SPACE 41 



the three planes of direction. Around the point of intei- 

 section of the three planes place a number of increasingly 

 larger and larger hollow spheres. The small spheres nearest 

 to the centre are very close to one another. With the size of 

 the spheres, the distance between them increases, until the 

 last and largest stand quite by themselves. The distance 

 from one sphere to the next represents in each case a " step- 

 into-distance." Near the eye this is short, while direction- 

 signs got by convergent movement of the eyes permit us to 

 estimate the distance exactly. The step-into-distance be- 

 comes longer in the region which is sensed only by the aid of 

 the direction-signs of the muscles of accommodation : it 

 becomes very long as soon as criteria of distance alone can 

 be made use of in forming the estimate. Since the step- 

 into-distance stands for the interval recognisable at a given 

 moment between two points in the dimension of depth, 

 it does not matter by what means the measurement is 

 carried out. 



Each sphere has just as many places on it as there are 

 local signs available. Hence there are much fewer to the 

 same surface of the larger and more distant spheres than 

 there are on the smaller ones close at hand. The number 

 of the angles at the centre is fixed by the local signs, and 

 the angle determines the size of surface on the various sphere- 

 planes. 



While the same " place " in space means a series of tiny 

 surfaces lying one behind the other on all the spheres (and 

 present in equal number on all of them), the " position " 

 determines where the " place " lies on any one sphere. The 

 point in space which has both place and position is fixed with 

 certainty, (i) by the number of spheres (or steps-into-distance) 

 that lie between it and the centre, and (2) by the number of 

 places (or smallest surfaces) that separate it from the nearest 

 planes of direction : this number gives at the same time the 



