INORGANIC RESPONSE--RELATION BETWEEN STIMULUS AND
RESPONSE--SUPERPOSITION OF STIMULI
Relation between stimulus and response--Magnetic analogue--Increase of
response with increasing Stimulus--Threshold of
response--Superposition of Stimuli--Hysteresis.
#Relation between stimulus and response.#--We have seen what extremely
uniform responses are given by tin, when the intensity of stimulus is
maintained constant. Hence it is obvious that these phenomena are not
accidental, but governed by definite laws. This fact becomes still more
evident when we discover how invariably response is increased by
increasing the intensity of stimulus.
Electrical response is due, as we have seen, to a molecular disturbance,
the stimulus causing a distortion from a position of equilibrium. In
dealing with the subject of the relation between the disturbing force
and the molecular effect it produces, it may be instructive to consider
certain analogous physical phenomena in which molecular deflections are
also produced by a distorting force.
#Magnetic analogue.#--Let us consider the effect that a magnetising force
produces on a bar of soft iron. It is known that each molecule in such a
bar is an individual magnet. The bar as a whole, nevertheless, exhibits
no external magnetisation. This is held to be due to the fact that the
molecular magnets are turned either in haphazard directions or in closed
chains, and there is therefore no resultant polarity. But when the bar
is subjected to a magnetising force by means, say, of a solenoid
carrying electrical current, the individual molecules are elastically
deflected, so that all the molecular magnets tend to place themselves
along the lines of magnetising force. All the north poles thus point
more or less one way, and the south poles the other. The stronger the
magnetising force, the nearer do the molecules approach to a perfect
alignment, and the greater is the induced magnetisation of the bar.
The intensity of this induced magnetisation may be measured by noting
the deflection it produces on a freely suspended magnet in a
magnetometer.
The force which produces that molecular deflection, to which the
magnetisation of the bar is immediately due, is the magnetising current
flowing round the solenoid. The magnetisation, or the molecular effect,
is measured by the deflection of the magnetometer. We may express the
relation between cause and effect by a curve in which the abscissa
represents the magnetising current, and the ordinate the magnetisation
produced (fig. 82).
[Illustration: FIG. 82.--CURVE OF MAGNETISATION]
In such a curve we may roughly distinguish three parts. In the first,
where the force is feeble, the molecular deflection is slight. In the
next, the curve is rapidly ascending, i.e. a small variation of
impressed force produces a relatively large molecular effect. And
lastly, a limit is reached, as seen in the third part, where increasing
force produces very little further effect. In this cause-and-effect
curve, the first part is slightly convex to the abscissa, the second
straight and ascending, and the third concave.
#Increase of response with increasing stimulus.#--We shall find in dealing
with the relation between the stimulus and the molecular effect--i.e.
the response--something very similar.
On gradually increasing the intensity of stimulus, which may be done, as
already stated, by increasing the amplitude of vibration, it will be
found that, beginning with feeble stimulation, this increase is at first
slight, then more pronounced, and lastly shows a tendency to approach a
limit. In all this we have a perfect parallel to corresponding phenomena
in animal and vegetable response. We saw that the proper investigation
of this subject was much complicated, in the case of animal and
vegetable tissues, by the appearance of fatigue. The comparatively
indefatigable nature of tin causes it to offer great advantages in the
pursuit of this inquiry. I give below two series of records made with
tin. The first record, fig. 83, is for increasing amplitudes from 5° to
40° by steps of 5°. The stimuli are imparted at intervals of one minute.
It will be noticed that whereas the recovery is complete in one minute
when the stimulus is moderate, it is not quite complete when the
stimulus is stronger. The recovery from the effect of stronger stimulus
is more prolonged. Owing to want of complete recovery, the base line is
tilted slightly upward. This slight displacement of the zero line does
not materially affect the result, provided the shifting is slight.
[Illustration: FIG. 83.--RECORDS OF RESPONSES IN TIN WITH INCREASING
STIMULI, AMPLITUDES OF VIBRATION FROM 5° TO 40°
The vertical line to the right represents ·1 volt.]
