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.
| Vibration amplitude | E.M. variation |
|---|---|
| 5° | ·024 volt |
| 10° | ·057 " |
| 20° | ·111 " |
| 25° | ·143 " |
| 30° | ·170 " |
| 35° | ·187 " |
| 40° | ·204 " |
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.)
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.
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.
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.
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.
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.
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.
Fig. 87.—Cyclic Curve for Maximum Effects showing Hysteresis
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 Na2CO3 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.
We have seen that the ultimate criterion of the physiological character of electric response is held to be its abolition when the substance is subjected to those chemical reagents which act as poisons.
Fig. 88.—Action of Poison in Abolishing Response in Nerve (Waller)
Action of chemical reagents.—Of these reagents, some are universal in their action, amongst which strong solutions of acids and alkalis, and salts like mercuric chloride, may be cited. These act as powerful toxic agents, killing the living tissue, and causing electric response to disappear. (See fig. 88.) It must, however, be remembered that there are again specific poisons which may affect one kind of tissue and not others. Poisons in general may be regarded as extreme cases of depressants. As an example of those which produce moderate physiological depression, potassium bromide may be mentioned, and this also diminishes electric response. There are other chemical reagents, on the other hand, which produce the opposite effect of increasing the excitability and causing a corresponding exaltation of electric response.
We shall now proceed to inquire whether the response of inorganic bodies is affected by chemical reagents, so that their excitability is exalted by some, and depressed or abolished by others. Should it prove to be so, the last test will have been fulfilled, and that parallelism which has been already demonstrated throughout a wide range of phenomena, between the electric response of animal tissues on the one hand, and that of plants and metals on the other, will be completely established.
Action of stimulants on metals.—We shall first study the stimulating action of various chemical reagents. The method of procedure is to take a series of normal responses to uniform stimuli, the electrolyte being water. The chemical reagent whose effect is to be observed is now added in small quantity to the water in the cell, and a second series of responses taken, using the same stimulus as before. Generally speaking, the influence of the reagent is manifested in a short period, but there may be occasional instances where the effect takes some time to develop fully. We must remember that by the introduction of the chemical reagent some change may be produced in the internal resistance of the cell. The effect of this on the deflection is eliminated by interposing a very high external resistance (from one to five megohms) in comparison with which the internal resistance of the cell is negligible. The fact that the introduction of the reagent did not produce any variation in the total resistance of the circuit was demonstrated by taking two deflections, due to a definite fraction of a volt, before and after the introduction of the reagent. These deflections were found equal.
I first give a record of the stimulating action of sodium carbonate on tin, which will become evident by a comparison of the responses before and after the introduction of Na2CO3 (fig. 89). The next record shows the effect of the same reagent on platinum (fig. 90).
Action of depressants.—Certain other reagents, again, produce an opposite effect. That is to say, they diminish the intensity of response. The record given on the next page (fig. 91) shows the depressing action of 10 per cent. solution of KBr on tin.
Fig. 91.—Depressing Effect of KBr (10 per Cent.) on the Response of Tin
Effect of ‘poison.’—Living tissues are killed, and their electric responses are at the same time abolished by the action of poisons. It is very curious that various chemical reagents are similarly effective in killing the response of metals. I give below a record (fig. 92) to show how oxalic acid abolishes the response. The depressive effect of this reagent is so great that a strength of one part in 10,000 is often sufficient to produce complete abolition. Another notable point with reference to the action of this reagent is the persistence of after-effect. This will be clearly seen from an account of the following experiment. The two wires A and B, in the cell filled with water, were found to give equal responses. The wires were now lifted off, and one wire B was touched with dilute oxalic acid. All traces of acid were next removed by rubbing the wire with cloth under a stream of water. On replacing the wire in the cell, A gave the usual response, whereas that of B was found to be abolished. The depression produced is so great and passes in so deep that I have often failed to revive the response, even after rubbing the wire with emery paper, by which the molecular layer on the surface must have been removed.
We have seen in the molecular model (fig. 62, d, e) how the attainment of maximum is delayed, the response diminished, and the recovery prolonged or arrested by increase of friction or reduction of molecular mobility.
