THE
RELATION
BETWEEN
THE
WORK
PERFORMED
AND
THE
ENERGY
LIBERATED
IN
MUSCULAR
CONTRACTION.
BY
WALLACE
0.
FENN.
(From
the
Physiological
Laboratories
of
Manchester
and
of
University
College,
London.)
MEASUREMENTS
by
Hartree
and
A.
V.
Hill(i)
of
the
initial
heat
pro-
duction
of
the
sartorius
muscle
of
the
frog
arranged
to
contract
isometri-
cally
have
shown
that
the
total
energy
so
liberated,
I,
is
equal
to
A,
the
energy
necessary
to
set
up
the
tension,
plus
Bt,
the
energy
necessary
to
maintain
it
for
the
duration
of
the
contraction.
Thus:
I
=
A
+
Bt
......
(1).
In
a
previous
paper
(2)
based
upon
similar
measurements
of
the
initial
heat
produced
when
the
muscle
is
allowed
to
shorten
during
stimulation,
I
have
shown
that
when
work
is
done
by
the
muscle
an
extra
supply
of
energy
is
liberated
which
does
not
appear
in
an
isometric
contraction
and
which
is
roughly
proportional
to
the
work,
W,
which
is
done.
Thus
the
total
energy,
E,
liberated
is
given
by
the
formula:
E
=
A
+
Bt
+
kTs
=
I
+
kW
......
(2),
where
T
is
the
tension
of
the
muscle
during
shortening
and
s
is
the
amount
of
shortening.
It
is
the
purpose
of
this
paper
to
discuss
the
significance
of
the
term
kW,
particularly
from
the
point
of
view
of
the
theory
that
a
stimulated
muscle
can
be
regarded
as
an
elastic
body,
and
to
present
further
experiments
which
make
possible
a
more
detailed
analysis
of
the
excess
energy,
kW.
1.
The
muscle
as
an
elastic
body.
A
resting
muscle
is
obviously
an
elastic
body.
When
stretched
its
tension
increases
and
the
work
done
in
stretching
it
is
stored
in
it
as
potential
energy.
When
released
and
allowed
to
shorten
a
part
of
this
potential
energy
can
be
recovered
as
work,
the
remainder
being
lost
as
heat
owing
to
friction
in
irreversible
processes
within
the
muscle
sub-
stance.
By
analogy
with
a
resting
muscle
Weber(3)
first
regarded
a
stimulated
muscle
as
a
new
elastic
body
suddenly
created
from
the
old
one
at
the
moment
of
stimulation
and
reverting
to
it
again
in
relaxation.
PH.
LVIII.
24
W.
0.
FENN.
More
specifically
the
elastic
body
theory
in
its
original
form
states
that
if
a
muscle
is
able
to
shorten
to
a
length
1,
under
tension
T,
then
if
stimu-
lated
at
a
length
I
it
will
develop
a
maximum
tension
T.
In
other
words
the
maximum
tension
of
the
stimulated
muscle
is
dependent
only
upon
its
length
(compare
an
elastic
band).
This
is
true
for
a
muscle
stimulated
with
a
tetanising
current
of
sufficiently
long
duration
to
permit
it
to
come
into
equilibrium
with
its
load.
The
time
occupied,
however,
by
the
muscle
in
passing
from
a
given
length
and
tension
characteristic
of
the
muscle
as
a
resting
elastic
body
to
a
length
and
tension
characteristic
of
it
as
an
active
elastic
body
(under
prolonged
stimulation)
varies
with
the
mechanical
conditions.
Hence
it
happens
that
for
twitches
or
short
tetani,
relaxation
may
set
in
before
the
transformation
is
complete.
In
other
words
a
muscle,
which
in
a
twitch
or
short
tetanus
can
develop
a
tension
T
at
length
1
(isometrically),
may
not
have
time
to
shorten
to
length
1
under
a
tension
of
T
(isotonic).
This
is
a
particular
case
of
the
more
general
proposition
demonstrated
by
v.
Kries(4),
Fick5),
Blix(6)
and
Seemann(7)
(cf.
also
Bethe(8))
that
tension
is
not
a
simple
fuinction
either
of
length
alone,
or
of
length
and
time
(after
stimulation).
v.
Kries
in
particular
had
the
idea
that
the
mechanical
changes
in
contraction
actually
affected
the
rate
of
the
chemical
processes
underlying
the
con-
traction,
but
his
evidence
for
this
conception
was
hardly
concJusive.
These
facts
in
themselves
largely
disprove
the
original
elastic
body
theory,
or
at
least
they
necessitate
so
many
qualifications
that
it
loses
its
useful-
ness
as
a
simple
means
of
analysis.
Fick9()
alone
among
previous
writers
has
doubted
the
fundamental
conception
at
the
root
of
the
theory
which
postulates
a
development
of
elastic
potential
energy
at
the
mioment
of
stimulation,
at
the
expense
of
which
work
can
be
performed
so
long
as
this
new
elastic
state
is
maintained.
My
own
experiments
confirm
Fick
in
this
respect
and
suggest
that
a
stimulated
muscle,
although
under
considerable
tension,
may
possess
very
little
elastic
potential
energy,
and
that
the
energy
necessary
for
shortening
(i.e.
for
work)
is
liberated
as
the
shortening
proceeds.
Thus,
in
order
to
lift
a
weight
to
a
given
height
and
to
perform
work,
W,
it
is
not
enough
to
liberate
energy
A
to
set
up
the
tension
and
energy
Bt
to
maintain
it
during
the
shortening;
in
addition,
an
extra
amount
of
energy
klW
must
also
be
mobilised.
It
is
hard,
therefore,
to
escape
from
the
conviction
that
the
actual
motive
power
is
kW.
The
old
and
the
new
theories
of
the
nature
of
muscular
activity
in
the
performance
of
work
may
be
exemplified
by
the
following
two
methods
of
lifting
a
weight:
(a)
work
may
be
done
against
a
spring,
374
MUSCLE
WORK
AND
ENERGY.
which
may
then
be
allowed
to
shorten
and
lift
the
weight;
(b)
the
weight
can
be
raised
directly
by
means
of
a
chain
and
windlass.
In
the
latter
method
every
link
of
the
chain
which
is
wound
up
involves
the
ex-
penditure
of
so
much
energy
at
the
moment
of
winding.
The
chain
may
be
under
great
tension,
but
being
inextensible
it
possesses
no
potential
energy.
From
the
point
of
view
of
the
energy
exchange
the
shortening
of
a
muscle
appears
to
be
analogous
to
the
windlass
and
chain
rather
than
to
the
elastic
band
or
spring,
although
it
may
partake
to
a
limited
extent
of
the
characteristics
of
the
latter.
2.
Experimental
analysis
of
the
excess
energy,
kW.
Under
the
experimental
conditions
previously
described(2),
a
muscle
which
liberated
excess
energy,
kW,
in
the
performance
of
work,
W,
both
raised
and
lowered
the
weight,
so
that
the
work
W
reappeared
as
heat
in
the
muscle
in
relaxation.
It
was
conceivable
therefore
that
part
(C)
of
kW
is
due
to
shortening
in
contraction,
and
part
(R)
due
to
lengthening
in
relaxation:
thus,
E
=
I
+
kW
=
I
+
C
+
R
......
(3).
Two
methods
will
now
be
described
by
which
C
and
R
can
be
directly
and
separately
determined.
A.
The
measurement
of
R
directly
and
of
C
by
difference.
The
method
consists,
in
general,
in
measuring
the
variations
in
total
energy
output
caused
by
lowering
increasing
weights.
More
specifically,
it
involves
two
series
of
observations,
(a)
and
(b),
taken
alternately
with
varying
loads.
(a)
The
muscle
is
stimulated
with
a
short
tetanus
and
shortens
a
fixed
distance,
s,
isotonically,
under
tensions
T1],
T2,
T3,
etc.,
lowering
the
corresponding
weights
in
relaxation.
The
variations
in
heat
observed
are
thus
due
to
both
C
and
R.
The
total
heat
recorded
on
the
galvano-
meter
represents
the
total
energy
liberated,
Ea,
and
Ea=
I
+
(C-1)
+
R
......
(4),
1
is
that
small
fraction
of
the
energy
W
of
the
weight
falling
in
relaxation,
which
is
not
absorbed
by
the
muscle
as
heat
but
is
wasted
as
heat
in
the
apparatus
by
friction
and
impact.
Measurements
show
that
this
is
small
enough
to
be
neglected
(cp.
Table
IV).
(b)
The
muscle,
previously
slightly
stretched,
is
caused
to
shorten
the
same
fixed
distance,
s,
just
before
stimulation
and
under
no
tension,
and
to
lengthen
in
relaxation
under
varying
tensions,
T1,
T2,
T3,
etc.
