On the apparent size of objects

by W.H.R.Rivers

The most definite experimental evidence in favour of sensations of movement as factors in spatial perception has in the past been derived from the experiments of Wundt^[1] on the monocular estimation of distance of a thread. Hillebrand^[2] however has recently shown that Wundt’s results probably depended, not on the movements of accommodation and their accompanying sensations, but on other factors, especially alteration in the size of the thread. On the other hand as Dixon^[3] has pointed out, Hillebrand’s experiments hardly justify him in concluding that movement factors are wholly without influence on the sense of depth.

I have investigated some other phenomena which have been held to prove the influence of movement and especially of accommodation in spatial perception, and I consider one of them in the present paper, viz. the alteration of the apparent size of objects when the accommodation apparatus of the eye is paralysed by atropin.

One of the first to record this phenomenon was Donders^[4] and his explanation is still generally accepted. He noticed the appearance especially when the ciliary muscle was only partially paralysed and supposed the effort necessary to see an to see an object distinctly was greater than normal; that the object was in consequence supposed to be nearer, and that as the visual angle had not become greater, there was an apparent diminution in size. The condition was more fully investigated by Förster^[5] and Aubert^[6], who noticed that an object appeared not only small but more distant. They explained the micropsia on the same lines as Donders, and supposed that the appearance of greater distance was due to a secondary inference from the known size of the object. A similar appearance is often observed as a symptom of paralysis of the third nerve from disease that has received the same explanation.

My own observations have led me to the conclusion that under the influence of atropin micropsia may arise from two wholly distinct causes, under certain conditions an object may appear to be diminished in size when looked at directly; under other conditions an object beyond the fixation point appears small, and these two appearances are of very different nature. I phenomenon observed by Förster and Aubert was micropsia at the fixation point and micropsia beyond the fixation point respectively.

The phenomenon observed by Förster and Aubert was micropsia at the fixation point, and I will consider this first. Förster found that with partial paralysis of one eye by atropin Jaeger’s type appeared smaller to this than to the normal eye, and the diminution in size increased as the type was brought nearer to the eye up to a certain limit. Both far and near limits of the region in which micropsia occurred varied in different individuals depending on the condition of refraction. Aubert saw No. 4 Jaegar at 7 inches only half as large as to the normal eye.

In repeating these experiments I dropped a solution of homatropin (one grain to the ounce) in the left eye). At the end of 20 minutes Jaeger’s type appeared distinctly small with this eye when fixed directly. I am myopic, (-3 D in the vertical meridian and -4 D in the horizontal), and the far limit of the micropsia was 20cm: the decrease in size became more marked as the type was brought nearer to the eye, so that at the nearest point where the type could be focussed No. 10 to the left eye appeared nearly as small as No. 6 to the right eye. On trying squares of paper of different sizes, I found that while black squares on a white ground showed marked diminution in size, no such change occurred in the case of white squares on a black ground; these looked even rather larger to the left eye than to the right eye. Mr E.T Dixon (emmetropic) kindly made observations for me under homatropin. He observed Jaegar’s type smaller with the affected (right) eye from 100 cm up to 40 cm. No. 10 to the right eye appeared smaller than No. 8 to the left eye. A black square on white ground appeared smaller, a white square on black background rather larger to the right than to the left eye. The change in size observed by us was evidently due to irradiation, and as might be expected printed type is a very favourable object for showing the effects of irradiation. It became probable that this form of micropsia depended rather on the dilation of the pupil than on affection of accommodation and this was proved by the further observation, that with a small artificial pupil before the affected eye no micropsia was observed; the type was equally large to either eye.

Förster gives several reasons for his belief that the micropsia observed by him was due to the change of accommodation and not to the pupil. His three observers did not notice the micropsia till from 30 to 80 minutes after instillation, although the pupil had dilated earlier. I noticed the micropsia after 20 minutes and it was well marked after 25 minutes. Förster also noticed the micropsia especially with strong effort to accommodate and together with lessening or disappearance of blurring, and regarded this as proof of its dependence on the accommodation. He does not appear however to have tried the effect of an artificial small pupil, and he only describes experiments with Jaeger’s type.

