The following is an English translation of:

	Charpentier, A. (1891).  Analyse expérimentale: De quelques 
éléments de la sensation de poids.  Archives de Physiologie Normale et 


Pathologique, 3, 122-135.

I. Since 1886, the date of publication of a preliminary note on sensations of weight (Société de biologie, 3rd April, 1886), I have had the opportunity on several occasions to study those conditions that to some degree exert an influence on those sensations, and it is the results of these studies that I wish to summarize today in order to draw from them certain conclusions that may be inferred.

The extent to which weight sensations are discriminable from each other has already been the subject of several works; their authors (Weber, Fechner, Volkmann, etc.) have proposed investigating this topic by continuing to use a method already employed in the study of other senses, namely the determination of the smallest difference between two given weights that is just noticeable. A particular conclusion has been arrived at, namely that the smallest difference of this kind is not a fixed quantity, but increases in proportion to the absolute magnitude of the weights that are being compared. Otherwise stated, the evaluation of weights, just like the evaluation of sounds, luminances, or stimuli varying in heat, is subject to a psychophysical law according to which the intensity of sensation, which appears to vary inversely with the just noticeable difference with which it is associated, is proportional to the logarithm of the excitation. Is this law absolute? I do not believe so, and I have already demonstrated, at least for the case of visual sensation, that it did not correspond exactly with the facts. [See particularly my work entitled la Lumière et les couleurs au point de vue physiologique (Light and colours from a physiological point of view), 1888, p. 294]. The law can be contested to a varying extent in the context of every modality of sensation. One fact alone remains incontrovertible, namely, that sensation magnitude always grows more slowly than does excitation magnitude.

However I have not attempted to revise the psychophysical law with respect to its application to sensations about weights; I find it extremely difficult to make numerical comparisons between several given weights, and the results of such comparisons are so markedly subject to modification caused by several conditions that are not always taken into consideration during the experiments that I have therefore limited my efforts for the moment to carrying out research on the influence of a certain number of those conditions. This research is instructive; it leads to certain consequences that are often unexpected and are not without significance; one can judge this for oneself by the following facts that I shall briefly set out.

II. A weight can be perceived at one and the same time both as a pressure and as a resistance: it compresses the hand or body area which is supporting it to a greater or lesser degree, but at the same time it resists, again to a greater or lesser degree, any displacement to which one may subject it. In general both modes of perceiving contribute to the evaluation of a given weight; moreover such an evaluation includes a comparison made either with another real weight that is physically present, or with a mentally imagined standard.

An evaluation of a weight can be achieved on the basis of pressure sensations only, but it then has a considerably lower degree of resolution [est alors bien moins délicate] than is the case where pressure sensations are augmented by muscular contractions: for example, it is known that if one places two weights successively on a hand that is held flat and motionless, one can only tell that there is a difference between the two weights if they differ by at least 1/3 from each other; it is much easier to be precise about this judgment if one carries out the action of weighing it in the hand [soupèsement], where the hand does not simply remain passive while supporting the obstacle to be evaluated, but lifts it slowly once or several times; in this case sensations from the muscles, whatever their nature, acting concomitantly with sensations of pressure, yield a much smaller differential fraction; the two weights that are lifted [soupesés] can readily be discriminated one from the other even if they only differ by 6/100 (or approximately 1/16).

It would confound the issue were we to make the error of attributing a unique influence on weight sensation to one or the other of these two factors, sensations of pressure or sensations arising from the muscles. Both contribute to the formation of such sensations; but which predominates? Is it a sense of touch? Or is it a feeling engendered from the expenditure of muscular energy?

One thing is certain, namely, that we judge a weight much as if it were a resistance that opposes a voluntary movement initiated by us with a certain effort; given this degree of effort, the less the resistance offered by the weight, the easier the movement, whence it follows that, the more efficient the effort, the lighter the weight will seem. The opposite also holds.

But from another point of view, the more motor energy we have at our disposal, or, in other words, the better our muscles respond to a given effort, then the less resistance such a weight will appear to present to us. That is to say, a weight identical to the one above will appear lighter.

The value that we assign to a weight depends therefore both on its absolute magnitude and on our own exertion or rather, on that of our muscles. This is not simply a matter of opinion, it is a fact based on experience.