Under
these
circumstances
there
is
no
energy
change
associated
with
the
24-2
375
W.
0.
FENN.
shortening,
except
for
the
small
loss,
p,
of
potential
energy
by
the
resting
muscle,
and
a
thermoelastic
cooling,
e,
as
shown
by
Hartree
and
Hill
(10).
In
relaxation
the
energy
W
of
the
falling
weight
is
absorbed
as
heat
by
the
muscle.
Hence
the
total
energy,
Eb,
measured
as
heat
is:
Eb=(p-e)+I+R+(W-l)-(p-e)=I+R+(W-1)
(5).
The
quantity
(p
-
e)
appears
both
in
the
shortening
and
in
the
length-
ening
process,
but
with
opposite
signs
so
that
it
cancels
out.
I,
the
average
of
the
isometric
heat
in
both
positions,
can
be
determined.
Hence,
knowing
Eb
and
W,
the
value
of
R
can
be
calculated.
Knowing
R
and
I,
C
can
be
determined
from
E.
in
equation
(4).
It
should
be
noted
that
in
case
(a),
equation
(4),
the
energy
W,
although
appearing
in
relaxation,
is
actually
expended
by
the
muscle
in
contraction
and
is
thus
a
part
of
C.
In
order
to
compare
E.
and
Eb
it
is
necessary
that
the
stimulus,
initial
length,
initial
tension
and
amount
of
shortening
allowed
be
the
same
in
all
cases.
Hence
after-loaded
limited
contractions
have
been
used.
For
the
observations
of
Eb
a
magnet
was
arranged
to
raise
the
weight
to
the
fixed
height
just
before
stimulation,
and
to
return
it
to
the
muscle
for
lowering,
so
to
speak,
when
the
muscle
tension
had
reached
its
maximum.
The
muscle,
therefore,
is
stimulated
at
its
shorter
length
and
"discovers"'
in
relaxing
that
it
must
lower
a
weight.
By
permitting
the
muscle
to
shorten
just
before
stimulation
the
correction
(p
-
e)
can
be
made
to
cancel
out,
so
that
it
does
not
record
on
the
galvanometer.
The
special
lever
used
in
these
experiments
and
in
many
of
those
reported
previously
is
shown
in
Fig.
1.
It
is
essentially
an
ordinary
lever
of
the
first
class;
the
weight
is
hung
7
mm.
from
the
fulcrum
at
one
end
and
the
muscle
pulls
down
28
mm.
from
the
fulcrum
at
the
other.
By
means
of
the
screws
S
and
L
under
opposite
ends
of
the
lever
the
amount
of
shortening
or
lengthening
of
the
muscle
can
be
confined
within
the
desired
limits.
The
attachment,
T,
for
releasing
the
lever
is
not
used
in
this
experiment.
The
only
other
feature
of
the
apparatus
which
is
essential
for
the
present
purpose
is
the
bell
magnet
above
the
lever.
The
electric
circuit
through
the
magnet
was
closed,
however,
not
as
shown
in
the
figure
but
by
a
special
key
on
a
revolving
drum,
so
that
the
moment
of
closure
could
be
timed
to
within
005
second
in
relation
to
the
moment
of
stimulation.
When
the
circuit
is
closed,
the
weight
end
of
the
lever
is
lifted
rapidly
until
the
lever
strikes
the
screw
S.
The
muscle
is
thus
per-
mitted
to
shorten
under
no
load.
When
the
circuit
is
broken
by
the
opening
of
another
key,
the
weight
becomes
free
to
fall
and
stretch
the
muscle
until
the
lever
hits
the
screw
L.
The
whole
lever
is
mounted
on
a
376
MUSCLE
WORK
AND
ENERGY.
stand
with
a
screw
adjustment,
so
that
its
height
above
the
muscle
can
be
regulated.
1~~~~~
~~~~~~~w.
Fg.
1.
Muscle
lever
and
attachments.
The
lever
is
of
light
brass
with
a
bamboo
writing
tip.
The
support
is
also
of
brass.
m
represents
the
muscle
attached
to
the
lever
and
resting
on
the
thermopile,
Th,
which
is
connected
to
the
galvanometer,
G.
The
stimu-
lating
electrodes,
8tiM.,
are
applied
to
either
end
of
the
muscle.
C
is
a
counterpoise
which
holds
the
movable
attachment,
T,
in
position
against
the
lever
where
the
shoulders,
a
and
b,
serve
to
prevent
the
weight
from
falling
or
rising
respectively,
according
to
the
desire
of
the
experimenter.
On
the
screw,
8,
is
an
ebonite
cap
bearing
a
contact
point
which
makes
electrical
contact
with
the
lever
when
it
is
pulled
down
and
thereby
operates
the
bell
magnet
above
the
lever.
The
brass
release
mechanism,
T,
is
operated
by
the
bell
magnet
below
the
lever.
The
weight,
wt.,
is
hung
on
a
wire
passing
through
a
hole
in
the
support.
L
and
S
are
set
screws
(cp.
also
Text).
In
all
six
complete
experiments
of
this
type
have
been
performed_.
A
typical
one
is
shown
in
Fig.
2.
The
experimental
points
E.
and
Eb
(equations
(4)
and
(5))
are
indicated
by
circles.
The
isometric
heat
is3
given
in
both
the
long
and
the
short
positions.
The
average
may
be
used
in
the
calculations.
It
should
be
noted
that
the
axis
of
abscissse
in
the
figure
does
not
represent
the
zero
ordinate,
and
hence
that
the
excess
heat,
W,
is
really
fairly
small
compared
to
the
isometric.
The
excess
heat,
kW,
is
represented
by
the
vertical
distance
between
E.
and
the
isometric;
it
consists
of
two
parts
C
and
R
associated
with
contraction
1
In
addition
positive
values
for
(E6
-Eb)
for
single
weights
have
been
found
in
a
considerable
number
of
other
experiments.
377
W.
0.
FENN.
and
relaxation
respectively.
Part
of
C
is
W,
the
mechanical
work
per-
formed.
The
relative
values
of
C,
W
and
R
are
dependent
upon
the
Ergs
x
IO«
Em
7.1
X
fSI+R
6
short
\b
isometric
1-
I
<
lo'n3
50
100
1
50
9,MS.
Fig.
2.
Variations
of
C,
R,
kW
and
W
with
variations
in
load.
kW
is
the
excess
energy
for
the
combined
process
of
raising
and
lowering;
W
is
the
work;
C
and
R
are
the
fractions
of
kW
associated
with
contraction
and
relaxation
respectively.
Duration
of
stimulus
0-2
second.
Weight
of
muscle
0
33
gm.
Temp.
00
C.
Muscle
shortens
2*4
mm.
in
each
case.
accuracy
of
the
calibration
but
the
rather
considerable
variations
observed
in
different
experiments,
particularly
in
the
values
of
R,
are
too
great
to
be
explained
in
this
way.
The
fact,
however,
that
EB
>
Eb
is
entirely
independent
of
the
calibration,
and
proves
that
in
shortening
under
a
load
the
muscle
liberates
as
heat
a
certain
amount
of
energy
(C
-W
in
excess
of
the
isometric,
in
addition
to
the
energy,
W,
which
is
stored
in
the
weight
as
potential
energy.
The
value
of
(E.
-
Et)
or
(C
-
W)
increases
slightly
with
the
load,
but
does
not
diminish
to
zero
at
zero
load
if
the
dotted
prolongations
of
E.
and
Eb
are
correct.
This
suggests
that
a
considerable
part
of
(C
-
W)
is
associated
with
the
frictional
loss,f,
involved
in
the
change
in
shape
of
the
muscle.
If
(C
-
W)
equalsf
then
the
simple
conclusion
can
be
drawn
that
the
excess
energy,
kW,
associated
with
contraction
is
equal
to
the
sum
of
the
external
work,
W,
and
the
internal
work,
f.
The
difference
between
E.
and
Eb
can
hardly
be
due
to
the
fact
that
the
muscle
is
stimulated
in
the
long
position
in
the
former
and
in
the
short
position
in
the
latter
because,
to
judge
from
the
isometric
heats
in
the
two
positions,
Eb
should
then
be
larger
than
E,,.
The
fact
that
the
reverse
is
true
at
zero
loads
indicates
that
shortening
without
tension
involves
a
greater
expenditure
of
energy
than
tension
without
shortening.
378
MUSCLE
WORK
AND
ENERGY.
The
most
important
new
point
in
connection
with
Fig.
2
is
the
existence
of
R,
the
excess
energy
associated
with
the
lowering
of
the
weight
in
relaxation.
The
existence
of
such
an
effect
has
occasionally
been
de-
bated
(Frank
(11))
but
no
convincing
experiments
have
been
forthcoming,
chiefly
on
account
of
the
difficulty
of
expressing
both
heat
and
work
in
the
same
units.