I have found that the same process of irradiation explains another alteration of apparent size which I have observed. Some time ago I noticed that objects and especially printed letters appeared slightly smaller to my left eye than to my right; the difference was very slight and was only detected when the object was doubled by looking beyond it so that I had my right and left eye images side by side for comparison. There is a very slight difference of refraction between my two eyes and it occurred to me that in cases of marked inequality, there might be a decided difference in the apparent size of objects to the two eyes. This I found to be the case. In one case the apparent difference in size associated with a difference of 2 D in refraction was so considerable that No. 10 Jaeger to one eye appeared only as large as No. 6 to the other. In the early cases I examined the micropsia occurred with the relatively more hypermetropic eye and I supposed that it was associated with the greater effort of accommodation necessary to see an object distinctly. Since making the experiments with atropin I have re-examined some of these cases and found the appearance to be due to irradiation. In the case I have already mentioned a black square on a white ground is considerably diminished in size, but a white square on a black ground is not appreciably altered. With an artificial pupil of 1.5 mm diameter before each eye, the difference in size was less marked but still present; with a pupil of 1.5 mm before the hypermetropic eye and one of 2 mm. Before the normal eye, no difference of size was observed.

One form of micropsia which occurs under the influence of atropin appears then to be due to dilation of the pupil, and so far as this form is concerned, there is no evidence in favour of accommodation as a factor in spatial perception. The other form which I have called micropsia beyond the fixation point is of more interest psychologically. It is an appearance of the same nature as one which may be observed with the normal eye. If one eye be closed, the other fixed on a near object, and at the same time a distant object observed, the distant object will appear to decrease in size if the fixed object be brought nearer to the eye; when the fixed object is moved away from the eye, the distant object will appear to increase in size. Similarly an object nearer than the fixed object will appear to increase in size when the fixed object recedes from the eye, and to decrease in size when the object approaches the eye. The appearance may be well observed with Jaeger’s type. If this be held at ordinary reading distance and a nearer point be fixed the type will appear smaller; on bringing the fixed point nearer, further diminution will take place and the micropsia may be so marked that No. 10 may look as small as No. 4 or even No. 2. At the same time the type becomes blurred, which interferes to a certain extent with the illusion. Enlargement of the type nearer than the fixation point is less easy to observe but does occur. These appearances may be summed up by saying that objects beyond the fixation point appear smaller and objects nearer than the fixation point larger than they would do if fixed directly. One apparent exception occurs to this; if type is brought quite close to the eyes within the near point, it appears slightly diminished in size. The diminution however entirely disappears with a small artificial pupil, which the micropsia beyond the fixation point is not affected by this means. These appearances have been previously described by Ludwig^[7], Panum^[8], Hering^[9], Stumpf^[10] and Martius^[11]. I will reserve their explanations till after I have described some further observations.

The apparent diminution in size is in the case of most observers, and among them myself, accompanied by an appearance of greater distance; a few on the other hand have had indefinite ideas of distance and have seen the object sometimes nearer, sometimes farther. I need hardly say that in all cases where I have asked for observations I have avoided leading questions. To myself change of distance is occasionally more obvious than change of size; after fixing a near object and then suddenly releasing accommodation I have seen an apparent approach of the distant object, and this has been especially well marked in cases where I have been attending to the question of size and have not been thinking of change of distance. The question arose whether the apparent change of distance was secondary to change of size as supposed by Förster and Aubert in their explanation of the micropsia of atropin. To determine this point I tried some experiments in which I was unaware of the size and distance of the object. I looked through an eye-piece at one end of a cylindrical box at the uniform grey wall; a point to be fixed was placed within the box: the point being fixed, squares of paper of various distances between the box and the wall by an assistant. It soon became obvious that knowledge of the size was a very important factor in the case; in nearly all cases however the square appeared either smaller or more distant or both smaller and more distant than when fixed directly and Mr. E.T. Dixon also tried this experiment with similar results.

I will now describe the experiments with atropin. I applied a solution of atropin sulphate (2 gr. to the ounce) three times a day for four days. The appearances to be described were present during the whole time. Owing to my myopia I could see type distinctly without glasses at about 25cm. Holding the type at this distance, I fixed the point of a pencil in front of the type and brought it nearer to the eye, making an effort to accommodate for the point. The effort was of course unsuccessful and the point of the pencil became more and more blurred as it approached the eye. At the same time the type diminished in size just as in normal vision, but owing to the absence of blurring the diminution in size was more obvious than with the normal eye till with near approach of the pencil No. 10 appeared quite as small as No. 2. With the diminution in size there was an appearance of greater distance as in the normal experiment, and the phenomenon appeared to be identical in nature with the normal micropsia beyond the fixation point but more easily observed owing to the absence of blurring. In an emmetropic individual it is to be expected that the experiment would succeed only with distant objects, and it seems possible that one cause of the micropsia which has been observed clinically by ophthalmologists may have been a want of correspondence between a seen object and the point of fixation. Under ordinary circumstances it is a phenomenon which will only be observed if it is looked for.

