal only at the centre of the
contact area. In this study no attempts have been made to calculate the contact radius;
the special design of the Plexiglass rod permits an estimation of this parameter with an
accuracy sufficient for our purposes.
When osmotic water permeability is studied the internal pressure p is usually
neglected, because it is assumed to be very small compared to the osmotic pressure
difference, All, across the membrane. A commonly used experimental technique is to
place the egg in a hypotonic solution and follow the swelling as a function of
time.
The
equation describing the volume flow is given by Katchalsky
&
Curran (1965) as
(4)
where Jv is the volume flow, Lp the phenomenological coefficient for mechanical
filtration and a is the reflexion coefficient.
In order to employ this equation to evaluate the permeability coefficient from experi-
mental data, the term
A/>
is neglected compared to All. If the egg is placed in
7-5
%
Ringer solution, All is
0-205
osm at the beginning of the experiment, corresponding to
an osmotic pressure difference of 4-6 x io6 dyn/cm2. Hence, even with pressure dif-
ferences as high as 2000 dyn/cms (cf. Fig. 13)
A/>
is here negligible compared with All.
This also seems to be valid for sea-urchin eggs. Rieser (1950) found that the maximum
pressure these
eggs
can withstand without rupture
is
of the order o-o
1
atm
(10*
dyn/cma)
and since this is a maximum value the pressure being built up during the swelling
process can be only a fraction of this; hence, Ap can be neglected in comparison with
All for this type of
egg
also.
It should be noticed that this conclusion is restricted to the
initial phase of the swelling and implicitly the assumption is made of a semipermeable
membrane. Sigler
&
Janacek
(1969,
1971) have recently studied the ion content of frog
ovarian eggs after incubation in both hypo- and hypertonic media. They found that,
due to the efflux of K+ and Cl~ and a small influx of
Na+,
the difference between the
intracellular and the external osmolarity was almost zero after 3 h in hypotonic solu-
tion. The volume changes are of the order 15-20
%.
At this
stage
of the swelling process
we thus have almost isosmolarity, and under these circumstances the mechanical
properties of the membrane may very well play a role in the regulation of the volume
since Ap in equation (4) cannot be neglected under these conditions. It has been pro-
posed (Berntsson, Haglund & Lovtrup, 1965) that the elastical properties of the vitel-
line membrane play a significant role in the osmoregulation process. In view of the
present findings and some preliminary experiments on ovarian eggs, it appears that the
return to the original volume observed by the mentioned authors may be explained in
this way, provided that the initial difference in osmotic pressure is abolished through
the loss of ions from the egg.
At this stage we can offer no explanation of the anomalous temperature-dependence
of the pressure, but merely discuss alternative possibilities. Theoretically it is to be
expected that the curves in Figs. 14-16 should be slightly convex towards the tempera-
ture axis. This follows from the following reasoning.
In an elastic spherical shell with zero pressure initially a change in the volume causes
a pressure change which according to equation (2) is proportional to AR. As a first

818 K. HANSSON MILD, S. LOVTRUP AND T. BERGFORS
approximation AJ? may be obtained from equation (4), neglecting Ap and assuming
that the reflexion coefficient a is equal to unity,
% = dRjdt = -£,AII. (5)
From equations (2) and (5) it is seen that the temperature-dependence of the pressure
should be approximately the same as that of the water permeability. If the latter is
presumed to follow an Arrhenius equation, the behaviour at 16 °C in Figs. 14-16 is
anomalous. This, however, is not an unusual situation in biological systems. Drost-
Hansen
(1971,
1973) has reviewed different phenomena in which thermal anomalies
occur. No exhaustive explanation at molecular level has been given so far, but some
interesting attempts have been published by Drost-Hansen
(1971,
1973) and Forslind
(1970-
However, macroscopically there are at least three different parameters that could
explain the anomaly in the pressure, namely {a) Young's modulus, (b) the water
permeability and (c) the concentration difference across the membrane.