To
verify
this
result
I
have
conducted
on
14
muscles
24
series
of
observations
similar
to
those
in
the
Eb
series,
Fig.
2,
in
which
the
conditions
of
stimulation
and
contraction
have
been
constant,
while
the
loads
lowered
in
relaxation
have
been
varied.
The
work,
W,
done
on
the
muscle
by
the
weight
in
falling
also
has
been
calculated,
and
Eb
has
been
found
to
increase
more
rapidly
than
could
be
accounted
for
by
the
increase
in
W.
Thus
(Eb
-Eb)
>
(Wn
-
W),
where
EbL
and
W,
apply
to
the
smallest
weight
used
and
Ebn
and
W,
to
any
larger
weight.
This
result
has
been
obtained
invariably
in
ten
out
of
the
14
muscles
used:
it
is
perhaps
significant
that
I
have
never
failed
to
obtain
it
except
during
the
summer
months
when
the
temperature
was
higher
and
the
frogs
were
in
very
poor
condition.
In
Table
I
the
results
of
four
typical
experiments
of
this
sort
have
been
collected,
all
of
which
show
an
extra
liberation
of
energy
involved
in
lowering
the
various
weights.
It
should
be
noted
that
this
excess
is
calculated
on
the
assumption
that
R
=
0
with
the
smallest
weight.
Both
TABLE
I.
Increased
heat
due
to
relaxing
under
increasing
weights.
Exp.
A
Exp.
B
Increase
Increase
in
heat
Increase
Increase
in
heat
in
work
A-
in
work
A
W,
-
21
Eb
-693
E-
638
W.
-
15
E1
-
729
Eb
-728
14
44
52
15
21
20
28
73
75
31
60
51
42
120
116
46
85
102
56
145
-
61
135
116
67
147
-
0-31
gm.;
00
C.
0-26
gm.;
8.20
C.
E,xp.
C
Exp.
D
Increase
Increase
in
heat
Increase
Increase
in
heat
in
work
A
in
work
A
W,-47
Ebn
2040
Ebn-
1340
W,-13
Eb
-910
Eb
-798
38
159
80
14
3
30
75
345
218
41
81
89
113
384
233
68
113
108
150
449
-
95
162
0-54
gm.;
9.7°
C.
0-17
gm.;
150
C.
Both
heat
and
work
are
given
in
units
of
100
ergs.
The
muscle
was
stimulated
for
0-2
second
in
each
case
with
a
current
of
suitable
strength
from
the
alternating
current
mains.
The
weight
of
each
muscle
and
the
temperature
are
given
under
each
experiment.
Two
series
of
observations
with
each
muscle
are
recorded.
Each
of
these
is
the
average
of
two
readings,
one
in
the
ascending,
the
other
in
the
descending
order
of
weights.
379
W.
0.
FENN.
Fig.
2
and
Fig.
3
make
it
probable
that
R
>
0
even
for
zero
loads,
so
that
the
values
of
(Eb.
-
Eba)
-
(W,,
-
W,)
from
Table
I
are
probably
less
than
the
true
value
of
R.
The
first
column
shows
the
increase
in
work
with
increasing
weights,
above
that
involved
in
lowering
the
smallest
weight,
i.e.
W,,
-
W.
In
this
case
the
work
is
done
by
the
weight
upon
the
muscle.
The
second
and
third
columns
give
the
corresponding
increase
in
heat
Ebn
-
Eb1
as
observed
in
two
duplicate
series.
The
second
and
third
columns
are,
with
a
single
exception,
larger
than
the
corresponding
values
in
the
first
column.
The
effect
of
fatigue
becomes
evident
when
the
two
values
of
Eb,
for
each
experiment
are
compared.
Fatigue
was
least
in
Exp.
B,
Eb1
decreasing
from
729
to
728
only,
and
was
greatest
in
Exp.
C,
where
Eb,
fell
from
2040
to
1340.
Because
of
fatigue
the
observa-
tion
with
the
highest
weight
in
each
second
series
had
to
be
omitted.
The
existence
of
R
cannot
be
explained
by
an
error
in
the
calibration,
for
R
is
usually
larger
than
W
and
a
100
p.c.
error
in
the
calibration
is
impossible.
The
interpretation
of
R,
the
excess
heat
associated
with
lengthening
of
the
muscle
in
relaxation,
is
difficult
but
it
is
probably
misleading
to
regard
it
as
an
expression
of
an
"effort"
made
by
the
muscle
in
lowering
the
weight.
It
may
be
suggested
rather
that
it
is
best
correlated
with
the
time
at
which
lengthening
begins.
Thus
the
larger
the
weight
the
earlier
in
relaxation
the
stretching
begins
and
the
greater
the
tension
of
the
muscle
during
the
stretching.
It
is
because
of
this
greater
tension
with
the
larger
weights
that
the
muscle
is
able
to
absorb
as
heat
all
the
energy
liberated
by
the
various
weights
in
falling.
In
a
previous
paper(2)
it
was
found
that
the
excess
energy
involved
in
work
on
an
isotonic
lever
was
1-8
times
the
work
performed,
while
the
corresponding
figure
for
an
inertia
lever
where
the
work
was
not
re-
absorbed
as
heat
in
relaxation
was
only
1x3.
This
difference
is
doubtless
due
to
the
excess
energy
liberated
in
lowering
the
weights
in
relaxation
and
is
good
indirect
evidence
in
support
of
the
experiments
just
described.
Thus
1-3W
+
R
=
1-8W.
The
figures
are
approximate
only.
B.
The
measurement
of
C
directly
and
of
R
by
difference.
This
method
consists
essentially
in
letting
the
muscle
lift
increasing
weights
through
the
same
interval.
After
being
lifted
the
weights
are
held
up
by
an
electromagnet
so
that
the
muscle
does
not
lengthen
again
in
relaxation
and
the
galvanometer
reading
is
taken
with
the
muscle
in
the
short
position.
The
muscle
is
also
calibrated
in
that
position
after
the
ex-
periment.
The
electromagnet
is
arranged
above
the
lever
as
shown
in
Fig.
1,
the
circuit
being
closed
as
soon
as
the
lever
makes
contact
with
380
MUSCLE
WORK
AND
ENERGY.
the
insulated
metal
cap
on
the
screw
S1.
This
circuit
is
broken
again
by
hand
after
the
galvanometer
deflection
is
taken.
In
an
experiment
of
this
sort
the
heat,
H,
recorded
by
the
galvano-
meter
is
given
by
the
formula:
H=I+C-W+(p-e)
......
(6).
The
energy,
W,
actually
used
in
lifting
the
weight
is
stored
in
the
weight
as
potential
energy
and
does
not
appear
in
the
muscle
as
heat.
The
total
energy,
E,
liberated
by
the
muscle
in
the
contraction
therefore
is
E=H+W-(p-
e)=
I+C
C.......
(7).
Usually
H
turns
out
to
be
roughly
constant,
indicating
that
the
increase
in
heat
with
increase
in
load
is
just
equal
to
the
increase
in
work
done.
It
does
not
mean,
however,
that
the
total
excess
heat,
C
(associated
with
the
shortening),
is
equal
to
the
work
done,
W.
It
may
be
observed
that
part
or
all
of
the
energy
C
-
W
+
p
has
been
expended
by
the
muscle
in
changing
its
own
shape,
i.e.
in
doing
work,
f
(frictional
loss)
upon
itself,
which
of
course
appears
finally
as
heat
in
the
muscle.
So
far
it
has
not
been
possible
to
measuref
directly
in
the
stimulated
muscle
but
it
does
not
seem
impossible
that
C
=
W
+
f
-
p,
i.e.
that
the
excess
energy
of
the
contraction
phase
is
equal
to
the
total
work,
external
and
internal,
which
is
performed,
after
making
the
small
correction,
p,
for
the
potential
energy
lost
by
the
resting
muscle
in
shortening.
Data
of
this
sort
are
given
in
Table
II.
For
each
experiment
the
work,
W,
done
by
the
muscle
in
lifting
the
various
weights
and
the
corresponding
amounts
of
heat,
H
(equation
(6)),
liberated
as
such
in
the
muscle
have
been
tabulated.
The
total
energy,
E,
is
equal
to
the
sum
of
the
work
and
the
heat,
minus
the
small
correction
(p
-
e).
The
shortening
of
the
muscle
was
about
3
mm.
in
every
case.
In
all
these
experiments
the
heat
remains
practically
constant,
or
at
least
the
variations
of
heat
are
small
compared
to
the
variations
in
work
done.
There
is
a
fairly
well-
marked
tendency
for
the
heat
to
decrease
with
the
highest
weights.
Later
experiments
with
certain
of
these
same
muscles,
when
they
were
more
fatigued,
showed
a
decrease
in
heat
with
increase
in
weight.