It would appear as if the reagents which act as poisons produced some kind of molecular arrest. The following records seen to lend support to this view. If the oxalic acid is applied in large quantities, the abolition of response is complete. But on carefully adding just the proper amount I find that the first stimulus evokes a responsive electric twitch, which is less than the normal, and the period of recovery is very much prolonged from the normal one minute before, to five minutes after, the application of the reagent (fig. 93, a). In another record the arrest is more pronounced, i.e. there is now no recovery (fig. 93, b). Note also that the maximum is attained much later. Stimuli applied after the arrest produce no effect, as if the molecular mechanism became, as it were, clogged or locked up.
In connection with this it is interesting to note that the effect of veratrine poison on muscle is somewhat similar. This reagent not only diminishes the excitability, but causes a very great prolongation of the period of recovery.
In connection with the action of chemical reagents the following points are noteworthy.
Fig. 93.—‘Molecular Arrest’ by the Action of ‘poison’
In each, curves to the left show the normal response, curve to the right shows the effect of poison. In (a) the arrest is evidenced by prolongation of period of recovery. In (b) there is no recovery.
(1) The effect of these reagents is not only to increase or diminish the height of the response-curve, but also to modify the time relations. By the action of some the latent period is diminished, others produce a prolongation of the period of recovery. Some curious effects produced by the change of time relations have been noticed in the account given of diphasic variation (see p. 113).
(2) The effect produced by a chemical reagent depends to some extent on the previous condition of the wire.
(3) A certain time is required for the full development of the effect. With some reagents the full effect takes place almost instantaneously, while with others the effect takes place slowly. Again the effect may with time reach a maximum, after which there may be a slight decline.
Fig. 94.—Opposite Effects of Small and Large Doses (Tin)
(a) is the normal response; (b) is the stimulating action of small dose of potash (3 parts in 1,000); (c) is the abolition of response with a stronger dose (3 parts in 100).
(4) The after-effects of the reagents may be transitory or persistent; that is to say, in some cases the removal of the reagent causes the responses to revert to the normal, while in others the effect persists even after the removal of all traces of the reagent.
Opposite effects of large and small doses.—There remains a very curious phenomenon, known not only to students of physiological response but also known in medical practice, namely that of the opposite effects produced by the same reagent when given in large or in small doses. Here, too, we have the same phenomena reproduced in an extraordinary manner in inorganic response. The same reagent which becomes a ‘poison’ in large quantities may act as a stimulant when applied in small doses. This is seen in record fig. 94, in which (a) gives the normal responses in water; KHO solution was now added so as to make the strength three parts in 1,000, and (b) shows the consequent enhancement of response. A further quantity of KHO was added so as to increase the strength to three parts in 100. This caused a complete abolition (c) of response.
It will thus be seen that as in the case of animal tissues and of plants, so also in metals, the electrical responses are exalted by the action of stimulants, lowered by depressants, and completely abolished by certain other reagents. The parallelism will thus be found complete in every detail between the phenomena of response in the organic and the inorganic.
The effect of the stimulus of light on the retina is perceived in the brain as a visual sensation. The process by which the ether-wave disturbance causes this visual impulse is still very obscure. Two theories may be advanced in explanation.
(1) Chemical theory.—According to the first, or chemical, theory, it is supposed that certain visual substances in the retina are affected by light, and that vision originates from the metabolic changes produced in these visual substances. It is also supposed that the metabolic changes consist of two phases, the upward, constructive, or anabolic phase, and the downward, destructive, or katabolic phase. Various visual substances by their anabolic or katabolic changes are supposed to produce the variations of sensation of light and colour. This theory, as will be seen, is very complex, and there are certain obstacles in the way of its acceptance. It is, for instance, difficult to see how this very quick visual process could be due to a comparatively slow chemical action, consisting of the destructive breaking-down of the tissue, followed by its renovation. Some support was at first given to this chemical theory by the bleaching action of light on the visual purple present in the retina, but it has been found that the presence or absence of visual purple could not be essential to vision, and that its function, when present, is of only secondary importance. For it is well known that in the most sensitive portion of the human retina, the fovea centralis, the visual purple is wanting; it is also found to be completely absent from the retinæ of many animals possessing keen sight.
(2) Electrical theory.—The second, or electrical, theory supposes that the visual impulse is the concomitant of an electrical impulse; that an electrical current is generated in the retina under the incidence of light, and that this is transmitted to the brain by the optic nerve. There is much to be said in favour of this view, for it is an undoubted fact, that light gives rise to retinal currents, and that, conversely, an electrical current suitably applied causes the sensation of light.