(a) If the elastic modulus of the egg membrane has a local maximum at 16 °C this
would cause the pressure to rise at that temperature. Anomalous behaviour of this
parameter has been observed in sea-urchin eggs (Mela, 1968), but here a minimum was
found at 16 °C. The interpretation of these experiments is questionable however - a
point which will be discussed later.
(b) If the water permeability is abnormally high at 16 °C proportionally more water
will move across the membrane per unit time than at adjacent temperatures, thereby
increasing R and hence also p. Investigations of the water permeability by means of
isotopic exchange at different temperatures (Hansson Mild & Levtrup, 1974, to be
published) have revealed no anomalies in the permeability. We have reason to believe
that this is true also for the osmoticaJly measured permeability, and therefore this
alternative
(A)
seems to be ruled out.
(c) By using a reflexion coefficient
cr
=
1 -o
it is implicitly assumed that the mem-
brane of the frog's egg is impermeable to the ions of the Ringer solution and that only
water moves across the membrane. This may hold for the initial stage of the experi-
ment, since the permeabilities to Na+ and K+ are some orders of magnitude smaller
than that to water, but, as discussed
above,
when the swelling goes on for several hours
this assumption is no longer valid (Sigler
&
JanaSek, 1971).
The fluxes of Na+ and K+ in red blood cells have a paradoxical temperature-depen-
dence (Wieth, 1970, 1971). The passive fluxes of Na+ can be described as having two
different components, one having a Qlo of 0-3 for the temperature range 0-18 °C and
the other having a Q10 of 3-7 for 18-38 °C. Thus, the curve of flux versus temperature
has a minimum around 18 °C. A similar effect is seen for the K+ flux. If the ion fluxes
through the frog egg membrane have this kind of temperature-dependence this could
explain the peaks in the pressure seen in Figs. 14-16, since the effective concentration
gradient over the membrane would have a local maximum at the particular tempera-
ture,
hence causing a proportionally larger flow of water across the membrane than at
slightly lower or higher temperatures.
This phenomenon could also explain the anomalous behaviour of Young's modulus
found for sea-urchin eggs and oyster eggs (Mela, 1968). This author presumed that the

Mechanical properties of
the
vitelUne membrane
819
pressure difference is given by the osmotic pressure difference across the membrane at
equilibrium in hypotonic solution.
where R is the gas constant, V the volume of the egg, Vb the osmotic inactive volume,
0 the osmotic coefficient,
n
the number of moles of solutes and Um the osmolarity of the
external medium. The assumption that the product
<fm
is constant during the experi-
ment may cause the observed minimum in the value for Young's modulus since,
according to his derivation of the formula for calculating the modulus, the latter is
proportional to the pressure. If the temperature-dependence of the ion fluxes is that
given by Wieth (1970) the product
<jm
would then have a maximum at 18 °C and hence
the equilibrium volume would be large, giving a low pressure. At higher or lower
temperatures the product
<fm
would be smaller giving a lower value of the volume and a
correspondingly higher pressure.
SUMMARY
Cole's method is employed to measure the internal pressure in body cavity eggs of
Rana
temporaria.
In the interpretation of the results the effect of bending resistance is
considered.
The internal pressure in the undeformed egg in isotonic solution, at
25
°C, is 30 dyn/
cm2, corresponding to a stress resultant, or tension, in the vitelline membrane of 1-5
dyn/cm. In hypotonic solutions substantial increases in the pressure have been
recorded.
When the pressure is studied as a function of temperature an anomalous high pres-
sure is found at 16 °C for all the different incubation media employed.
A new method is applied to determine Young's modulus of the membrane. The
result obtained is 3-7 x io6 dyn/cm2 at 23 °C.
We wish to thank professor Arne Claesson for his constant advice and the many
stimulating discussions concerning the theoretical aspects of this study.
The work was supported by the Swedish Natural Science Research Council.
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Note added in
proof.
Recent measurements in 75% Ringer at 10-5 °C have given
the following results: r hour, po=9° dyn/cm*; 2 hours,
p0
=
9O
dyn/cm2; 3 hours,
po=i25 dyn/cm2.