Two
other
muscles
showed
a
decrease
in
heat
even
when
first
dissected.
This
also
may
have
been
an
effect
due
to
the
poor
condition
of
the
muscle,
for
many
of
the
muscles
were
unfit
to
use
even
when
first
put
on
the
thermo-
pile.
The
work
in
these
exceptional
cases
must
have
been
performed,
in
'
The
kinetic
energy
of
the
weight
when
the
lever
hits
the
screw
S
and
makes
electrical
contact
has
been
measured
from
its
velocity
as
obtained
from
records
on
a
moving
drum.
It
is
so
small
that
it
has
been
neglected.
381
382
W.
0.
FENN.
part
at
least,
by
the
energy
mobilised
in
an
isometric
contraction.
In
fatigue
the
whole
mechanism
by
which
excess
energy
is
liberated
for
the
performance
of
work
seems
to
be
eliminated,
as
I
have
observed
in
many
experiments.
TABLE
II.
Heat
production
when
varying
loads
are
lifted
a
constant
height.
Exp.
A
Exp.
B
Heat
Heat
A
,A
Work
a
b
c
Work
a
b
c
0
117
92-1
63-6
0
71.9
214
98-9
1.0
116
91*4
66-5
1*3
74.4
2-1
117
93-8
67*2
2-7
74*8
214
98-6
3-2
124
5*4
73.7
217
99.1
4-2
119
93-4
66*4
8-1
70*4
219
102-2
6*2
125
89-9
61*4
10*8
219
8*4
115
92*9
-
13-5
212
10.5
120
906
16*2
209
12-7
117
89-6
-
-
14-8
118
0-2
sec.;
12-7'
C.;
0*27
gm.
0
05
sec.
(a
and
c);
0-2
sec.
(b);
140
C.;
022
gm.
Exp.
C
Exp.
D
Exp.
E
Work
Heat
Work
Heat
Work
Heat
1-4
98-4
07
94.3
5*0
215
2-5
100*8
2-1
95.4
12-8
219
5.4
100.5
4*8
94-8
19-6
226
8-1
99.3
7.5
94.1
26-3
224
10-9
97.7
10-2
95.7
12*9
91
9
02
sec.;
150
C.;
0*12
gm.;
02
sec.;
150
C.;
02
sec.;
17°
C.;
isom.
88-5
x
103
ergs
isom.
93.4
x
103
ergs
isom.
205
x
10
ergs
Work
and
heat
are
given
in
units
of
1000
ergs.
Duration
of
stimulus,
temp.
of
the
muscle,
weight
of
the
muscle
between
electrodes
are
given
where
possible.
The
isometric
heat
where
given
applies
to
the
short
position
of
the
muscle.
Each
figure
is
the
average
of
two
series
taken
in
ascending
and
descending
order
of
weights
respectively.
In
A
and
B
the
initial
tension
was
greater
than
0
and
the
observations
with
zero
work
were
obtained
by
preventing
shortening
until
the
moment
of
stimulation
by
the
method
described
below
in
§§
4
and
5.
In
three
of
the
experiments
of
this
type
simultaneous
observations
were
made
of
the
energy,
E.,
necessary
to
lift
and
drop
the
same
weights.
These
readings
alternated
with
those
taken
when
the
weight
was
not
dropped
(as
in
Table
II)
so
that
the
muscle
first
lifted
the
weight,
then
lifted
and
dropped
it.
A
larger
weight
was
then
hung
on
the
lever
(after-
loaded)
and
the
procedure
repeated.
A
typical
experiment
is
plotted
in
Fig.
3
and
is
instructive
in
showing
the
inter-relationships.
In
the
upper
curve
values
of
E.
(equation
(4))
are
plotted
as
in
Fig.
2.
The
lower
curve
gives
values
of
the
heat,
H
(equation
(6)),
recorded
when
the
weight
was
not
lowered
in
relaxation.
MUSCLE
WORK
AND
ENERG
Y.
The
middle
curve
gives
the
values
of
H
+
W
H
+
W
EC=
I
+
C
+
(p-e)
......
(8).
261rgs
x
10
4-
E
26
24
22H
10fl9~~~4
20
short
isornetr;c
10o
200
3bo
400
&6o
gmns.
Fig.
3.
Similar
to
Fig.
2,
but
by
a
different
method.
Variations
in
load
on
the
excess
energy,
kW,
and
its
two
fractions
C
and
R,
associated
contraction
and
relaxation
respectively.
Experimental
points
are
indicated
by
circles.
Duration
of
stimulus,
0-2
second.
Weight
of
muscle
0-27
gm.
Muscle
shortens
2-7
mm.,
i.e.
from
103
p.c.
to
95
p.c.
of
its
extended
length
in
the
frog.
Temp.
180
C.
Absciss&
represent
weights
on
the
lever.
The
corresponding
tension
on
the
muscle
during
shortening
was
a
quarter
as
great.
In
order
to
correct
for
(p
-
e)
measurements
were
made
of
the
galvano-
meter
deflection
obtained
when
the
resting
muscle
was
stretched
by
the
smallest
weight
(75
gms.).
Contrary
to
the
theoretical
expectations
a
slight
cooling,
025
x
104
ergs,
was
observed.
In
E.
the
muscle
has
lengthened;
in
E,
and
H
it
has
not.
Hence
the
cooling
due
to
lengthening
has
been
deducted
in
the
figure
from
values
of
E,
and
H.
Actually
the
correction
should
have
been
slightly
larger
(thus
increasing
R
slightly)
because
in
measuring
it
the
muscle
must
have
been
heated
somewhat
by
the
energy
of
the
falling
weight,
i.e.
W
-
p
-
1
+
e.
Thus
the
correction
p
-
e
is
automatically
taken
care
of.
This
method
of
correction
will
be
analysed
in
more
detail
below.
It
is
evident
that
the
experiment
in
Fig.
3
serves
the
same
purpose
as
that
in
Fig.
2,
in
making
possible
a
subdivision
of
the
excess
energy,
kW,
above
the
isometric
into
two
fractions,
C
associated
with
the
lifting
of
the
weight
and
R
associated
with
the
lowering
of
the
weight.
Now
C
is
obviously
larger
than
W,
even
at zero
load,
if
the
dotted
extrapolations
are
justified.
C
-
W
at
zero
load
should
represent
the
work
done
in-
ternally
in
changing
the
shape
of
the
muscle,
i.e.
frictional
loss,
f.
This
383'
W.
0.
FENN.
figure
agrees
with
Fig.
2,
therefore,
in
lending
support
to
the
possibility
that
C
=
W
+
f
-
p
as
suggested
above.
In
Fig.
3,
unlike
Fig.
2,
there
is
more
isometric
heat
at
the
long
position
than
the
short.
The
values
of
E.
pass
through
a
maximum,
decreasing
at
the
highest
weight.
This
fall
was
accompanied
by
a
fall
in
the
work
which
is
not
shown
in
the
figure.
3.
Energy
liberation
when
work
is
done
upon
the
muscle
by
afalling
weight
during
the
contraction
period.
It
has
been
shown
that
when
positive
work
is
done
by
the
muscle
there
is
a
positive
excess
heat
liberation,
C,
associated
with
the
shortening
period.
If
this
represents
a
fundamental
process
in
the
muscle
economy,
the
converse
should
also
be
true.
Thus
when
the
muscle
does
negative
work
the
excess
energy
C
should
also
be
negative.
The
performance
of
negative
work
by
the
muscle
can
be
arranged
by
stretching
it
so
that
s
becomes
negative
in
the
formula
W
=
Ts.
The
method
employed,
in
principle,
is
to
hang
on
the
muscle
a
weight
which
is
supported
previous
to
stimulation
but
is
released
shortly
afterwards
and
allowed
to
fall
a
fixed
distance,
thus
stretching
the
muscle
a
distance
s.
By
properly
varying
the
size
of
the
weight
and
the
time
of
release
the
muscle
can
be
stretched
at
any
time
during
contraction
or
relaxation.
If
a
small
weight
is
released
when
the
muscle
tension
is
near
its
maximum
it
will
not
fall
until
toward
the
end
of
relaxation.
Larger
weights
will
fall
earlier
in
relaxation.
A
weight
too
heavy
for
the
muscle
to
lift
will
fall
as
soon
as
it
is
released
in
spite
of
the
"contraction"
of
the
muscle.
Thus
the
abnormal
process
of
stretching
during
the
contraction
period
can
be
made
to
grade
imperceptibly
into
the
normal
process
of
relaxing
under
different
loads.
The
energy,
E,
liberated
in
the
muscle
as
heat
as
a
result
of
the
physiological
processes
of
contraction
is
determined
by
deducting
the
energy,
W,
put
into
the
muscle
by
the
falling
weight
from
the
total
heat,
H,
found
in
the
muscle
by
the
galvanometer.