Another drug with which I have experimented is eserin. This causes spasm of the ciliary muscle and with this condition objects appear increased in size. I used a solution of eserin (1 in 320) to the left eye. At the end of ten minutes, my far point was brought down to 15cm. Type was distinctly larger to the left eye at 15 cm and increased further in size on bringing nearer to the eye, so that No. 10 became larger than No. 12 to the right eye. Five minutes later the far point was at 10 cm, and the macropsia was more marked, No. 10 to the left eye being almost as large as No. 14 to the right eye at the nearest point where it could be seen distinctly. The macropsia began to pass off before the end of an hour and had disappeared three hours after instillation. Apparently the macropsia occurred both at the fixation point and nearer than the fixation point, but much more marked when nearer. During the first hour, however, any effort to accommodate was decidedly painful. The ordinary explanation given of this condition is on the same lines as that of micropsia; that owing to the spasm of accommodation, no effort or less effort than normal is necessary to see an object distinctly. This gives rise to an idea of greater distance and consequent appearance of greater size. I may mention here that the increase in size was very much greater than would have been die to the contraction of the pupil due to the eserin.

The explanation of micropsia beyond the fixation point is a much more difficult matter than that at the fixation point. I have satisfied myself that it is not due to irradiation. The experiments under atropin would be sufficient to disprove this, marked micropsia occurring with effort of accommodation, no effort or less effort than normal is necessary to see an object distinctly. This gives rise to an idea of greater distance and consequent appearance of greater size. I may mention here that the increase in size was very much greater than would have been due to the contraction of the pupil due to the eserin.

The explanation of micropsia beyond the fixation point is a much more difficult matter than of that at the fixation point. I have satisfied myself that it is not due to irradiation. The experiments under atropin would be sufficient to disprove this, marked micropsia occurring with effort of accommodation unaccompanied by alteration in the pupil or dioptric apparatus. This form of micropsia also occurs with a small artificial pupil and is present for a white object on a black ground as well as for black on white. The first to observe the phenomenon, Ludwig, was unable to suggest an explanation. Panum’s explanation was similar to the ordinary explanation of the micropsia of atropin. He supposed that there is an illusion of judgement having as its sensory basis the peculiar feeling of the sensation of accommodation and that the idea of nearness or fairness so arising is translated by an instinctive process into a judgement of size. He suggests however the possibility ‘that the mode of sensation of the visual organ as regards distance is changed in an unknown and incomprehensible manner by the nerve excitation which accompanies accommodation.’ Stumpf’s view resembles very closely that of Panum. The phenomenon is also mentioned by Martius. He describes an object beyond the point of fixation as shortened by perspective and he refers the phenomenon to apparent localisation at the fixation point.

More satisfactory is the explanation given by Hering. He supposes that the appearance is due to a change in the mutual relations of the near and far objects. If the hand as the near object is brought nearer to the eye, the change may be perceived as an enlargement of the hand or as a diminution in size of the distant object, according to the direction of the of the attention to the distant or near object respectively; that when the hand is near the eye and is yet perceived as of the same size as previously at a greater distance, the distant object will be measured by different standard; that the retinal image will be multiplied by a smaller factor. This explanation however does not wholly meet the case. Objects beyond the fixation point may appear smaller when there is no measureable near object for comparison. Then if a sheet of paper be held before the eye and its edge fixed, a distant object will appear to diminish in size when the paper is brought nearer, although the near object has been a separating line which has not altered in size. Still more convincing is the objection that the micropsia occurs when an imaginary near point is fixed and then an effort of accommodation made for a nearer point in space.

Hering’s explanation needs some modification and then seems to me to meet the case. In his theory of binocular vision Hering distinguishes between localisation relative to the fixation point and localisation of the fixation point itself, and the same distinction may be applied to monocular vision. He regards the fixation point at any moment as the centre of the visual space (‘‘Kernpunkt des Sehraums’’) at that moment. With alteration of the fixation point, the relation of a stationary object to the visual space as a whole will be altered. If a point be fixed and an object beyond be moved farther away from the eye, the object will appear more distant and smaller. If the fixed point be moved instead of the object, the object appears more distant and smaller. It is the relation of the object to the fixation point and not to the eye which determines the apparent size and distance. The retinal image has remained constant, but, as Hering says, it is multiplied by a larger factor with decreased distance from the fixation point; it is the relation of the object to the fixation point and not to the eye which determines its apparent size and distance. It may be objected that this explanation is little more than a restatement which emphasises the importance of the fixation point as the centre of the visual space and as the determining factor of the apparent relations within that space.

