THE PERCEPTION OF 8PACE. 267 



Measurement implies a stuff to measure. Retinal sensa- 

 tions give the stiff; objective things form the yard-stick ; mo- 

 tion does the measuring operation; wliich can, of course, be 

 well performed only Avhere it is jDossible to make the same 

 object fall on many retinal tracts. This is practically im- 

 possible where the tracts make a wide angle with each 

 other. But there are certain directions in the field of view, 

 certain retinal lines, along which it is particularly easy to 

 make the image of an object slide. The object then be- 

 comes a 'ruler' for these lines, as Helmholtz puts it,* 

 making them seem straight throughout if the object looked 

 straight to us in that part of them at which it was most 

 distinctly seen. 



But all this need of siiperposition shows how devoid of 

 exact space-import the feelings of movement are per se. As 

 we compare the space- value of two retinal tracts by super- 

 posing them successively' upon the same objective line, so 

 we also have to compare the space-value of objective angles 

 and lines by superposing them on the same retinal tract. 

 Neither procedure would be required if our eye-movements 

 were apprehended immediately, by pure muscular feeling 

 or innervation, for example, gls distinct lengths and direc- 

 tions in space. To compare retinal tracts, it would then 

 suffice simply to notice how it feels to move any image over 

 them. And two objective lines could be compared as 

 well by moving different retinal tracts along them as by 

 laying them along the same. It would be as easy to com- 



* "We can witb a short ruler draw a line as long as we please on a 

 plane surface by first drawing one as long as tlie ruler permits, and then 

 sliding the ruler somewhat along the drawn line and drawing again, etc. 

 If the ruler is exactly straight, we get in this way a straight line. If it is 

 somewhat curved we get a circle. Now, instead of the sliding ruler we 

 use in the field of sight the central spot of distinctest vision impressed with 

 a linear sensation of sight, which at times may be intensified till it becomes 

 an after-image. We follow, in looking, the direction of this line, and in 

 so doing we slide the line along ilself and get a prolongation of its length. 

 On a plane surface we can carry on this procedure on any sort of a straight 

 or curved ruler, but in the field of vision there is for each direction and 

 movement of the eye only one sort of line which it is possible for us to 

 slide along in its own direction continually." These are what Helmholtz 

 calls the ' circles of direction ' of the visual field — lines which he has 

 studied with his usual care. Cf. Physiol. Optll:, p. 548 ff. 