If
it
is
true
that
negative
work
causes
negative
excess
heat,
then
it
is
to
be
expected
that,
when
the
stretching
takes
place
during
stimulation,
W
will
not
add
itself
to
H
but
will
to
some
extent
replace
H.
In
practice
this
experiment
is
carried
out
by
means
of
an
attachment
to
the
lever
which
is
shown
in
Fig.
1.
At
the
end
of
the
lever
opposite
to
the
muscle
is
a
triangular
piece
of
brass,
T,
held
in
position
by
a
counterpoise,
C,
and
carrying
two
shoulders,
a
and
b.
Only
the
lower
of
these,
a,
is
used
for
this
experiment;
it
serves
to
support
the
lever
before
its
release.
When
the
circuit
is
closed
through
the
electromagnet
below
384
MUSCLE
WORK
AND
ENERGY.
the
lever,
the
magnet
pulls
upon
T
by
means
of
a
connecting
thread
and
releases
the
lever.
The
weighted
end
of
the
lever
then
falls
until
it
hits
the
screw
L,
thus
stretching
the
muscle
and
recording
the
moment
when
stretching
begins
on
a
revolving
drum.
The
electric
contact
on
the
screw
S
is
not
used
for
this
experiment.
S
is
so
adjusted
that
it
just
touches
the
lever
when
the
other
end
of
the
lever
rests
upon
the
shoulder
a,
thus
preventing
the
least
bit
of
shortening
in
the
muscle
until
it
is
released.
If
not
prevented
by
the
tension
of
the
muscle
the
weight
begins
to
fall
*03
to
*04
second
after
the
circuit
through
the
electromagnet
is
closed,
this
being
the
mechanical
delay
in
the
releasing
apparatus.
The
circuit
is
closed
automatically
by
an
arm
and
a
knock-down
key
on
the
same
revolving
drum
which
is
used
for
the
timing
of
the
duration
of
the
stimulus.
The
moment
of
release
in
relation
to
the
beginni
g
of
stimula-
tion
is
thus
known
to
within
005
of
a
second.
Short
tetani
of
02
second
have
been
used.
The
source
of
current
was
a
rotating
commutator
rapidly
reversing
a
direct
current
or
a
small
A.c.
bicycle
dynamo
(D
owning(12)).
Before
describing
the
experimental
results
the
energy
changes
in
the
muscle
during
the
experimental
procedure
must
be
analysed
in
more
detail.
The
heat,
H,
developed
in
the
muscle
and
measured
on
the
gal-
vanometer
is
given
by
the
formula
H
=
I
+
C
(if
any)
+
R
(if
any)
+
(W-I)-(p-
e)
......
(9).
As
before
p
is
that
portion
of
W
which
goes
to
restore
the
resting
potential
energy
of
the
stretched
muscle;
I
is
that
portion
of
W
which
is
not
ab-
sorbed
by
the
muscle
but
wasted
as
heat
when
the
lever
strikes
the
screw
L.
The
energy,
E,
liberated
physiologically
by
the
muscle
is
given
by
the
formula:
E
=
I
+
Ca+
R
=
H
-(W
-I)
+
(p
-e)
...................
(10).
The
quantity
of
physiological
interest
is
E,
obtained
by
adding
p
+
l
-
e
to
H
-
W.
Now
p
+
I-
e
is
in
any
case
small
and
does
not
vary
with
the
weight
and
time
of
stretching
so
that
the
relative
values
of
H
-
W
are
significant
without
this
correction.
But
in
order
to
compare
the
isometric
heat
in
either
position,
I,
or
I,
with
H
-
W,
it
is
necessary
to
know
p
+
l
-
e.
I
have
sought
to
determine
this
by
measuring
on
the
galvanometer
the
heat,
g,
produced
when
the
smallest
weight
is
allowed
to
stretch
the
resting
muscle
a
distance
s
under
tension
T,
the
potential
energy
lost
by
the
weight
being
Ts
=
W1.
The
value
of
g
should
then
be
g
=
W1-p-1
+
e.
Now
W1
>
p
+
1.
Hence
g
should
be
positive.
Actually
it
was
negative
which
must
indicate
a
cooling,
-
c,
due
pre-
385
386
W.
0.
FENN.
sumably
to
minute
differences
of
temperature
along
the
muscle.
This
new
factor
must
be
introduced
into
the
above
equations
as
follows:
g+
W1=p+l-e+c,
E=H-
W+p+l-e+c.
Hence
E=H-
W+(g+
W,)*
......
(11).
In
other
words,
simple
lengthening
of
the
unstimulated
muscle causes
a
cooling
so
that
H
-
W,
as
observed,
is
too
small
by
this
amount.
The
necessary
correction,
g
+
W1,
has
been
determined
in
three
of
the
six
experiments
in
Table
III,
and
its
value
has
been
found
to
be
too
small
to
affect
the
sense
of
the
results
although
it
mars
their
technical
per-
fection.
Some
of
the
results
of
ten
series
of
this
sort
are
collected
in
Table
II1.
The
work
is
calculated
directly
in
ergs.
The
heat
is
calculated
as
ergs
from
the
galvanometer
deflection
by
means
of
the
electrical
calibration
of
the
muscle.
The
calibration
was
usually
taken
in
the
long
position.
The
isometric
heat
in
the
short
position
was
obtained
by
means
of
an
additional
calibration
in
that
position.
TABLE
III.
The
decrease
in
the
energy
liberation
caused
by
stretching
the
muscle
during
the
contraction
period.
Work
done
on
the
muscle
Energy
liberated
by
the
muscle
Exp.
W,
WV2
W3
W4
HI
-
1V1
H2-
W2
113-
W3
14-
W4
ISOM.
$
ISOM.
I
1
27
163
326
380
1633
1769
1509
1414
1726
1761
2
13
109
326
326
725
671
468
408
784
663
2a
13
81
272
326
609
555
380
354
554
570
3
13
109
326
1013
1028
818
-
(941)
1012
3a
13
109
326
-
1068
1122
1015
-
-
1069
4
13
109
217
846
940
682
-
-
861
5
13
109
271 271
560
597
499
461
-
-
6
13
109
271
1012
995
853
-
-
-
6a
13
109
271
271
1014
950
812
800
1056
994
6b
13
109
271
941
921
753
-
-
All
quantities
are
expressed
in
units
of
100
ergs.
The
value
of
the
correction
g
+
Ta
or
g
+
W1
was
98,
33
and
40
x
100
ergs
in
Exps.
1,
2
and
3
respectively.
All
muscles
at
room
temp.
about
15°
C.
Amount
of
shortening
was
2-2
mm.
throughout.
Isom.
8
and
isom.
1
=isometric
heat
in
short
and
long
positions.
Each
complete
experiment
started
with
an
isometric
contraction
in
the
short
position.
The
smallest
weight,
W1
(25
gms.
in
Exps.
2-6;
50
gms.
in
Exp.
1),
was
then
hung
on
the
lever,
supported
in
the
short
position
until
released
at
about
the
ehid
of
stimulation.
With
this
weight
the
muscle
was
stretched
toward
the
end
of
the
relaxation
period
(0.4
second
after
stimulation).
Larger
weights
were
then
used
in
the
same
*
This
calculation
is
not
strictly
accurate
because
the
value
of
I
varies
with
the
load,
and
1
for
the
unstimulated
muscle
is
not
necessarily
equal
to
I
for
the
stimulated
muscle.
MUSCLE
WORK
AND
ENERGY.
way
until
the
muscle
was
stretched
as
soon
as
the
weight
was
released
at
about
the
end
of
the
stimulation
(0.2
second).
W2
in
Table
III
repre-
sents
a
weight,
usually
200
gms.
which
was
just
large
enough
to
stretch
the
muscle
at
0
3
second
after
the
beginning
of
stimulation,
and
which
was
approximately
the
largest
weight
under
which
the
muscle
could
shorten
as
much
as
2-2
mm.
W3
represents
a
weight
(500
or
600
gms.)
large
enough
to
stretch
the
muscle
as
soon
as
it
is
released,
i.e.
between
0.1
and
0-2
second
after
the
beginning
of
stimulation.
W4
is
a
weight
which
was
released
sooner
and
began
to
stretch
the
muscle
in
less
than
0.1
second
after
the
beginning
of
stimulation.
W1
and
W2,
therefore,
represent
normal
relaxations;
W3
and
W4
stretch
the
muscle
during
the
contraction
period
when
the
muscle
should
be
shortening.
Other
inter-
mediate
weights
were
also
used
in
addition
to
those
included
in
Table
III.
After
the
observation
with
the
largest
weight
the
muscle
was
stimulated
isometrically
in
the
long
position
and
then
the
various
weights
were
used
again
in
the
reverse
order.