Retinal currents.—Holmgren, Dewar, McKendrick, Kuhne, Steiner, and others have shown that illumination produces electric variation in a freshly excised eye. About this general fact of the electrical response there is a widespread agreement, but there is some difference of opinion as regards the sign of this response immediately on the application, cessation, and during the continuance of light. These slight discrepancies may be partly due to the unsatisfactory nomenclature—as regards use of terms positive and negative—hitherto in vogue and partly also to the differing states of the excised eyes observed.
Waller, in his excellent and detailed work on the retinal currents of the frog, has shown how the sign of response is reversed in the moribund condition of the eye.
As to the confusion arising from our present terminology, we must remember that the term positive or negative is used with regard to a current of reference—the so-called current of injury.
Fig. 95. Retinal Response To Light
The current of response is from the nerve to the retina.
When the two galvanometric contacts are made, one with the cut end of the nerve, and the other on the uninjured cornea, a current of injury is found which in the eye is from the nerve to the retina. In the normal freshly excised eye, the current of response due to the action of light on the retina is always from the nerve, which is not directly stimulated by light, to the retina, that is, from the less excited to the more excited (fig. 95). This current of response flows, then, in the same direction as the existing current of reference—the current of injury—and may therefore be called positive. Unfortunately the current of injury is very often apt to change its sign; it then flows through the eye from the cornea to the nerve. And now, though the current of response due to light may remain unchanged in direction, still, owing to the reversal of the current of reference, it will appear as negative. That is to say, though its absolute direction is the same as before, its relative direction is altered.
I have already advocated the use of the term positive for currents which flow towards the stimulated, and negative for those whose flow is away from the stimulated. If such a convention be adopted, no confusion can arise, even when, as in the given cases, the currents of injury undergo a change of direction.
Normal response positive.—The normal effect of light on the retina, as noticed by all the observers already mentioned, is a positive variation, during exposure to light of not too long duration. Cessation of light is followed by recovery. On these points there is general agreement amongst investigators. Deviations are regarded as due to abnormal conditions of the eye, owing to rough usage, or to the rapid approach of death. For just as in the dying plant we found occasional reversals from negative to positive response, so in the dying retina the response may undergo changes from the normal positive to negative.
The sign of response, as we have already seen in numerous cases, depends very much on the molecular condition of the sensitive substance, and if this condition be in any way changed, it is not surprising that the character of the response should also undergo alteration.
Unlike muscle in this, successive retinal responses exhibit little change, for, generally speaking, fatigue is very slight, the retina recovering quickly even under strong light if the exposure be not too long. In exceptional cases, however, fatigue, or its converse, the staircase effect, may be observed.
Inorganic response under the stimulus of light.—It may now be asked whether such a complex vital phenomenon as retinal response could have its counterpart in non-living response. Taking a rod of silver, we may beat out one end into the form of a hollow cup, sensitising the inside by exposing it for a short time to vapour of bromine. The cup may now be filled with water, and connection made with a galvanometer by non-polarisable electrodes. There will now be a current due to difference between the inner surface and the rod. This may be balanced, however, by a compensating E.M.F.
Fig. 96.—Record of Responses To Light given by the Sensitive Cell
Thick lines represent the effect during illumination, dotted lines the recovery in darkness. Note the preliminary negative twitch, which is sometimes also observed in responses of frog’s retina.
We have thus an arrangement somewhat resembling the eye, with a sensitive layer corresponding to the retina, and the less sensitive rod corresponding to the conducting nerve-stump (fig. 96, a).
The apparatus is next placed inside a black box, with an aperture at the top. By means of an inclined mirror, light may be thrown down upon the sensitive surface through the opening.
On exposing the sensitive surface to light, the balance is at once disturbed, and a responsive current of positive character produced. The current, that is to say, is from the less to the more stimulated sensitive layer. On the cessation of light, there is fairly quick recovery (fig. 96, b).
The character and the intensity of E.M. variation of the sensitive cell depend to some extent on the process of preparation. The particular cell with which most of the following experiments were carried out usually gave rise to a positive variation of about ·008 volt when acted on for one minute by the light of an incandescent gas-burner which was placed at a distance of 50 cm.
Fig. 97 (a)
A, B are the two faces of a brominated sheet of silver. One face, say A, is acted on by light. The current of response is from B to A, across the plate.