I need not delay by listing such well known facts as that a given weight will appear heavier to a child, an old man, or a sick or tired man than it will to a man in good health. There is nobody who has not already ascertained these and related facts for himself.

But other facts can be ascertained more directly and easily that confirm this viewpoint.

First of all, the more numerous the muscles that cooperate in the lifting of a weight, the lighter the weight appears. One can arrange matters, for example, so that a load can be lifted either by the fingers' alone being flexed from the hand, or by a combination of this movement with other movements that increase systematically in number, e.g. flexion of the hand itself, then flexion of the forearm, then finally a lifting from the shoulder. One needs only to take two main precautions: 1. That the length of arm serving as a lever for lifting the weight should not be longer in one condition than in another, because in practice this would change the resistance offered by the weight; 2. That the area of surface contact with the weight should always be kept the same as each of these actions succeeds the other, for reasons soon to be given. Using these conditions, one can easily ascertain that the load that is imposed (a stone, a metal weight, a chair etc.) appears the less heavy, the greater the number of muscles involved in lifting it; this is so even though to its own weight are successively added those of the hand, then the forearm, then the arm.

Second, the larger a muscle is, the more easily it moves the obstacle, which as a result seems to be easy to displace; Monsieur Brown-Séquard pointed this out to me and it is easily verified. The muscles of the lower limbs are larger (plus gros) than the corresponding muscles in the upper limbs; so a weight appears lighter when it is lifted by the former as opposed to the latter, provided that the experimental precautions just indicated are taken.

From the fact that the apparent heaviness of a weight varies inversely with the number and thickness of the muscles lifting it, there follows a conclusion which may seem very simple, which is that a weight lifted by two or more limbs working simultaneously will appear less heavy than if it were lifted using only one muscle.

This in fact can be readily attested to by experiment: I have a little wooden chair whose weight is 3.5 Kg; the lower edge of the upper cross-piece of the back of the chair [la barre supérieure] was 0.74 metres from the floor; the chair can therefore be very conveniently weighed using one's hand [soupesée] and I have often used it for making comparisons of this kind; and indeed this chair, when it is lifted with both hands, seems much less heavy than when it is lifted with only one hand. To be more rigorous, I ought to have determined the difference in the apparent weight of the chair under the two conditions; but I did not do this because such measurements are more time-consuming than their accuracy warrants, and any comparison that is made between two sensations of weight should be made as quickly as possible if it is to be of full value.

When the chair was lifted using both my hands and my leg, it seemed even lighter.

III. The preceding experiment would appear to have a very simple interpretation: the chair seems less heavy because the energy used to lift it is greater. However another factor can come into play; if, instead of placing the two hands a certain distance apart from each other in order to lift the obstacle, let us cup one hand in the other in such a way that only one hand is directly in contact with the upper cross-piece of the back of the chair; its weight will now appear somewhat heavier to us than it did previously. Here is another experiment. After having lifted the chair with one hand, for example the right hand, apply the other hand to the upper surface of the cross-piece at the same time leaving the corresponding limb inert and, keeping these positions of the hands, let us lift the obstacle again with the right hand; the weight will appear less than if the left hand had no contact with the chair despite the fact that the weight of the left upper limb has been added to that of the chair.

What new condition has come to influence these two experiments? It is the surface area of the obstacle that is in contact with the body; when this surface contact area increases, the apparent weight of the obstacle decreases, and vice versa. This condition is not the sole determinant of the decrease in the apparent weight of the object when two limbs are acting in place of one, because the apparent decrease in weight is even greater in this case than when only one limb is in operation, the other remaining simply in contact with the object; but there is no doubt as to the influential role that it plays.

Let us study more closely the influence of the contact area on the perception of weight.

IV. Everybody knows the baroscope; this device consists of two copper spheres, one of which is solid and the other hollow; the first is also much smaller than the second but the two spheres have the same weight in the medium of air. I have a version of this device in which the small sphere is 4 centimetres in diameter, and the other is 10 centimetres in diameter; the larger sphere possesses therefore 15 or 16 times the volume of the former and has 6 times the surface area. One can compare their apparent weights by weighing them in the hand [soupesant] one after the other with the weights placed flat either on the palm of the supine hand or on the fingers of that hand. Now the large ball always feels much lighter than the little one. I wanted to see just how large this error could be; the two spheres each weighed 266 grams; the larger sphere could only be made to seem as heavy as the smaller sphere if one added about 200 grams to the larger sphere.