The
results
of
the
two
observations
with
each
weight
were
averaged
in
order
to
eliminate
the
effects
of
fatigue.
The
results
show
that
less
energy
is
mobilised
by
the
muscle
when
it
is
stretched
during
stimulation
(H.3-
W3
and
H4-
W4)
than
when
the
same
lengthening
is
carried
out
in
relaxation
(H,
-
W1
and
H2
-
W2)
or
than
when
the
muscle
is
similarly
stimulated
isometrically
in
either
the
long
or
the
short
positions
(I,
or
II).
The
result
is
most
evident
in
H4-
W4
where
the
stretching
took
place
most
nearly
at
the
moment
when
the
tension
was
being
increased.
In
the
first
experiment,
Is
and
I,
are
172,600
and
176,100
ergs
respectively.
It
might
be
supposed
that,
if
the
muscle
changed
from
one
length
to
the
other
at
any
moment
during
the
contraction
or
relaxation
period,
the
resulting
energy
liber-
ated
would
be
intermediate
between
the
isometric
heats
for
the
two
positions.
This
is
not
the
case.
If
the
change
is
from
the
long
to
the
short
position
during
the
contraction
period
the
energy
liberated
is
greater
(i.e.
C
and
W
are
both
positive)
than
either
Is
or
I,
as
already
shown.
Table
III
shows
that
if
the
change
is
in
the
opposite
direction
from
the
short
to
the
long
position
that
the
heat
liberated
is
considerably
less
than
Is
or
II,
i.e.
C
and
W
are
both
negative.
Thus
H4-
W4
(Exp.
1)
or
141,400
ergs
plus
the
correction
9800
ergs
=
151,200
ergs,
which
is
less
than
172,600
or
176,100
ergs.
When
38,000
ergs
work
is
done
upon
the
muscle
in
stretching
it,
the
energy
liberated
is
decreased
176,100
-
151,200
ergs
=
24,900
ergs.
The
work
done
in
stretching
the
muscle
does
not
therefore
add
itself
to
the
"physiological"
heat
but
249/380
or
65
p.c.
of
it
(in
this
case)
replaced
energy
387
W.
0.
FENN.
which
would
have
been
liberated
by
the
muscle
if
it
had
not
been
stretched.
Again
in
the
same
experiment
comparing
H3
and
114
it
is
found
that
when
32,600
ergs
work,
W.,
is
done
upon
the
muscle
the
heat
observed
is
150,900
+
32,600
=
183,500
ergs;
and
when,
by
stretch-
ing
the
muscle
earlier
after
the
begInning
of
stimulation,
38,000
ergs
work,
W4,
is
done
upon
the
muscle
the
heat
observed
is
only
141,400
+
38,000
=
179,400
ergs.
In
the
latter
case
the
heat
observed
is
4100
ergs
less
than
in
the
former
although
5400
ergs
more
work
was
done
upon
the
muscle
and
appeared
within
it
as
heat.
This
is
perhaps
a
particularly
strildng
case
but
it
is
in
agreement
with
the
general
trend
of
all
ten
series
as
well
as
with
four
others
not
sufficiently
complete
to
tabulate.
That
inappreciable
fractions
of
the
energy
of
the
various
weights
were
dissipated
as
heat
in
the
apparatus
is
shown
in
Table
IV.
This
gives
for
the
various
values
of
W
the
corresponding
values
of
the
kinetic
energy
of
the
weight,
I
=
mv2/2
just
at
the
moment
when
the
lever
hits
the
screw
L,
and
the
times
after
the
beginning
of
stimulation
when
the
muscle
began
to
lengthen.
At
most
10
p.c.
of
the
energy
of
W
may
be
wasted
in
the
apparatus.
TABLE
IV.
Energy
waste
in
apparatus
and
time
of
lengthening
with
varying
amounts
of
negative
work,
W.
Time
when
lengthening
Work
Energy
waste,
I
begins
in
seconds
13
0
*58
27
1
*35
54
4
*32
109
11
*30
163
12
*28
216
20
*25
326
10
*15
326
0
*10
326
0
07
326
0
03
W
represents
the
work
in
units
of
100
ergs
done
upon
the
muscle
by
weights
(on
the
lever)
varying
from
25
to
600
gms.
The
energy
waste
is
the
kinetic
energy
of
the
weight
in
ergs
x
100
at
the
moment
when
lengthening
is
complete
and
represents
that
fraction
of
W
which
was
not
absorbed
by
the
muscle
as
heat.
The
time
when
lengthening
begins
is
measured
from
the
beginning
of
the
stimulus
(0-2
second)
and
was
obtained
from
records,
on
a
moving
drum.
In
the
last
four,
lengthening
began
in
each
case
*03
second
after
the
closure
of
the
electric
contact
which
operated
the
releasing
mechanism.
Data
taken
from
Exp.
2,
Table
III.
The
experiments
in
this
section
show
that
stretching
of
a
muscle
during
the
contraction
phase
causes
a
decrease
in
the
heat
production.
This
may
be
interpreted
as
due
to
the
performance
of
negative
work
by
the
muscle.
Positive
work
increases
the
heat
production;
negative
work
decreases
it.
388
MUSCLE
WORK
AND
ENERGY.
4.
The
heat
liberated
when
a
muscle
is
prevented
from
shortening
until
some
time
after
stimulation.
The
experiments
fall
into
two
groups.
In
the
first,
the
muscle
lifts
a
weight
as
it
shortens
and
is
pulled
back
to
its
original
position
by
the
weight
in
relaxation.
In
the
second
group,
considered
in
section
5,
no
external
work
is
done
in
shortening
and
the
muscle
is
not
pulled
back
to
its
original
position
in
relaxation.
In
order
to
carry
out
these
experiments
it
is
necessary
to
hold
the
muscle
isometrically
for
various
times
after
stimulation
and
to
release
it
at
a
desired
moment.
This
is
accomplished
by
the
release
mechanism
T,
and
the
shoulder
b,
attached
to
the
lever
(Fig.
1).
The
screw
L
is
arranged
so
that
the
lever
is
held
snugly
between
it
and
the
shoulder
b.
The
screw
S
is
then
adjusted
to
permit
the
desired
amount
of
shortening;
or
it
is
screwed
down
out
of
the
way
altogether.
At
the
desired
moment
the
circuit
through
the
bell
magnet
under
the
lever
is
closed
automatically;
T
is
pulled
down
and
the
lever
released.
In
the
first
type
of
experiment
the
initial
tension
is
constant
and
small
(6-12
gms.).
The
weight,
if
greater
than
that
necessary
to
set
up
the
initial
tension,
is
after-loaded.
The
muscle
is
first
stimulated
and
allowedc
to
shorten
freely.
The
initial
isometric
interval
is
then
increased
until
the
whole
contraction
becomes
isometric.
The
results
are
averaged
with
a
similar
series
of
observations
taken
in
the
reverse
direction
to
avoid
errors
due
to
fatigue.
The
result
of
an
experiment
is
plotted
in
Fig.
4.
The
muscle
was
stimulated
for
04
second.
The
height
of
the
contraction
was
not
limited
and
the
amount
of
shortening
progressively
decreased.
until
the
contraction
became
isometric.
Abscissse
represent
the
time
of
release
of
the
lever,
no
allowance
having
been
made
for
the
time
(04
second)
consumed
in
effecting
this
release
after
the
circuit
was
closed.
At
zero
time
when
the
muscle
was
not
restrained
at
all
the
heat
pro-
duction
was
considerably
greater
than
the
isometric,
as
was
to
be
ex-
pected.
There
is
then
a
very
slight
increase
in
heat
which
does
not
always'
appear
and
may
be
due
to
a
somewhat
higher
tension
in
the
muscle
when
the
shortening
begins.
With
further
increase
in
time
the
heat
and
work
both
decrease
to
the
isometric
point.
For
mechanical
records
of
the
changes
of
length
of
muscles
carrying
out
contractions
of
this
sort,
"mit
Anfangshemmung,"
see
the
figures
of
v.
Kries
(4)
which
show
that
the
greater
the
isometric
interval
the
more
the
completion
of
relaxation
is
delayed.
The
fall
in
heat
in
Fig.
4
may
be
due
to
a
decreased
shortening
andc
PH.
LVIII.
25
389
W.
0.
FENN.
hence
decreased
work.
In
order
to
show
that
the
tinme
when
shortening
takes
place
is
also
a
factor,
similar
experiments
have
been
carried
out
Ergs
x.
104
Ergs
x
13
9
tetatnus
t
1
1~tto
138
18t
orn
et
r
ic
q
7
1.0
0.
'~isrntri'c.
Os
worl(
I
0
O.S
1.0
1.5
s
OS
1.0
secornds
-
secondcs
->
Fig.
4.
Fig.
5.
Fig.
4.
