The development of the insect nervous system. I. An analysis of postembryonic growth in the terminal ganglion of Acheta domesticus


Gymer, A.; Edwards, J.S.

Journal of Morphology 123(2): 191-197

1967


This study describes the post-embryonic growth of the terminal ganglion in Acheta domesticus in terms of volume and cell number. All measurements were made at the beginning of each instar from hatching until the final moult on animals reared under controlled conditions. The terminal ganglion increases about 40-fold in volume from 2 × 10'/.1,3 in the first instar to 85 × 10' A' in the adult. A double logarithmic plot of ganglion volume against body weight shows that the ganglion volume is a function of body weight to the 0.56 power. Initially the neuropile grows at a greater rate than the cortex; in later stages they increase at the same rate. Increase in cell number was determined from serial sections. The total number of cells, based on corrected nuclear counts, increases from 3,400 to 20,000. There is little or no increase in the number of neurons. There are approximately 2,000 association neurons and 100 motor neurons in all stages. The number of glial cells increases from 1,000 to 17,000. Their multiplication rate appears to be related to the increase in neuron volume. Despite the increase in glial cell number, increase in cell volume is primarily responsible for the increase in total volume of the ganglion.

The
Development
of
the
Insect
Nervous
System
I.
AN
ANALYSIS
OF
POSTEMBRYONIC
GROWTH
IN
THE
TERMINAL
GANGLION
OF
ACHETA
DOMESTICUS
1
ANNE
GYMER
AND
JOHN
S.
EDWARDS
2
Developmental
Biology
Center,
Western
Reserve
University,
Cleveland,
Ohio
ABSTRACT
This
study
describes
the
post
-embryonic
growth
of
the
terminal
gan-
glion
in
Acheta
domesticus
in
terms
of
volume
and
cell
number.
All
measurements
were
made
at
the
beginning
of
each
instar
from
hatching
until
the
fi
nal
moult
on
animals
reared
under
controlled
conditions.
The
terminal
ganglion
increases
about
40
-fold
in
volume
from
2
X
10'
/.1,
3
in
the
first
instar
to
85
X
10'
A'
in
the
adult.
A
double
logarithmic
plot
of
ganglion
volume
against
body
weight
shows
that
the
ganglion
vol-
ume
is
a
function
of
body
weight
to
the
0.56
power.
Initially
the
neuropile
grows
at
a
greater
rate
than
the
cortex;
in
later
stages
they
increase
at
the
same
rate.
Increase
in
cell
number
was
determined
from
serial
sections.
The
total
number
of
cells,
based
on
corrected
nuclear
counts,
increases
from
3,400
to
20,000.
There
is
li
ttle
or
no
increase
in
the
number
of
neurons.
There
are
approximately
2,000
associa-
tion
neurons
and
100
motor
neurons
in
all
stages.
The
number
of
glial
cells
increases
from
1,000
to
17,000.
Their
multiplication
rate
appears
to
be
related
to
the
increase
in
neuron
volume.
Despite
the
increase
in
glial
cell
number,
increase
in
cell
volume
is
primarily
re-
sponsible
for
the
increase
in
total
volume
of
the
ganglion.
The
postembryonic
growth
of
the
nerv-
ous
system
in
insects
has
been
examined
in
several
volumetric
studies
which
consider
allometric
function
(e.g.
Hinke,
'62;
Lucht-
Bertram,
'62)
or
the
relation
of
growth
to
the
moulting
cycle
(e.g.
Power,
'52).
Stud-
ies
such
as
that
by
Panov
('62)
of
the
growth
and
development
of
the
component
glial
and
neuronal
elements
are
few;
and
most
treat
the
nervous
system
incidentally
in
respect
to
the
general
question
of
cell
number
versus
cell
volume
in
the
growth
of
insects
(e.g.
Abercrombie,
'36;
Grosch,
'50).
A
variety
of
patterns
of
growth
is
reported:
Trager
('37)
reported
that
cell
division
accompanies
the
growth
of
the
thoracic
ganglion
of
Aedes
aegypti
while
Johansson
('57)
discounted
cell
division
as
a
factor
in
the
growth
of
the
thoracic
ganglion
of
Oncopeltus.
There
is
not
yet
sufficient
quantitative
data
to
separate
the
particular
from
the
general.
