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that in the letter S the upper curve has a definitely smaller radius than the lower one； but the inverted S shows this at once。 To such types other false estimations belong： inclinations； roofs； etc。； appear so steep in the distance that it is said to be impossible to move on them without especial help。 But whoever does move on them finds the inclination not at all so great。 Hence； it is necessary； whenever the ascension of some inclined plane is declared impossible； to inquire whether the author of the declaration was himself there； or whether he had judged the thing at a distance。
＇2＇ Cf。 Lotze： Medizinische Psychologie。 Leipzig 1852。
Slight crooks are underestimated。 Exner＇1＇ rightly calls attention to the fact that in going round the rotunda of the Viennese Prater； he always reached the exit much sooner than he expected。 This is due to the presence of slight deviations and on them are based the numerous false estimates of distance and the curious fact that people； on being lost at night in the woods； go round in a significantly small circle。 It is frequently observed that persons； who for one reason or another； i。 e。； robbery； maltreatment； a burglarious assault； etc。； had fled into the woods to escape； found themselves at daybreak； in spite of their flight； very near the place of the crime； so that their honesty in fleeing seems hardly believable。 Nevertheless it may be perfectly trustworthy； even though in the daytime the fugitive might be altogether at home in the woods。 He has simply underestimated the deviations he has made； and hence believes that he has moved at most in a very flat arc。 Supposing himself to be going forward and leaving the wood； he has really been making a sharp arc； and always in the same direction； so that his path has really been circular。
＇1＇ Cf。 Entwurf； etc。
Some corroboration for this illusion is supplied by the fact that the left eye sees objects on the left too small； while the right eye underestimates the right side of objects。 This underestimation varies from 0。3 to 0。7％。 These are magnitudes which may naturally be of importance； and which in the dark most affect deviations that are closely regarded on the inner side of the eyei。 e。； deviations to the left of the left eye or the right of the right eye。
Such confusions become most troublesome when other estimations are added to them。 So long as the informant knows that he has only been estimating； the danger is not too great。 But as a rule the informant does not regard his conception as an estimate； but as certain knowledge。 He does not say； ‘‘I estimate；'' he says； ‘‘It is so。'' Aubert tells how the astronomer Frster had a number of educated men； physicians； etc。； estimate the diameter of the moon。 The estimation varied from 1'' to 8'' and more。 The proper diameter is 1。5'' at a distance of 12''。
It is well known that an unfurnished room seems much smaller than a furnished one； and a lawn covered with snow； smaller than a thickly…grown one。 We are regularly surprised when we find an enormous new structure on an apparently small lot； or when a lot is parcelled out into smaller building lots。 When they are planked off we marvel at the number of planks which can be laid on the sur… face。 The illusions are still greater when we look upward。 We are less accustomed to estimation of verticals than of horizontals。 An object on the gutter of a roof seems much smaller than at a similar distance on the ground。 This can be easily observed if any figure which has been on the roof of a house for years is once brought down。 Even if it is horizontally twice as far as the height of the house； the figure still seems larger than before。 That this illusion is due to defective practice is shown by the fact that children make mistakes which adults find inconceivable。 Helmholtz tells how； as child； he asked his mother to get him the little dolls from the gallery of a very high tower。 I remember myself that at five years I proposed to my comrades to hold my ankles so that I could reach for a ball from the second story of a house down to the court…yard。 I had estimated the height as one…twelfth of its actual magnitude。 Certain standards of under and overestimations are given us when there is near the object to be judged an object the size of which we know。 The reason for the fact that trees and buildings get such ideal sizes on so…called heroic landscape is the artistically reduced scale。 I know that few pictures have made such a devilish impression on me as an enormous landscape； something in the style of Claude Lorraine； covering half a wall。 In its foreground there is to be seen a clerk riding a horse in a glen。 Rider and horse are a few inches high； and because of this the already enormous landscape becomes frightfully big。 I saw the picture as a student； and even now I can describe all its details。 Without the diminutive clerk it would have had no particular effect。
In this connection we must not forget that the relations of magnitude of things about us are； because of perspective； so uncertain that we no longer pay any attention to them。 ‘‘I find it difficult；'' says Lipps；＇1＇ ‘‘to believe that the oven which stands in the corner of the room does not look larger than my hand when I hold it a foot away from my eyes； or that the moon is not larger than the head of a pin； which I look at a little more closely。。。。 We must not forget how we are in the custom of comparing。 I compare hand and oven； and I think of the hand in terms of the oven。'' That is because we know how large the hand and the oven are； but very often we compare things the sizes of which we do not know； or which we can not so easily get at； and then there are many extraordinary illusions。
＇1＇ Die Grundtatsachen des Seelenlebens。 Bonn 1883。
In connection with the cited incident of the estimation of the moon's diameter； there is the illusion of Thomas Reid who saw that the moon seemed as large as a plate when looked at with the unhampered eye； but as large as a dollar when looked at through a tube。 This mistake establishes the important fact that the size of the orifice influences considerably the estimation of the size of objects seen through it。 Observations through key…holes are not rarely of importance in criminal cases。 The underestimations of sizes are astonishing。
｛illust。 caption = FIG。 1。｝
｛illust。 caption = FIG。 2。｝
Arial perspective has a great influence on the determination of these phenomena； particularly such as occur in the open and at great distances。 The influence is to be recognized through the various appearances of distant objects； the various colors of distant mountains； the size of the moon on the horizon； and the difficulties which arial perspective offers painters。 Many a picture owes its success or failure to the use of arial perspective。 If its influence is significant in the small space of a painting； the illusions in nature can easily become of enormous significance； particularly when extremes are brought together in the observations of objects in unknown regions。 The condition of the air； sometimes foggy and not pellucid； at another time particularly clear； makes an enormo