Even better: if we have two unequal masses, the heavier can actually seem to us to be the lighter and vice versa; for example I can place a massive copper weight alternating with an empty alcohol-lamp, also made of copper, on myself; the weight seems heavier than the lamp; but the actual value of the weight is only 50 grams whereas the lamp weighs 87 grams.

How do these extensive errors arise? The following experiments will teach us the answer:
If we take our two spheres and, instead of placing them in such a way as to stimulate the hand over areas of contact which are clearly unequal, we lift them with a finger using a hook from which the spheres are suspended and which itself has the same dimensions and shape for both spheres, the spheres will seem to us to possess equal weights.

Or instead, we can devise a small container that neatly holds them and which also has a handle into which we can place one or several fingers or the whole hand; they will still appear equal to us.

Or we can weigh them in the hand [soupeser] but in such a way that the weights themselves do not contact the palm of the hand, for example, by using a light layer of cork on which they rest; again, there will be no apparent difference in their weights that can be perceived.

Moreover if the copper weight and the lamp are placed alternatingly upon this supporting layer, they will seem to us unequal in heaviness, but the direction of this inequality will be reversed from that previously experienced and become identical with that associated with their true heaviness.

It is clear from these facts that we do not so much experience the total pressure exerted by an object but rather we experience what we might call its specific pressure, that is, the pressure it exerts on the corresponding surface area of the body.

We can demonstrate that this must be so by the following experiment: one takes a rather small but heavy mass which initially is placed directly on the skin; then one places it successively on flat lightweight supporting surfaces which themselves gradually increase in area; these themselves serve as media that subject the hand to new degrees of pressure; but the apparent weight of the object becomes lighter, the greater the area of the supporting surface.

This experiment can be varied in many ways: for example, a weighty object suspended by a cord seems heavier when it is lifted by one finger as opposed to two, by two fingers as opposed to a large number of fingers, etc.

To summarize, the greater the area of the base which acts as a support for the weight, or, otherwise expressed, the less the pressure per unit of surface area, the lower the corresponding sensation of heaviness.

V. This law helps us to understand what took place during the experiment with the chair that was described in section II: when the two hands lift the chair part of the apparent weakening of its heaviness may be associated with the increase in the surface of the body-area in contact with the object.

But I only attribute a part of this weakening to this cause. In fact, if it were true that we do not evaluate the absolute weight of a body, but only its specific pressure, that is, the pressure produced per unit of body surface area, we ought to find that there is an exact proportionality that exists between the increase in base-area contacting our body and the apparent diminution in weight. But it is in no wise like this, because the apparent weight decreases relatively less than the surface area increases. Indeed we saw, in the experiment with the two spheres, that the larger appeared to be just over half as heavy as [pas tout à fait deux fois moins que] the smaller; its surface, however, had six times the area of the latter. All of our other experiments have confirmed that no proportionality exists between the two measures under consideration.

This should not surprise us if we distinguish, as appears to be appropriate, between two main components that contribute to weight sensation: one is the feeling of the muscular effort required to lift the object to be weighed, a feeling that is clearly proportional to the actual weight of that object; the other is the sensation arising from the pressure exerted by the object on the skin and on its underlying tissues. But this sensation of pressure appears not to be perceived as a whole, but rather is contributed to individually by each single region within the stimulated area; the sensation does not appear to be the result of a summation but instead is determined by the pressure imposed on each individual nervous element involved.

So, in estimating a weight, it is probable that the sensation of pressure depends only on the area of the body surface in contact with the applied load, while the feeling of muscular contraction varies only with the absolute weight of that load.

VI. Now let us extend our analysis somewhat further. A mass of a certain weight is presented to us to be estimated; we carry out a muscular action of greater or lesser complexity whereby we displace the weight in order to determine the resistance it offers. The conscious impression that we obtain from this focus of concentration [axé] is, as we all know, one of the fundamental elements in the idea that we form about the weight of that given object [masse]. But this sensation itself is not a simple one: it includes not only a more or less clear notion of the movement that was executed, of the degree of muscular contraction that was achieved, of its energy as well as of the extent of the displacement of the mass produced at the same time, but also (and this is essential) a notion of the degree of effort set into operation by the brain when we command that the movement be executed. Now this sense of effort plays a major role in determining our concept of weight. This is the conclusion that will emerge from a new listing of highly remarkable facts that I have yet to describe.