This
study
is
a
first
step
in
an
attempt
to
quantify
the
growth
of
the
central
nerv-
ous
system
in
terms
of
cell
multiplication,
cell
enlargement
and
accession
of
afferent
fi
bers.
It
forms
part
of
an
approach
to
the
question
of
the
specificity
in
the
nervous
system
for
which
the
compact
and
rela-
tively
simple
insect
nervous
system
seems
to
be
apt
material.
We
have
examined
the
terminal
(last
abdominal)
ganglion
of
the
house
cricket,
Acheta
domesticus.
Although
it
is
derived
embryologically
from
the
fusion
of
three
segmental
ganglia,
it
is
morphologically
a
simple
structure
amenable
to
cell
counts
during
the
successive
instars
of
post
-em-
bryonic
development
which,
under
the
con-
ditions
adopted
for
this
study,
occupy
about
80
days.
Volume
measurements
and
cell
counts
using
the
methods
of
Marrable
('62)
were
made
from
serial
sections
of
speci-
mens
at
each
instar.
In
order
to
maintain
uniformity
of
sampling,
all
animals
were
fixed
within
one
hour
of
moulting.
This
study
does
not
therefore
take
into
account
the
changes
occurring
within
the
instar,
which
will
be
the
subject
of
a
further
paper.
I
This
work
was
supported
in
part
by
a
grant
NB
05137
from
the
Public
Health
Service
to
J.S.E.
A.G.
received
support
from
a
P.H.S.
Developmental
Biology
Training
Grant.
2
Address
correspondence
to:
John
S.
Edwards,
De-
partment
of
Zoology,
University
of
Washington,
Seattle,
Washington
98105.
3.
MORPH.,
123;
191-198.
191
192
ANNE
GYMER
AND
JOHN
S.
EDWARDS
MATERIALS
AND
METHODS
Synchronous
batches
of
crickets
were
obtained
by
providing
gravid
females
with
damp
sand
for
oviposition
within
a
limited
period.
They
were
raised
in
small
groups
in
Petri
dishes,
and
fed
a
standard
diet
(Nowosielski
and
Patton,
'65)
supple-
mented
with
lettuce.
Water
was
supplied
in
cotton
-plugged
capillary
tubing.
Devel-
oping
eggs
and
nymphs
were
maintained
in
incubtaors
at
30°C
during
the
12
-hour
light
period
and
28°C
during
the
dark
period.
The
relative
humidity
was
kept
at
about
76%
with
a
saturated
solution
of
sodium
chloride
in
an
open
bowl.
The
nymphs
were
immobilized
by
chill-
ing
them
every
two
days
for
changing
food,
cleaning
and
staging,
during
which
they
were
handled
with
a
soft
brush.
The
use
of
carbon
dioxide
for
anaesthesia
was
avoided,
since
repeated
use
was
found
to
depress
growth
rate.
Animals
which
closely
conformed
to
the
average
developmental
schedule
were
fi
xed
for
sectioning
within
one
hour
of
ecdysis.
Ganglia
were
fixed
for
4-6
hours
in
Helly's
fi
xative
and
serial
sectioned
in
paraffin
at
5
p.
All
series
were
stained
with
Hansen's
trioxyhematin
and
Eosin
Y.
Each
section
of
a
series
was
traced,
using
a
Reichert
projection
microscope,
on
graph
paper.
All
tracings
of
cortical
and
neuropile
area
for
one
ganglion
were
cut
out
and
weighed
together,
and
from
these
values
the
volumes
of
the
cortex
neuropile
and
whole
ganglion
were
determined.
The
nuclei
in
every
section
of
the
ganglia
were
counted.
All
nuclei
were
counted
except
those
of
tracheal
and
perilemma
cells.
Since
fragmentation
in
sectioning
in-
creases
the
apparent
number
of
nuclei,
a
correction
formula
(Marrable,
'62)
was
applied:
N
=
(1)
T
(D
2k)°
where
N
is
the
number
of
whole
nuclei;
n
the
apparent
number
of
nuclei
obtained
by
counting,
T
the
average
section
thick-
ness,
D
the
mean
nuclear
diameter,
and
k
is
a
correction
for
invisible
fragments
de-
termined
as
the
thickness
of
the
smallest
visible
fragment.