Further, this explanation is of interest in relation to the problem mentioned at the beginning of this paper. So far as localisation relation to the fixation point goes, there is no evidence that the alteration of spatial relations is in any way dependent on accommodation. It is in the localisation of the fixation point itself that this may play a part, and in this connection the atropin experiments present several points of interest. In the normal experiment, the localisation might have as its basis the sensations arising from the peripheral accommodation, and this seems to point to the fact that the localisation of the fixation point depends altogether on central factors. Several objections may be brought forward; first, that the ciliary muscle was not completely paralysed. It is not easy to say that the power of accommodation is completely abolished, but the appearance occurred after the application of atropin for four days, and I was unable to detect the existence of any accommodation. I used fine hairs stretched across a hole in a card. I could only see the hairs clearly at a distance; vertical hairs at 25 cm, horizontal at 23 cm, and when the hairs were slightly blurred I was unable to make them distinct by any effort of accommodation. A second possible objection would be that the localisation depended on associated movements. If I had only paralysed one eye, the localisation might have been explained by contraction of the ciliary muscle of the opposite eye in the same way that G.E Müller^[12] and James^[13] explain erroneous projection with paralysis of an ocular muscle. I excluded this by using atropin to both eyes. A further possibility however is that the localisation depended on associated movements of convergence, of eyelids, etc. on making the efforts to accommodate, I experienced distinct sensations of tension referable to the eyeball and parts around as generally occur with strong accommodation effort, and it might be urged that localisation depended on sensations arising from these peripheral conditions. If this were the case, it seems unlikely that the changes of apparent size and distance associated with the effort should have been in no way lessened, and in fact even increased by removal of the share taken by the ciliary muscle. I regard these experiments as going far towards proving that the localisation of the fixation point depends on central factors, and I may record an observation which bears out this view. In trying the experiment with the normal eye, I have seen type beyond the fixation point much diminished in size but yet distinct and well defined; the accommodation apparatus must have been adapted for the type, and the micropsia due to central conditions.

The problem is from one point of view a special case of the sense of effort. Those who advocate its central origin usually speak of sensations of innervations or of consciousness of the outgoing impulse. The atropin experiment seems to show that the effort alone to carry out a movement may produce a sensory change of the same degree of vividness as occurs when the effort is followed by the movement.

I have throughout described micropsia beyond the fixation point as a monocular phenomenon. According to Martius it may be observed with both eyes. I think that this is the case but the observation does not satisfy owing to the double images. With distinct double images beyond the fixation point I have not been able to satisfy myself that micropsia occurs certainly it does not occur to the same extent as with one eye. There is, however, a binocular phenomenon which is possibly of the same nature, viz. the apparent small size of the binocular image of two objects combined by the converging the eyes for a point nearer than the objects. The smaller size of the combined image is in my case associated with an appearance of greater distance and the phenomenon may be regarded as an instance of micropsia beyond the fixation point. One appearance, however, which does not fit in with this view is that the lateral monocular images are not appreciably diminished in size. The apparently large size of the binocular image of two objects combined by diverging beyond the objects may also be of the same nature as the monocular phenomenon.

As regards the eserin experiments, I am inclined to regard the increase in apparent size as an example of the normal macropsia nearer than the fixation point. The whole region in which the type appeared large was well within the ordinary reading distance. It is possible that the enlargement at 15 cm, the far limit of distinct vision may have been due to the diminished size of the pupil and diminished irradiation compared with the sound eye, and it is possible that the increase in size on bringing the type nearer was directly due to the increase in the size of the retinal image, the accommodation apparatus and fixation point remaining stationary. The pain produced by any effort to accommodate rendered the observation unsatisfactory, and may also have tended to keep the fixation point beyond the object.

I have endeavoured in this paper to show that at least two kinds of micropsia may be observed as the result of the action of atropin on the eye; that one, probably that most commonly observed, is due solely to irradiation and depends on dilation of the pupil and not on paralysis of accommodation; that the other is a phenomenon of normal vision which may be observed more easily under atropin, and that this second form lends no support to the view that peripheral accommodation changes are factors in spatial perception.

It must be a matter for future investigation to determine which kind is present in the cases which have been reported clinically, and the possibility must not be neglected that micropsia may occur under atropin from causes other than those I have described.

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