If one uses one's right hand to lift an object of a given weight, one notices that it appears less heavy if the left hand is occupied in lifting another object than if only the right hand is acting. The difference in apparent weight is very striking and never fails to be demonstrated.

This fact is not restricted to the right hand, but can be produced just as well if it is the left hand that is being used to estimate the weight: the weight seems clearly lighter if the other hand is working at some other activity [travaille].

This phenomenon, moreover, can be easily confirmed no matter what the nature of the weight to be estimated or the kind of work being carried out by the second hand. Instead of lifting an object, the second hand can just as well be firmly gripping a stick, pressing against something, pulling something, etc.

Nor is the apparent diminution in the weight being judged connected with the use of the other hand in particular; any kind of activity carried out by a lower limb can produce the same effect. Nor is it necessary that it be a hand that is supporting the weight to be judged; a large object like a chair, lifted by the right or left foot while the body is simply seated on a surface that is high enough for the lower limb to move freely, will seem heavier than is the case when, while lifting the object in the manner just described, one uses the other lower limb or any part of the body to carry out some other action; for example, if one tries to lift oneself up by one's arms to the level of a trapeze-bar hanging fairly low down, the chair that is currently weighing down on one of one's feet will seem incomparably lighter.

We can vary the experiment in many ways, for example, we can breathe heavily by constricting the glottis, or we can lean firmly against a wall etc. The result is the same; the weight to be judged always appears lighter.

Of course, if the experiment is to be convincing, it is necessary that the extrinsic or auxiliary activity be carried out with a certain vigour.

In addition, one can easily be persuaded that the apparent diminution in heaviness of the weight to be judged increases concomitantly with the amount of effort needed to activate the other part of the body in question.

This result was obtained in experiments that I carried out with an American exerciser [lanière américaine], which consisted of a cylindrical band of rubber several decimeters long and 1 or 11/2 centimetres wide provided with two wooden handles that had cords which could be adapted to fit either the foot or the hand; when one pulls a particular handle, the other handle being held stationary by some means, one can expend more or less effort according to the degree of traction one produces and therefore according to the degree to which the band is stretched; with the model I possess I can pull on it with a force that can go up to 12 kilograms. Now if one holds a weight of 2 to 5 kilograms in one hand, the other hand, or any other part of the body, can be pulling on the exerciser with any degree of traction; one can then easily discover that the larger this degree of traction, the less heavy the weight seems to be.

In order to produce this decrease in apparent weight, the activity of the other body-part does not necessarily have to involve external mechanical work; a simple static contraction of the muscles will suffice.

Furthermore, the limb that is actively being used to judge the weight can itself participate in the extrinsic task that is required for this experiment; the drop in apparent heaviness, far from being reduced, seems, on the contrary, to be enhanced. So, for example, the right hand, while it is still supporting the weight, can also be pulling on the rubber exerciser (whether the latter has its fixed end above, below, or on a level with that hand), and in any direction (favourable or unfavourable with respect to the movements necessary to hold up the weight), without there being any disruption to the perception that the weight feels lighter; in fact it is in such instances that the degree of apparent lightening of the weight seems at its greatest.

Without wishing to supplement these observations with numerical values whose precision will be quite illusory, it still seemed interesting to me to estimate approximately the magnitude of the error produced; in a few instances, I took a given weight and at the same time as carrying out some concomitant extrinsic activity I determined just what the value of the weight would be that yielded the same impression as the given weight even though no extrinsic activity was present. I could achieve this by lifting these weights making use of a plate suspended from the hand. The plate could be loaded with more or fewer weights of known heaviness. In fact, I often obtained differences that lay between single and double; in one case where my right hand was carrying a load of 5 kilograms, this object felt as if it only weighed 1.5 kilograms if, at the same time, a strong horizontal pull was exerted by the other hand on the right hand without the latter's actually being displaced laterally.