To
estimate
the
true
in-
crease
in
cell
number
throughout
develop-
ment,
the
mean
diameter
for
the
entire
range
of
visible
nuclei
was
calculated
sepa-
rately
for
each
instar.
The
nuclear
diam-
eters
were
found
to
have
a
trimodal
dis-
tribution.
The
entire
population
of
nuclei
of
one
instar
was
thus
divided
into
three
categories
and
the
mean
diameter
deter-
mined
for
each
so
that
the
true
number
of
cells
in
each
category
could
be
esti-
mated.
RESULTS
Growth
of
the
ganglion
relative
to
general
growth
The
ganglion
volumes
for
each
animal
are
recorded
in
table
1,
along
with
the
standard
deviation
(estimated
by
s,
the
sample
standard
deviation,
where
applica-
ble).
The
terminal
ganglion
increases
in
vol-
ume
about
40
-fold
from
2
x
10
6
p
3
in
the
hatching
to
85
X
10
6
11
3
in
the
adult.
The
variation
among
nonsiblings
was
no
greater
than
that
of
sibling
cultures.
The
differ-
ence
between
single
sample
values
and
the
true
mean
values
for
the
fourth
and
suc-
cessive
instars
is
not
yet
known;
measure-
ments
beyond
the
third
instar
establish
a
growth
trend
but
are
not
an
exact
measure
TABLE
1
Volume
changes
and
absolute
growth
rate
of
the
terminal
ganglion
of
Acheta
domesticus
Instar
Average
length
No.
of
samples
in
days
Mean
ganglion
volume
x
10
6
es
.d.
for
S
total
ganglion
x
10
6
ea
Percentage
increase
per
day
Mean
cortex
volume
x
10
8
ea
S.d.
for
cortex
volume
x
10
6
p.
3
Mean
neuropile
volume
x10
6
µa
S.d.
for
neuropile
volume
x
10
6
e
3
1
5.5
5
1.933
±
0.646
1.131
0.339
0.802
±
0.282
2
5.5
6
3.184
±
0.624
23
1.643
±
0.325
1.542
±
0.293
3
5.5
5
3.810
±
0.210
11
1.785
±
0.071
2.012
0.152
4
6.0
1
7.016
57
3.320
3.696
5
7.0
1
8.002
16
3.450
4.552
6
11.5
1
15.42
110
6.46
8.96
7
37.5
1
39.07
210
17.51
21.55
Adult
1
84.90
120
40.10
44.80
DEVELOPMENT
OF
THE
INSECT
NERVOUS
SYSTEM
193
of
that
trend.
From
table
1
it
is
clear
that
the
absolute
growth
rates,
that
is
the
addi-
tions
of
mass
per
day,
show
a
general
in-
crease
with
each
succeeding
instar.
The
increase
in
volume
of
the
terminal
ganglion
with
respect
to
increase
in
body
weight
is
shown
in
fi
gure
1,
which
indi-
cates
that
the
volume
of
the
ganglion,
ex-
pressed
as
a
power
function
of
body
weight,
has
a
value
of
0.56.
The
allometric
growth
of
the
ganglion
is
negative
in
all
stages
of
postembryonic
development.
These
re-
sults
agree
closely
with
the
differential
growth
ratios
obtained
by
Teissier
(cited
by
Huxley,
'32)
for
ganglia
of
four
other
insect
species,
all
of
which
were
about
0.6.
Neder
('59)
also
found
a
clearly
negative
allometric
growth
ranging
in
value
from
0.47-0.58
in
the
brain
of
several
Blattaria
during
the
entire
postembryonic
develop-
ment.
Relative
growth
of
cortex
and
neuropile
In
the
hatchling
cricket
the
cortical
re-
gion
of
the
ganglion,
which
is
composed
3.0
2.0
1.0
0
0
_En
0
rn
0
of
glial
cells
and
neuron
cell
bodies,
oc-
cupies
58%
of
the
volume
of
the
ganglion
(fig.
2).
During
the
fi
rst
20
days
of
devel-
opment,
i.e.
during
the
fi
rst
four
stadia,
the
neuropile
increases
rapidly
in
relative
volume,
reaching
a
maximum
of
55%
in
the
fourth
instar.
The
proportions
of
cor-
tex
and
neuropile
do
not
change
appreci-
ably
thereafter.
Increase
in
total
number
of
cells
Total
cell
counts
were
determined
for
fi
ve
animals
in
each
of
the
first
three
stadia.