Typical experiment on the electrical effect induced by light.—This subject of the production of an electrical current by the stimulus of light would appear at first sight very complex. But we shall be able to advance naturally to a clear understanding of its most complicated phenomena if we go through a preliminary consideration of an ideally simple case. We have seen, in our experiments on the mechanical stimulation of, for example, tin, that a difference of electric potential was induced between the more stimulated and less stimulated parts of the same rod, and that an action current could thus be obtained, on making suitable electrolytic connections. Whether the more excited was zincoid or cuproid depended on the substance and its molecular condition.
Let us now imagine the metal rod flattened into a plate, and one face stimulated by light, while the other is protected. Would there be a difference of potential induced between the two faces of this same sheet of metal?
Let two blocks of paraffin be taken and a large hole drilled through both. Next, place a sheet of metal between the blocks, and pour melted paraffin round the edge to seal up the junction, the two open ends being also closed by panes of glass. We shall have then two compartments separated by the sheet of metal, and these compartments may be filled with water through the small apertures at the top (fig. 97, a).
Fig. 97 (b).—Record of Responses obtained from the Above Cell
Ten seconds’ exposure to light followed by fifty seconds’ recovery in the dark. Thick lines represent action in light, dotted lines represent recovery.
The two liquid masses in the separated chambers thus make perfect electrolytic contacts with the two faces A and B of the sheet of metal. These two faces may be put in connection with a galvanometer by means of two non-polarisable electrodes, whose ends dip into the two chambers. If the sheet of metal have been properly annealed, there will now be no difference of potential between the two faces, and no current in the galvanometer. If the two faces are not molecularly similar, however, there will be a current, and the electrical effects to be subsequently described will act additively, in an algebraical sense. Let one face now be exposed to the stimulus of light. A responsive current will be found to flow, from the less to the more stimulated face, in some cases, and in others in an opposite direction.
It appears at first very curious that this difference of electric potential should be maintained between opposite faces of a very thin and highly conducting sheet of metal, the intervening distance between the opposed surfaces being so extremely small, and the electrical resistance quite infinitesimal. A homogeneous sheet of metal has become by the unequal action of light, molecularly speaking, heterogeneous. The two opposed surfaces are thrown into opposite kinds of electric condition, the result of which is as if a certain thickness of the sheet, electrically speaking, were made zinc-like, and the rest copper-like. From such unfamiliar conceptions, we shall now pass easily to others to which we are more accustomed. Instead of two opposed surfaces, we may obtain a similar response by unequally lighting different portions of the same surface. Taking a sheet of metal, we may expose one half, say A, to light, the other half, B, being screened. Electrolytic contacts are made by plunging the two limbs in two vessels which are in connection with the two non-polarisable electrodes E and E′ (fig. 98, a). On illumination of A and B alternately, we shall now obtain currents flowing alternately in opposite directions.
Just as in the strain cells the galvanometer contact was transferred from the electrolytic part to the metallic part of the circuit, so we may next, in an exactly similar manner, cut this plate into two, and connect these directly to the galvanometer, electrolytic connection being made by partially plunging them into a cell containing water. The posterior surfaces of the two half-plates may be covered with a non-conducting coating. And we arrive at a typical photo-electric cell (fig. 98, b). These considerations will show that the eye is practically a photo-electric cell.
Fig. 99.—Responses To Light in Frog’s Retina
Illumination L for one minute, recovery in dark for two minutes during obscurity D. (Waller.)
We shall now give detailed experimental results obtained with the sensitive silver-bromide cell, and compare its response-curve with those of the retina. A series of uniform light stimuli gives rise to uniform responses, which show very little sign of fatigue. How similar these response-curves are to those of the retina will be seen from a pair of records given below, where fig. 99 shows responses of frog’s retina, and fig. 100 gives the responses obtained with the sensitive silver cell (fig. 100).
It was said that the responses of the retina are uniform. This is only approximately true. In addition to numerous cases of uniform responses, Waller finds instances of ‘staircase’ increase, and its opposite, slight fatigue. In the record here given of the silver cell, the staircase effect is seen at the beginning, and followed by slight fatigue. I have other records where for a very long time the responses are perfectly uniform, there being no sign of fatigue.
Fig. 100.—Responses in Sensitive Silver Cell
Illumination for one minute and obscurity for one minute. Thick line represents record during illumination, dotted line recovery during obscurity.
Another curious phenomenon sometimes observed in the response of retina is an occasional slight increase of response immediately on the cessation of light, after which there is the final recovery. An indication of this is seen in the second and fourth curves in fig. 99. Curiously enough, this abnormality is also occasionally met with in the responses of the silver cell, as seen in the first two curves of fig. 100. Other instances will be given later.