TABLE SHOWING THE INCREASING ELECTRIC RESPONSE DUE TO INCREASING
AMPLITUDE OF VIBRATION
+---------------------+----------------+
| Vibration amplitude | E.M. variation |
+---------------------+----------------+
| 5° | ·024 volt |
| 10° | ·057 " |
| 20° | ·111 " |
| 25° | ·143 " |
| 30° | ·170 " |
| 35° | ·187 " |
| 40° | ·204 " |
+---------------------+----------------+
The next figure (fig. 84) gives record of responses through a wider
range. For accurate quantitative measurements it is preferable to wait
till the recovery is complete. We may accomplish this within the limited
space of the recording photographic plate by making the record for one
minute; during the rest of recovery, the clockwork moving the plate is
stopped and the galvanometer spot of light is cut off. Thus the next
record starts from a point of completed recovery, which will be noticed
as a bright spot at the beginning of each curve. With stimulation of
high intensity, a tendency will be noticed for the responses to approach
a limit.
[Illustration: FIG. 84.--A SECOND SET OF RECORDS WITH A DIFFERENT
SPECIMEN OF TIN
The amplitudes of vibration are increased by steps of 10°, from 20° to
160°. (The deflections are reduced by interposing a high external
resistance.)]
[Illustration: FIG. 85.--EFFECT OF SUPERPOSITION ON TIN
A single stimulus produces the feeble effect shown in the first
response. Superposition of 5, 9, 13 such stimuli produce the
succeeding stronger responses.]
#Threshold of response.#--There is a minimum intensity of stimulus below
which there is hardly any visible response. We may regard this point as
the threshold of response. Though apparently ineffective, the subliminal
stimuli produce some latent effect, which may be demonstrated by their
additive action. The record in fig. 85 shows how individually feeble
stimuli become markedly effective by superposition.
[Illustration: FIG. 86.--INCOMPLETE AND COMPLETE FUSION OF EFFECT IN TIN
As the frequency of stimulation is increased the fusion becomes more and
more complete. Vertical line to the right represents ·1 volt.]
#Superposition of stimuli.#--The additive effect of succeeding stimuli
will be seen from the above. The fusion of effect will be incomplete if
the frequency of stimulation be not sufficiently great; but it will tend
to be more complete with higher frequency of stimulation (fig. 86). We
have here a parallel case to the complete and incomplete tetanus of
muscles, under similar conditions.
By the addition of these rapidly succeeding stimuli, a maximum effect is
produced, and further stimulation adds nothing to this. The effect is
balanced by a force of restitution. The response-curve thus rises to
its maximum, after which the deflection is held as it were rigid, so
long as the vibration is kept up.
[Illustration: FIG. 87.--CYCLIC CURVE FOR MAXIMUM EFFECTS SHOWING
HYSTERESIS]
It was found that increasing intensities of single stimuli produced
correspondingly increased responses. The same is true also of groups of
stimuli. The maximum effect produced by superposition of stimuli
increases with the intensity of the constituent stimuli.
#Hysteresis.#--Allusion has already been made to the increased
responsiveness conferred by preliminary stimulation (see p. 127). Being
desirous of finding out in what manner this is brought about, I took a
series of observations for an entire cycle, that is to say, a series of
observations were taken for maximum effects, starting from amplitude of
vibration of 10° and ending in 100°, and backwards from 100° to 10°.
Effect of hysteresis is very clearly seen (see A, fig. 87); there is a
considerable divergence between the forward and return curves, the
return curve being higher. On repeating the cycle several times, the
divergence is found very much reduced, the wire on the whole is found to
assume a more constant sensitiveness. In this steady condition,
generally speaking, the sensitiveness for smaller amplitude of vibration
is found to be greater than at the very beginning, but the reverse is
the case for stronger intensity of stimulation.
#Effect of annealing.#--I repeated the experiment with the same wire,
after pouring hot water into the cell and allowing it to cool to the old
temperature. From the cyclic curve (B, fig. 87) it will be seen (1) that
the sensitiveness has become very much enhanced; (2) that there is
relatively less divergence between the forward and return curves. Even
this divergence practically disappeared at the third cycle, when the
forward and backward curves coincided (C, fig. 87). The above results
show in what manner the excitability of the wire is enhanced by purely
physical means.
It is very curious to notice that addition of Na_2CO_3 solution (see
Chap. XV--Action of Stimulants) produces enhancement of responsive power
similar to that produced by annealing; that is to say, not only is there
a great increase of sensitiveness, but there is also a reduction of
hysteresis.