The
counts
for
subsequent
stadia
are
based
on
single
animals
for
each
in
-
star.
The
neuron
population
of
a
second
adult
was
also
counted.
A
comparison
of
the
counts
of
total
visible
nuclear
fragments
showed
a
con-
siderable
increase
in
number
(table
2).
However,
a
comparison
of
apparent
nu-
clear
counts
is
not
an
adequate
measure
of
cell
multiplication,
since
the
nuclei
also
increase
in
diameter
during
development.
The
mean
nuclear
diameters
and
the
cor-
rection
factors
which
must
be
applied
sepa-
0
1.0
2.0
3.0
3.6
log
(wt.
in
gm
x
10
4
)
whole
animal
Fig.
1
Growth
in
volume
of
the
terminal
ganglion
of
Acheta
domesticus
relative
to
in-
crease
in
body
weight.
194
ANNE
GYMER
AND
JOHN
S.
EDWARDS
60
ai
55
J
E
0
1
5
'
0
131
-
6
0
1
z
40
0
0
J
3
50-
'
•2
45
-
A
1
I
I
I
1
I
1
10
20
30
40
50
80
90
Ganglion
volume
J
o'
x
10'
Fig.
2
Volume
of
neuropile
expressed
as
a
percentage
of
total
ganglion
volume.
TABLE
2
Sample
values
for
apparent
and
corrected
total
nuclear
counts
in
terminal
ganglia
of
Acheta
domesticus
Instar
Apparent
count,
n
Mean
diam.,
D
Correction
factor
Corrected
count,
N
Corrected
mean,
X
N
Corrected
N(sN)
1
6,983
5.8
0.49
3,295
3,421
210
1
6,478
3,174
1
7,183
3,520
1
6,600
3,234
1
6,383
3,128
2
7,057
6.4
0.46
3,246
3,220
±
236
2
7,243
3,332
2
6,313
2,904
2
6,798
3,127
2
7,691
3,538
3
8,666
7.1
0.43
3,726
3,650
±235
3
8,239
3,543
3
9,393
4,039
3
8,126
3,429
3
8,881
3,819
4
10,800
8.0
0.40
4,320
5
11,700
8.9
0.37
4,350
6
15,700
9.3
0.36
5,650
7
31,400
9.7
0.35
11,000
8
30,000
10.0
0.34
10,200
9
57,700
10.3
0.34
19,600
rately
for
each
instar
are
also
given
in
table
2.
The
total
number
of
cells,
in
the
ter-
minal
ganglion,
based
on
corrected
nu-
clear
counts
and
excluding
neurilemma
and
tracheal
cells,
increases
from
about
3,400
in
the
first
instar
to
about
20,000
in
the
young
adult.
Addition
of
new
cells
is
negligible
during
the
first
three
instars,
a
DEVELOPMENT
OF
THE
INSECT
NERVOUS
SYSTEM
195
period
during
which
the
relative
volume
of
neuropile
is
rapidly
increasing.
In
every
instar,
the
nuclear
diameters
have
a
trimodal
distribution.
The
increase
in
cell
number
can
be
best
examined
in
terms
of
the
proportion
of
nuclear
types
in
successive
instars
as
shown
in
table
3.
Although
the
grouping
of
nuclei
in
table
3
is
by
size
and
not
by
histological
type,
the
smallest
class
of
nuclei
consists
of
type
ii
and
type
iv
glial
cells
(Wigglesworth,
'59).
The
glial
nuclei
are
readily
identified,
not
only
by
size,
but
also
by
their
dense
basophilia,
lack
of
a
prominent
nucleolus
and
by
their
location.
Their
cytoplasm
is
not
readily
distinguished
in
light
micros-
copy
sections.
The
cytological
detail
of
nuclear
frag-
ments
revealed
that
fragments
of
larger
nuclei
contribute
very
little
to
the
count
of
small
nuclei.
It
may
be
concluded
that
the
population
of
small
nuclei
repre-
sents
glial
cells
almost
entirely.
Thus
only
the
glial
population
increases
in
number
during
postembryonic
development.
Glial
cell
numbers
Glial
cells
increase
in
number
from
about
1,000
in
the
first
instar
to
about
17,000
in
the
adult.
This
increase
in
num-
ber
is
evidently
accompanied
by
progres-
sive
differentiation,
especially
within
the
cortical
part
of
the
ganglion.