Decrease
in
heat
production
and
work
caused
by
preventing
a
muscle
from
shorten-
ing
for
increasing
periods
after
the
beginning
of
stimulation
(see
Text).
Temp.
00
C.
Weight
of
muscle
between
the
electrodes
was
0
33
gm.
Lever
weighted
with
125
gms.
Tension
on
muscle
during
shortening
='l-
or
31
gms.
Initial
tension
6-2
gms.
Fig.
5.
Variation
in
heat
production
(ordinates)
with
increase
in
the
time
after
stimulation
when
shortening
begins
(abscisse).
Similar
to
Fig.
4,
except
that
the
shortening
was
limited
in
every
case
to
2-7
mm.
Muscle
at
room
temperature,
80
C.
Weight
of
muscle,
026
gm.
The
lever
was
weighted
with
25
gms.
giving
a
muscle
tension
of
6-2
gmis.
except
that
the
degree
of
shortening
was
limited
in
each
case
to
2-7
mm.
It
is
thus
possible
to
determine
the
effect
of
the
same
shortening
under
the
same
tension
(i.e.
the
same
performance
of
work)
when
it
takes
place
at
different
times
after
the
beginning
of
the
stimulus.
The
resulting
curves
are
shown
in
Fig.
5.
The
general
feature
is
the
same
as
in
Fig.
4,
the
heat
falling
off
rapidly
toward
the
isometric.
It
may
be
concluded,
therefore,
that
the
longer
the
isometric
interval
before
shortening
begins
the
less
the
excess
heat
liberation
for
the
same
work,
until
it
fails
to
appear
altogether.
Fig.
5
shows,
however,
an
additional
feature
in
the
minimum
through
which
the
curve
passes.
This
minimum
is
a
very
characteristic
feature
of
such
experiments
whether
the
height
of
con-
traction
is
limited
or
not,
and
indicates
that
if
the
muscle
is
released
at
just
about
the
time
that
relaxation
begins
(or
at
the
time
of
maximum
tension)
the
heat
production
is
less
than
if
it
had
been
held
fast
in
the
390
MUSCLE
WORK
AND
ENERGY.
original
position.
One
is
thus
tempted
to
conclude
that
whereas
short-
ening
in
contraction
causes
an
increased
heat
production,
the
same
shortening
in
relaxation
(when
the
muscle
is
normally
lengthening
and
when
possibly
the
contractile
process
is
in
some
particulars
reversed)
causes
a
decreased
heat
production.
Conversely
it
has
been
shown
(§§
2
and
3)
that
lengthening
in
contraction
causes
a
decreased
heat
production
and
lengthening
in
relaxation
(usually)
an
increased
heat
production.
It
is
too
soon
to
speculate
upon
the
meaning
of
these
facts.
Summarising
the
experiments
just
described
it
is
found
that
17
curves
similar
to
those
published
have
been
obtained
on
four
different
muscles.
All
showed
a
marked
decrease
of
heat
with
increasing
pre-
liminary
isometric
interval;
nine
showed
a
slight
initial
increase
in
heat;
11
showed
a
minimum
of
heat
when
shortening
occurred
in
relaxation.
One
of
these
muscles
which
served
for
two
days
of
continuous
experimen-
tation
on
this
and
other
points,
failed
to
give
the
characteristic
curve
at the
end
of
the
first
day
when
it
was
much
fatigued.
On
the
following
day,
however,
when
it
had
recovered,
it
gave
five
very
good
series
all
showing
a
marked
decrease
in
heat
with
increasing
isometric
interval.
The
duration
of
stimulation
in
these
experiments
has
varied
from
'05
to
0.5
second.
The
heat
does
not
show
a
decrease
unless
the
lever
is
held
isometrically
until
approximately
the
end
of
the
stimulus,
whether
it
is
a
long
or
a
short
one.
Through
the
courtesy
of
Mr
Hartree
and
Prof.
A. V.
Hill,
I
am
permitted
also
to
mention
some
unpublished
experiments
performed
by
them
on
frog
sartorius
muscles
in
May
and
June,
1922.
The
experiments
were
similar
to
that
plotted
in
Fig.
4.
There
were
in
all
22
series
on
seven
different
muscles.
Sixteen
of
these
curves
resembled
mine,
particularly
as
to
the
minimum
in
the
heat
produced
just
before
the
contraction
became
completely
isometric
and
as
to
the
maximum
in
heat
when
the
muscle
was
not
restrained.
In
six
series
the
isometric
contraction
gave
the
most
heat
for
some
reason
not
at
present
understood.
The
tempera-
ture
varied
from
00
to
150
C.
and
the
stimulus
from
single
shocks
to
0
4
seconds
tetanus.
It
is
very
reassuring
to
find
that
I
have
confirmed
their
results
so
well
with
an
entirely
different
set
of
apparatus.
Similar
experiments
have
been
carried
out
by
Fick(l3)
and
by
Schenck(14)
using
the
inner
muscles
of
the
frog's
thigh
and
I
have
been
able
to
confirm
their
results
in
a
general
way
on
a
pair
of
gastrocnemius
muscles.
In
a
gastrocnemius
muscle
the
isometric
heat
is
greater
than
the
isotonic
heat.
Consequently
the
more
nearly
isometric
a
contraction
becomes
the
greater
the
heat
production.
The
experiments
described
25-2
391
W.
O.
FENN.
above
show
that
the
reverse
of
this
is
true
in
the
sartorius.
Reasons
for
this
important
difference
between
the
gastrocnemius
and
the
sartorius
muscles
have
been
suggested
in
a
previous
paper(2).
5.
Variations
in
energy
liberation
caused
by
releasing
a
stretched
muscle
at
various
times
before
and
afte?
stimulation.
The
experiments
are
made
in
the
same
way
as
in
§
4
but
without
a
weight
and
with
a
muscle
which
is
initially
so
much
stretched
that
it
will
shorten
the
required
distance
without
stimulation,
merely
by
the
elasticity
of
the
connective
tissue.
This
modification
enables
the
experimenter
to
make
the
muscle
shorten
before
stimulation
as
well
as
after
it
without
difficulty.
The
essential
diflerence
between
these
experiments
and
those
plotted
in
Figs.
4
and
5
is
that
in
this
case
no
external
work
is
done
because
the
shortening
takes
place
under
zero
tension
as
far
as
the
whole
muscle
is
concerned.
The
individual
muscle
fibres,
however,
may
shorten
under
some
slight
tension,
if
the
shortening
of
the
muscle
when
stimulated
is
more
rapid
than
the
shortening
unstimulated.
Thus
there
may
be
some
slight
internal
work
done
in
accelerating
the
change
of
shape
of
the
muscle.
For
these
reasons
one
might
expect
that
the
proposed
modification
of
experiments
of
Figs.
4
and
5
would
merely
decrease
the
maximum
heat
due
to
the
decrease
in
work.
The
results
of
the
five
experiments
plotted
in
Fig.
6
seem
to
justify
this
expectation
to
some
extent.
In
these
curves
(Fig.
6)
the
abscissee
represent
the
time
when
shortening
began,
-04
second
having
been
allowed
for
the
mechanical
delay
in
the
releasing
apparatus.
The
method
of
release
was
identical
with
that
de-
scribed
above
(§
4).
Each
point
plotted
is
the
average
of
two
observations,
one
made
while
the
time
after
stimulation
was
being
progressively
increased
and
the
other
while
it
was
being
decreased.
Points
at
the
extreme
left
of
the
figure
represent
the
heat
obtained
by
releasing
the
muscle
028
second
before
an
isometric
contraction
in
the
short
position.
Conversely
points
at
the
extreme
right
show
the
heat
liberated
in
an
isometric
contraction
at
the
long
position,
followed
by
the
usual
shorten-
ing.
It
will
be
noticed
that
the
isometric
long
are
always
lower
than
the
isometric
short
showing
that
the
muscle
in
the
long
position
had
been
stretched
beyond
the
optimum
length
for
the
maximum
isometric
heat
production.
Stimulation
began
in
all
cases
at
zero
time.
In
the
four
upper
curves,
A,
B,
C
and
D
the
stimulation
lasted
01
second
and
the
point
of
minimum
heat
is
correspondingly
later
than
in
E,
where
maximal
break
shocks
were
used.
392
MUSCLE
WORK
AND
ENERGY.
The
upper
three
curves
of
Fig.
6
are
perhaps
the
most
typical.
All
show
a
slight
rise
to
a
maximum
when
the
shortening
begins
just
at
the
Ergs
x
104
6
\
5
0
0~~~~~~~~~
0
D
El
2
'0.2
0
0.2
0.4
0.6
seco-nds
Fig.
6.
Variations
in
heat
production
caused
by
releasing
a
stretched
muscle
at
various
times
before
and
after
the
beginning
of
stimulation.