We shall next proceed to study the effect, on the response of the sensitive cell, of all those conditions which influence the normal response of the retina. We shall then briefly inquire whether even the abnormalities sometimes met with in retinal responses have not their parallel in the responses given by the inorganic.
Fig. 101.—Influence of Temperature on Response
Illumination 20″, obscurity 40″.
In (a) is shown a series of responses at 20° C.—the record exhibits slight fatigue. (b) is the slight irregular response at 50° C. (c) is the record on re-cooling; it exhibits ‘staircase’ increase.
Effect of temperature.—It has been found that when the temperature is raised above a certain point, retinal response shows rapid diminution. On cooling, however, response reappears, with its original intensity. In the response given by the sensitive cell, the same peculiarity is noticed. I give below (fig. 101, a) a set of response-curves for 20° C. These responses, after showing slight fatigue, became fairly constant. On raising the temperature to 50° C. response practically disappeared (101, b). But on cooling to the first temperature again, it reappeared, with its original if not slightly greater intensity (fig. 101, c). A curious point is that while in record (a), before warming, slight fatigue is observed, in (c), after cooling, the reverse, or staircase effect, appears.
Fig. 102.—Response-curves for Increasing Duration of Illumination from 1″ to 10″
In (a) the source of light was at a distance of 50 cm.; in (b) it was at a distance of 25 cm. Note the after-oscillation.
Effect of increasing length of exposure.—If the intensity of light be kept constant, the magnitude of response of the sensitive cell increases with length of exposure. But this soon reaches a limit, after which increase of duration does not increase magnitude of effect. Too long an exposure may however, owing to fatigue, produce an actual decline.
I give here two sets of curves (fig. 102) illustrating the effect of lengthening exposure. The intensities of light in the two cases are as 1 to 4. The incandescent burner was in the two cases at distances 50 and 25 cm. respectively. It will be observed that beyond eight seconds’ exposure the responses are approximately uniform. Another noticeable fact is that with long exposure there is an after-oscillation. This growing effect with lengthening exposure and attainment of limit is exactly paralleled by responses of retina under similar conditions.
Relation between intensity of light and magnitude of response.—In the responses of retina, it is found that increasing intensity of light produces an increasing effect. But the rate of increase is not uniform: increase of effect does not keep pace with increase of stimulus. Thus a curve giving the relation between stimulus and response is concave to the axis which represents the stimulus.
The same is true of the sensation of light. That is to say, within wide limits, intensity of sensation does not increase so rapidly as stimulus.
This particular relation between stimulus and effect is also exhibited in a remarkable manner by the sensitive cell. For a constant source of light I used an incandescent burner, and graduated the intensity of the incident light by varying its distance from the sensitive cell. The intensity of light incident on the cell, when the incandescent burner is at a distance of 150 cm., has been taken as the arbitrary unit. In order to make allowance for the possible effects of fatigue I took two successive series of responses (fig. 103). In the first, records were taken with intensities diminishing from 7 to 1, and immediately afterwards increasing from 1 to 7, in the second.
Fig. 103.—Responses of Sensitive Cell to various Intensities of Light
On the left the responses are for diminishing intensities in the ratios of 7, 5, 3, and 1. On the right they are for the increasing intensities 1, 3, 5, and 7. The thick lines are records during exposures of one minute; the dotted lines represent recoveries for one minute.
(The intensity of an incandescent gas-burner at a distance of 150 cm.
is taken as unit.)
| Intensity of Light |
Response (Light diminishing) |
Response (Light increasing) |
Mean | Value in volt |
|---|---|---|---|---|
| 7 | 43 | 39 | 41 | 63·0 × 10− volt |
| 5 | 31 | 29 | 30 | 46·1 ×" |
| 3 | 18·5 | 17·5 | 18 | 27·7 ×" |
| 1 | 10 | 9 | 9·5 | 14·6 ×" |
As the zero point was slightly shifted during the course of the experiment, the deflection in each curve was measured from a line joining the beginning of the response to the end of its recovery. A mean deflection, corresponding to each intensity, was obtained by taking the average of the descending and ascending readings. The two sets of readings did not, however, vary to any marked extent.
The deflections corresponding to the intensities 1, 3, 5, 7, are, then, as 9·5 to 18, to 30, to 41. If the deflections had been strictly proportionate to the intensities of light stimulus they would have been as 9·5 to 28·5, to 47·5, to 66·5.