Thus
several
structural
features
described
in
adult
gan-
glia
are
not
acquired
until
quite
late
in
de-
velopment.
For
example,
the
separation
of
the
cortical
glial
mass
into
two
layers
in
ganglia
of
adult
cockroaches
(Smith
and
Treherne,
'63)
and
in
the
cricket
(Ed-
wards
and
Gomez,
unpublished)
is
not
evident
in
light
microscope
preparations
before
the
sixth
instar.
Nor
can
the
three
types
of
glial
cell
described
by
Wiggles
-
worth
('59)
be
readily
distinguished
be-
fore
this
time.
Neurons
numbers
Cells
with
medium-
and
large
-sized
nu-
clei
are
neurons,
some
of
which
may
be
neurosecretory
(
Panov,
'63;
Delphin,
'65).
Neurons
are
characterized,
particularly
in
older
animals,
by
their
prominent
nucleoli
and
membranes,
distinct
chromatin,
and
by
connection
with
axons
in
favorable
sections.
Pipa,
Cook
and
Richards
('59)
note
that
in
the
cockroach
two
extreme
types
of
nerve
cell
bodies
may
be
distin-
guished:
massive
ovate
neurocytes
and
smaller,
more
spherical
cells
termed
glob-
uli
cells
which
are
regarded
as
association
neurons.
The
size
relationship
between
the
medium
(13
ti)
and
ovate
nuclei
(25
ti)
of
the
cockroach
is
paralleled
in
the
cricket,
where
the
measurements
in
the
adult
are
18
u
and
28
II
respectively.
The
differ-
ences
between
the
two
types
of
neurons
are
evident
even
in
the
first
instar,
but
they
become
more
pronounced
as
develop-
ment
progresses.
The
ovate
neurocytes
of
early
instars
are
smooth
in
outline
and
contain
relatively
little
cytoplasm.
The
neuron
cell
bodies
of
later
instars
become
deeply
penetrated
by
glial
invaginations
(Edwards
and
Gomez,
unpublished)
as
in
those
of
Rhodnius
(Wigglesworth,
'59)
and
Periplaneta
(Smith
and
Treherne,
'63).
Under
the
light
microscope,
the
glial
in-
vaginations
may
appear
to
be
cytoplasmic
inclusions.
TABLE
3
Size,
measured
as
diameter
or
major
axis,
and
number
of
nuclei
in
three
size
categories
in
the
terminal
ganglion
of
Acheta
domesticus
Instar
Small
Medium
Large
Diam.
N.
Diam.
N.
Diam.
N.
%
1
3
1,100
31
6.6
2,300
69
10
incl.
with
medium
2
4
1,150
32.5
7
2,300
67.5
10
incl.
with
medium
5
7
2,030
48
10.5
2,130
50.2
18
76
0.8
9
8
17,000
86.5
18
2,600
13.1
28
88
0.4
196
ANNE
GYMER
AND
JOHN
S.
EDWARDS
As
may
be
seen
in
table
3,
the
number
of
neurons
does
not
increase
significantly,
if
at
all.
If
medium
sized
nuclei
are
diag-
nostic
of
globuli
cells
and
the
large
nu-
clei
are
always
associated
with
the
large,
ovate
motor
nerve
cells,
it
seems
that
there
are
about
2,000
association
neurons
and
fewer
than
100
motor
neurons
in
the
ter-
minal
ganglion
in
all
stages
of
postembry-
onic
development.
Cell
volume
changes
The
volume
of
neuron
cell
bodies,
as
estimated
by
calculations
from
average
di-
ameter,
may
increase
by
as
much
as
70
-
fold
during
postembryonic
development.
It
is
impossible
to
make
a
comparable
esti-
mate
of
the
volume
of
glial
cytoplasm
be-
cause
of
the
complex
geometry
of
these
cells,
and
no
attempt
has
been
made
in
this
study
to
estimate
volume
changes
of
glia
during
development.
The
decreasing
ratio
of
cell
number
of
cortex
volume
shown
in
table
4
indicates
the
extent
to
which
total
cortical
cytoplasmic
volume
increases
concurrently
with
increase
in
nuclear
size.