Stimulation
began
at
zero
time,
and
lasted
for
0
1
second
except
in
B
where
maximal
break
shocks
were
used.
E
is
plotted
in
mm.
deflection
since
no
calibration
was
taken.
Curve
A
has
been
raised
in
all
points
4
x
108
ergs
to
avoid
overlapping.
The
shortening
was
2-7
mm.
throughout.
moment
of
stimulation.
This
is
probably
due
to
the
slight
internal
work
which
the
fibres
must
do
in
accelerating
the
shortening
of
the
muscle.
Evidence
of
this
same
fact
has
been
discussed
in
connection
with
Figs.
2
and
3.
Immediately
following
this
maximum
there
is
a
minimum
which
is
undoubtedly
the
homologue
of
the
minimum
obtained
in
Fig.
5,
and
in
other
similar
experiments
when
the
muscle
shortened
under
a
weight.
Whatever
the
explanation
it
is
certainly
a
most
constant
feature
of
such
experiments
and
has
been
obtained
in
20
out
of
24
series
with
eight
different
muscles.
The
maximum
corresponding
to
the
moment
of
stimu-
lation
is
not
so
common.
It
appeared
in
only
11
of
the
24
series.
Curves
D
and
E
are
typical
cases
where
it
failed.
Both
of
these
can
be
attributed
to
fatigue
of
the
muscles.
Possibly
other
failures
can
be
similarly
ex-
plained
because
all
of
the
experiments
of
this
type
were
performed
at
a
time
when
the
frogs
were
in
particularly
poor
condition.
The
same
muscle
which
gave
curve
D
on
the
fourth
trial
had
given
curve
C
and
two
other
very
similar
ones
previously.
Likewise
curve
B
was
the
fourth
obtained
with
another
muscle,
the
first
of
which
had
shown
an
initial
small
but
393
definite
maximum.
Curves
A
and
B
were
also
the
first
and
fourth,
respectively,
obtained
with
one
muscle.
The
second
of
these
four
had
failed
to
show
a
maximum
due
to
pronounced
fatigue;
but
after
a
rest
of
one
or
two
hours
in
Ringer's
solution
the
signs
of
fatigue
disappeared
and
the
typical
maximum
was
obtained
in
the
third
and
fourth
(B)
series.
A.
V.
HilIl5()
has
performed
experiments
with
the
g
ocnemius
and
semimembranosus
muscles
similar
to
those
describe
above,
but
owing
probably
to
the
anatomical
peculiarities
of
those
muscles
he
obtained
quite
different
results
from
mine.
He
found
that
a
muscle
allowed
to
shorten
freely
without
load
immediately
after
stimulation
liberated
less
beat
than
if
shortening
was
prevented
indefinitely
or
for
some
time
after
stimulation.
Reasons
for
this
difference
have
already
been
suggested
(1).
SUMMARY.
1.
Experiments
are
described
which
show
the
effects
of
a
small
amount
of
shortening
or
lengthening
of
a
sartorius
muscle,
at
various
times
during
contraction
and
relaxation,
on
the
total
energy
mobilised
in
the
muscle
as
a
result
of
a
given
stimulus.
2.
Shortening
during
the
contraction
period
increases
the
energy
liberated.
The
excess
energy
due
to
shortening
in
contraction
is
very
nearly
equal
to
the
work
done,
if
we
include
in
that
category
both
the
external
work
done
in
lifting
a
weight
and
the
internal
work
causing
the
change
in
shape
of
the
muscle.
There
may
be
a
slight
excess
heat
production
when
the
muscle
shortens
without
a
load,
due
to
the
internal
work
alone.
The
longer
the
shortening
is
delayed
after
the
beginning
of
stimulation,
the
less
is
the
excess
energy
liberated.
3.
Shortening
during
relaxation
decreases
(usually)
the
energy
liberated.
If
a
muscle
be
released
and
allowed
to
shorten
at
or
near
the
beginning
of
relaxation
the
energy
liberated
is
usually
somewhat
less
than
in
an
isometric
contraction.
4.
Lengthening
during
the
contraction
period
decreases
the
energy
liberated.
This
is
interpreted
as
meaning
that
when
the
work
done
by
the
muscle
is
negative
the
excess
energy
is
also
negative.
The
longer
this
lengthening
is
delayed
after
the
beginning
of
stimulation
the
less
the
decrease
in
energy
observed.
The
amount
of
this
decrease
is
somewhat
less
than
the
work
done
upon
the
muscle
in
stretching
it.
5.
Lengthening
during
relaxation
increases
(usually)
the
energy
liberated.
Thus
when
a
muscle
lifts
a
weight
in
contraction
and
lowers
it
in
relaxation
a
part
(30
to
40
p.c.)
of
the
excess
energy
observed
is
due
394
W.
O.
FENN.
MUSCLE
WORK
AND
ENERGY.
395
to
processes
involved
in
the
lengthening
of
the
muscle
rather
than
in
the
shortening.
0
6.
It
is
shown
that
the
existence
of
an
excess
heat
liberation
is
to
some
extent
inconsistent
with
the
idea
that
a
stimulated
muscle
is
a
new
elastic
body.
It
is
suggested
that
contraction
is
analogous
rather
to
the
winding
up
of
an
anchor
chain
by
a
windlass
than
to
the
lifting
of
a
weight
by
the
energy
of
a
stretched
spring.
It
is
a
pleasure
to
acknowledge
again
my
indebtedness
to
Prof.
A.
V.
Hill,
who
suggested
the
work
and
has
advised
me
continuously
during
the
experiments.
A
grant
to
Prof.
Hill
from
the
Royal
Society
has
defrayed
part
of
the
expenses
of
the
experiments
reported
in
this
and
the
previous
paper.
I
wish
to
express
also
my
gratitude
to
the
Rockefeller
Institute
for
Medical
Research,
New
York
City,
for
a
travelling
fellowship
which
made
this
work
possible.
REFERENCES.
(1)
Hartree
and
Hill,
A.
V.
This
Journ.
55.
p.
133.
1921.
(2)
Fenn.
Ibid.
58.
p.
175.
1923.
(3)
Weber.
Wagner's
Handwort.
d.
Physiol.
3.
(Braunschweig).
1846.
(4)
v.
Kries.
Arch.
f.
(Anat.
u.)
Physiol.
p.
348.
1880.
(5)
Fick.
Mech.
Arbeit.
u.
Warment.
u.s.w.
{Leipzig),
pp.
120
ff.
1882.
(6)
Blix.
Skand.
Arch.
f.
Physiol.
5.
pp.
150
and
173.
1895.
(7)
Seemann.
Pfluiger's
Arch.
106.
p.
420.
1904-5.
(8)
Bethe.
Ibid.
199.
p.
491.
1923.
(9)
Fick.
Ibid.
51.
p.
541.
1892.
Also
Ges.
Schriften,
2.
p.
363.
(10)
Hartree
and
Hill,
A.
V.
Proc.
Roy.
Soc.
Lond.
B,
210.
p.
153.
1920.
(11)
Frank,
0.
Ergeb.
d.
Physiol.
3.
p.
458.
1904.
(12)
Downing.
This
Journ.
57.
1923;
Proc.
Physiol.
Soc.
p.
viii.
(13)
Fick.
Verhandl.
der
Phys.
med.
Gesellsch.
zu
Wiirzburg,
N.F.
18.
1884.
Also
Ges.
Schriften,
2.
p.
295.
(14)
Schenck.
Pfliiger's
Arch.
51.
p.
509.
1892.
(15)
Hill,
A.
V.
This
Journ.
47.
p.
305.
1913.
In
my
previous
paper
I
overlooked
a
publication
by
Biirker
in
Pflfiger'8
Arch.
174.
p.
282,
1919,
in
which
the
author
described
experiments
similar
to
mine
with
the
semi-
membranosus
and
gracilis
muscles
of
the
frog.
It
is
to
be
regretted
that
he
did
not
continue
to
increase
the
weights
until
the
contractions
became
completely
isometric.
The
published
data
are
not
sufficiently
extensive
to
enable
one
to
determine
whether
the
muscles
used
by
him
behaved
like
the
sartorius
or
like
the
gastrocnemium
The
conception
of
an
increase
in
energy
liberation
associated
with
the
performance
of
work
fits
in
well
with
the
experiments
of
Chauveau
(C.
R.
Acad.
d.
Sci.,
122.
pp.
58,
113,
1896)
who
found
a
greater
oxygen
consumption
in
going
up
stairs
than
in
going
down
the
same
stairs
backwards
at
the
same
rate.
Here
the
tension-time
curve
of
the
muscles
must
have
been
the
same
in
both
cases
but
in
the
former
the
loaded
muscles
were
shortening
and
in.
the
latter
lengthening.
The
difference
in
oxygen
consumption
was
equivalent
to
something
more
than
twice
the
work
done.