All these experiments are in agreement in demonstrating that we are dealing here with a general phenomenon whose importance should not be underestimated. One can express the matter as follows: the sensation of weight that is produced by a given object will be weakened by the presence of all the other feelings of voluntary effort that are being produced in the organism at the same time as the object is actually being lifted, and the degree of weakening will seem to be in proportion to the intensity of those other feelings.

VII. How are we to interpret this phenomenon and how is it that extrinsic activities can operate in such a way as to reduce the sensation of weight? On which aspects of this sensation do they exercise their influence?

In the first place one can ask whether they modify one's sensitivity to pressure. However, if one repeats the preceding experiments with the variation that the weights, instead of being actively weighed by moving the hand, are placed onto the hand lying flat on the surface of a table or other resisting medium, one feels no observable change in the sensation of pressure if one simultaneously exerts some extrinsic effort: the weight seems just as heavy as before.

VIII. Do these extrinsic actions augment the strength of contraction of those muscles involved in mediating the activity of weight estimation? If there were indeed an augmentation of this power, the resistance offered by the weight would indeed appear to be reduced.

I have studied this question by making use of various dynamometers and dynamographs to investigate whether the maximum degree of pressure that could be exerted by one hand would vary with extrinsic efforts that themselves varied in intensity from large to small. I intend to return in a later report to these experiments, which are actually of interest from a quite different perspective: I do not have time today to go into detail except to give the main conclusion. They have proved to me that extrinsic effort does appear in general to increase the energy of the manual compression, but it is only to a very moderate extent, one that is quite disproportional to the very clear feeling, that goes along with this effort, of a diminution in the weight of the object being held in the hand.

Accordingly, it is impossible to account for this apparent diminution in weight, which is always quite noticeable, in terms of an increase in the muscular energy that is produced in proportion to the effort in question.

Since I first communicated studies of this kind to the Société de Biologie (3 May, 1890), I have been able to take up this research again using an apparatus which is much more satisfying and accurate than are the usual dynamometers, namely, the ergograph invented by Mosso; this apparatus records the work produced by one or several voluntary movements directly onto a cylinder in the form of an inscribed pattern. Such movements most often consist of the flexion of a middle finger that is lifting a given weight, while, at the same time, the other fingers and the whole of the limb are immobilized (a detail that is most important to control). In studying the flexion-movements involved in weighing by hand a weight whose absolute value was 5 kilograms at the same time as the subject carried out those extrinsic actions which most efficiently yielded the feeling that the weight was reduced in heaviness, I have been unable to detect any observable constant change in the maximum energy developed by that finger before or during the carrying out of those actions; in fact, at times, this energy seemed to diminish somewhat during the effort in question; at any rate, there was no regularity in the obtained inscribed records from the conditions being compared that would allow us to assert that the extrinsic efforts would modify the muscular energy in one direction or another. And yet the concomitant sensation of heaviness with respect to the weight remained clear and was reliably reduced during these efforts.

IX. What, then, remains to be established about the remarkable influence that is exerted on the sensation of weight by these various muscular efforts?

When we execute a deliberately predetermined motor action, consciousness reveals little (directly or immediately) about the magnitude of the mechanical work that we produce; it does give us two distinct notions, one of the effort demanded and the other of the displacement produced, but it is only from an association that combines these two notions that we can derive a third notion, that of work or energy.

Now a [feeling of] weight is neither a kind of energy nor a quantity of work; it is a magnitude representing the degree of exertion one experiences [une grandeur de l'ordre des efforts]; in physics one would say it constituted a force. It is counterbalanced by a feeling of exertion in the opposite direction, and one [normally] estimates the feeling of weight by the degree of exertion that one must initiate in order to counterbalance that opposite exertion. This is what the brain does: it sends a signal [donne une impulsion] to the muscle to set the latter in motion and records the feeling associated with this signal [ressent cette impulsion]; but in order to reproduce a movement identical to that involved when the muscle is supporting a load, it must also send a supplementary signal whose strength corresponds to that of the signal representing the load in the brain; but the brain can only estimate the extent to which that supplementary signal needs to be increased, by comparing it to something analogous; so it compares it either to an earlier representation or to a simultaneous signal; in this latter instance, because of a well-known physiological phenomenon, the greater the strength of the signal sent simultaneously to a muscle involved in the counterbalancing, the more feeble appears to be the signal yielded by the target weight itself.