TABLE
4
Ratio
of
cell
number
to
cortex
volume
in
the
terminal
ganglion
of
Acheta
domesticus
Instar
Cell
number
cortex
volume
1
3.06
2
1.95
3
2.04
4
1.30
5
1.26
6
0.85
7
0.63
Adult
0.49
DISCUSSION
Postembryonic
development
of
the
two
major
cell
types
The
constancy
of
the
neuron
population
reported
above
implies
that
the
neuron
population
of
the
terminal
ganglion
is
established
during
embryonic
development,
but
we
cannot
say
that
the
construction
of
the
complete
pattern
of
nerve
connections
is
organized
then,
for
we
have
not
elimi-
nated
the
possibility
that
some
of
the
cells
remain
as
neurobalsts
until
late
in
develop-
ment.
The
source
of
innervation
for
the
genital
musculature,
for
example,
which
develops
in
late
instars
is
not
yet
known.
It
may
be
that
these
motor
neurons
differ-
entiate
from
neuroblasts
at
the
time
of
de-
velopment
of
the
genital
musculature,
but
we
have
no
criteria
as
yet
by
which
to
make
this
distinction.
Our
observation
that
the
neuron
popula-
tion
of
the
terminal
ganglion
of
the
cricket
remains
almost
constant
during
postem-
bryonic
development
while
the
glial
cells
show
a
17
-fold
increase
indicates
a
change
in
the
ratio
of
neurons
to
glia
from
1:0.5
in
the
first
instar
to
about
1:
8
in
the
young
adult.
The
nature
of
the
pattern
of
divi-
sion
of
glia
is
beyond
the
scope
of
the
present
paper,
but
it
is
relevant
to
note
that
Panov
('61,
'62)
has
observed
cyclic
periods
of
cell
division
related
to
the
moult
in
the
brain
and
thoracic
ganglia
of
late
instar
house
crickets.
We
found
no
mi-
toses
in
the
immediately
postecdysis
stage
at
which
the
animals
were
fi
xed.
If,
as
Panov
('62)
and
the
present
work
indi-
cates,
glial
cells
are
still
dividing
as
late
as
the
penultimate
instar,
the
conse-
quences
for
neuron
function
during
the
cyclic
periods
of
division
should
be
ex-
amined.
Glial
cell
number
of
neuron
function
Neurons
grow
in
volume
while
the
glia
grow
in
number
and,
to
an
extent
as
yet
undertermined,
in
volume.
The
great
pro-
liferation
of
laminate
glial
cell
processes
that
occurs
as
the
ganglion
grows
and
which
is
so
marked
a
feature
of
the
adult
ganglion
is
doubtless
associated
with
their
supportive
role.
Perhaps
the
maintenance
of
a
cell
that
is
practically
all
surface
places
a
limit
on
the
volume
of
the
glial
unit,
and
this,
together
with
the
changing
demands
of
growing
neurons
may
deter-
mine
the
extent
of
multiplication
of
glia.
The
double
logarithmic
plots
of
fi
gure
3
show
that
there
is
a
close
correlation
be-
tween
the
cell
number
and
both
cortex
and
neuropile
volume.
While
the
multiplication
rate
for
cells
does
not
increase,
except
perhaps
in
the
sixth
instar,
the
rate
of
multiplication
relative
to
the
size
of
the
ganglion
increases
from
the
fi
fth
instar
to
the
adult.
Thus
the
ratio
of
cortex
volume
to
cell
number
(table
4)
decreases
as
de-
velopment
proceeds,
while
the
ratio
of
glia
DEVELOPMENT
OF
THE
INSECT
NERVOUS
SYSTEM
197
4.3
r .
4.3
4
0
30
All
cells
.
5
Glia
1.0
Log
(corset
volame
ins?
x10
6
)
Figure
3a
2.0
4.0
3
All
cells
Glia
logiNevrapila
valuate,
ie
µ
3
s
opa)
Figure
3b
2.0
Fig.
3
Relationship
between
increase
in
cell
number
and
increase
in
volume
of
cortex
(a)
and
neuropile
(b).
to
neurons
increases.
Although
we
cannot
yet
define
the
relationship
precisely,
the
proliferation
of
glia
cells
is
evidently
re-
lated
to
the
increase
in
volume
of
neurons.
ACKNOWLEDGMENT
We
are
grateful
to
Dr.
R.
Pipa
for
a
critical
reading
of
a
draft
of
this
paper.
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