106 TITCHENER AND PVLE— JUDGMENT OF DISTANCE. [April 18, 



ment at all, must affect it by more than the 0.5 mm. in 25 cm. which 

 is the average of Dunlap's observations. 



It remains, now, to seek an explanation of Dunlap's positive 

 results. We said above that the method pursued in these experi- 

 ments is not the method best suited to the problem. Similar excep- 

 tion may be taken to the apparatus. For while the setting of the 

 distances is sufficiently accurate, the illumination is not under 

 measurable control. We have spoken of " barely perceptible " 

 shadows, but w^e have not been able to specify the amount of light 

 thrown upon the back of the apparatus in any given series. We 

 do not think that this lack of quantitative control at all invalidates 

 our results ; but we confess that, from the physical point of view, 

 the experiment would have been prettier had such control been 

 exercised. 



Dunlap's work, after his preliminary experiments, was done 

 with an apparatus in which the shadows were thrown upon the 

 white screen from in front, and the amount of light employed to 

 produce them was measured by means of an episcotister.^ We 

 did not reproduce this apparatus, partly because our results seemed 

 conclusive, partly also because the apparatus is cumbrous, and 

 appears likely to introduce new sources of error. We have still, 

 however, to account for the positive outcome of Dunlap's investi- 

 gation. 



We grant, at once, that we can give no single or convincing 

 explanation of these figures. All that we can do is to suggest the 

 various possibilities of explanation that have occurred to us. Thus, 

 (i) the average illusion-effect is, as we have pointed out, 0.5 mm. 

 upon a standard line of 25 cm. Dunlap nowhere gives his MV ', 

 but there are indications in the paper that it must have been, at 

 the least, as large as our own.^ An illusion-effect of such incon- 

 siderable amount, absolute and relative, might very well be ascribed 

 to chance. (2) It is conceivable that the figures rest upon a mis- 

 calculation ; experimental psychologists, from Fechner down, have 

 been liable to slips in addition and subtraction. Nor is this sug- 

 gestion as gratuitous as it may at first sight appear; for the paper 



^ Op. cit., p. 440. 



2 Op. cit., 445 U AA7 f. 