In other words, a weight is estimated in connection with an equivalent motor exertion, whose site is clearly cerebral and which is similar in nature to a voluntary command signal even though it is not exactly the same thing. What makes this motor exertion different is that it is not appraised in an absolute fashion, or, if one prefers, it is not strictly localized; rather, it is, to a certain degree, intermixed with the general ensemble of analogous exertions that are being executed at the same time by the brain; and it is appraised only insofar as it is part of that ensemble, so that the larger that ensemble, the smaller the portion of that ensemble constituted by this motor exertion.

Moreover, a new experiment can serve to demonstrate that the above argument does indeed represent the best interpretation of the facts that we are trying to analyze.

One can estimate a weight in a manner other than actually displacing it or subjecting it to some sort of work such as lifting it, weighing it in the hands [soupèsement], etc. One can simply maintain it a certain constant height, counterbalancing it by way of a tonic muscular contraction whose magnitude is in the appropriate relation to the weight in question. In the course of this act, the muscle is neither displaced nor produces external work; there is only one thing that has changed, namely its tonicity, its level of tension, its potential energy or, to express it best and most simply, its potential. There is no question that this increase in potential, which will be equivalent to the weight being supported, will necessarily have to be kept steady by a never-ending consumption of nutritional matter and by molecular work which sooner or later will be compromised by fatigue.

Now if the hand is supporting a weight but nevertheless is not moving in any way, and if at the same time extrinsic muscular actions such as those described above are carried out by the organism, then the sensation of heaviness is decreased just as it was when the object was weighed in the moving hand, in fact slightly more noticeably.

In this case it was not possible for the level of tonicity in the muscle to have varied, because it had to have remained constant in order to support an identical weight. The only thing that was free to vary was the voluntary effort which controlled this level of tonicity. There is only one possible interpretation that remains therefore, one that can be expressed in several ways: the cerebral effort that determined those muscular actions that were alien to the maintenance of equilibrium of the weight was widely diffused and in this case entailed that only a minimum local effort was necessary to support the weight; or, alternatively put, this local effort, the intensity of which serves as a measure of the weight's heaviness, is only estimated in relation to the total feeling of effort that is dominating the brain at that time, and appears to be lessened in proportion to any increase in the latter.

In fact these two ways of expressing the matter are approximately equivalent and lead to the following conclusion: a weight is estimated in terms of [feelings of] cerebral effort, and no cerebral effort is ever strictly local in nature.

X. This phenomenon of diffusion of effort seems to me to be of general import. It can be found in tasks that are a little different, but of the same kind: for example, is not attention a cerebral effort of a particular genre? Indeed M. Féré has recently demonstrated that phenomena involving attention are accompanied by a state of muscular tension that is generalized.

Another notable influence on our sensations of weight is any accompanying mental idea. I have shown, in my earliest experiments on this question, that the idea that one forms of the magnitude of the weight to be lifted can cause, to a greater or lesser degree, a very real error in estimation. For example, I have established with several subjects that, after having had them compare the large sphere with the small sphere that I was using in my experiments and which, despite being of equal weight, appeared to differ in heaviness, the subjects never were able to perceive the two spheres as having the same heaviness even if they weighed them in the hand again, keeping the surface area in contact with the hand equal, but with the eyes held open; but on the other hand the spheres were apparently equal in heaviness during this last condition if the subject, with eyes closed, could not tell which sphere was presented and yet of which he had formed a first impression which had then become a defining mental standard for him [une idée devenue définitive].

Experimental trials of this kind can be varied in all sorts of ways; each demonstrates the important role played by a preliminary idea in the judgment of weight.

But is not such an idea itself a motor phenomenon, a cerebral effort, positive or negative as the case may be? These last facts can therefore be added to those we have already established, and do not oblige us to modify the manner in which we have been able to account for sensations of weight.

To summarize, sensations of weight depend mainly on two conditions: the pressure exerted on the skin and its underlying tissues, a pressure which is related to the unit area of surface or rather to the associated nervous element; and the cerebral effort that is provided to the muscles in the course of counterbalancing the effort required to hold the weight. But the feelings associated with the former effort can only be judged in relation to the total ensemble of analogous efforts that are currently co-existing in the brain.

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