792 



ESTIMATION OF SIZE AND DISTANCE. 



distant landscape, a fly should suddenly pass across our field of vision, near to our 

 eye, then the image of the fly, owing to the relatively great size of the retinal 

 image, may give one the impression of an object as large as a bird. If, owing to 

 defective accommodation, the image gives rise to diffusion circles, the size may 

 appear to be even greater. But objects of very unequal size give equally large 

 retinal images, especially if they are placed at such a distance that they form the 

 same visual angle (fig. 531) ; so that in estimating the actual size of an object, 

 as opposed to the apparent size determined by the visual angle, the estimate of 

 distance is of the greatest importance. 



As to the distance of an object, we obtain some information from the feeling of 

 accommodation, as a greater effort of the muscle of accommodation is required for 

 exact vision of a near object than for seeing a distant one. But, as with two 

 objects at unequal distances giving retinal images of the same size, we know from 

 experience that that object is smaller which is near, then that object is estimated 

 to be the smaller for which, during vision, we must accommodate more strongly. 



In this way we explain the following : A person beginning to use a microscope always ob- 

 serves with his eyes accommodated for a near object, while one used to the microscope looks 

 through it without accommodating. Hence beginners always estimate microscopic objects as 

 too small, and on making a drawing of them it is too small. If we produce an after-image in 

 one eye, it at once appears smaller on accommodating for a near object, and again becomes 

 larger during negative accommodation. If we look with one eye at a small body placed as near 

 as possible to the eye, then a body lying behind it, but seen only indirectly, appears smaller. 



Angle of Convergence of Visual Axes. In estimating the size of an object, 

 and taking into account our estimate of its distance, we also obtain much more 

 important information from the degree of convergence of the visual axes. We refer 

 the position of an object, viewed with both eyes, to the point where both visual axes 

 intersect. The angle formed by the two visual axes at this point is called the 

 "angle of convergence of the visual axes" (" Gesiclitswinkel"). The larger, there- 

 fore, the visual angle, the size of the retinal image remaining the same we judge 

 the object to be nearer. The nearer the object is, it may be the smaller, in order 



to form a " visual angle " of the same size, 

 such as a distant large object would give. 

 Hence, we conclude, that with the same appa- 

 rent size (equally large visual angle, or retinal 

 images of the same size) we judge that object 

 to be smallest which gives the greatest con- 

 vergence of the visual axes during binocular 

 vision. As to the muscular exertion necessary 

 for this purpose, we obtain information from 

 the muscular sense of the ocular muscles. 



Experiments and Proofs The chess-board pheno- 

 menon of H. Meyer. 1. If wc look at a uniform 

 chess-board-like pattern (tapestry or carpet), then, 

 when the visual axes are directed directly forwards, 

 the spaces on the pattern appear of a certain size. If, 

 now, we look at a nearer object, we may cause the 

 visual axes to cross, when the pattern apparently moves 

 towards the plane of the fixed point, so that the crossed 

 double images are superposed, and the pattern at once 

 appears smaller. 



2. Rollett looks at an object through two thick 

 prisms of glass placed at an angle. The plates are at 

 one time so placed that the apex of the angle is 

 directed towards the observer (fig. 574, II), at another in the reverse position (I). If both eyes, 

 /and t, are to see the object , in I, then as the glass plates so displace the rays, a, c, and a, g, 

 as to make them parallel with the direction of these rays, viz., c,/, and h, i, then the eyes 

 must converge more than when they are turned directly towards a. Hence the object appears 

 nearer and smaller, as at a. In II, the rays, b x k, and b x o, from the nearer object b x , fall upon 



Fig. 674. 

 Rollett's glass plate apparatus. 





