518 VISION 



into the vitreous body. The actual size of the pupil therefore is, other things 

 being equal, the factor determining the size of the dispersion circle. 



We have already seen (page 511) that the position of the retinal picture 

 of a luminous point can be determined in the schematic eye by drawing a 

 straight line from the objective point to the first nodal point and another 

 parallel to this from the second nodal point to the retina. In the reduced 

 eye the two nodal points coincide and the retinal image falls where a line 

 from the object through the nodal point meets the retina. Lines of this kind 

 by which the location of the image on the retina can be determined are called 

 lines of direction. 



That particular line of direction which connects the middle point of an 

 outer object with the center of the fovea in the retina is called the line of 

 vision. 



The lines of direction enable us to determine the size of the image of an 

 object formed on the retina. We have only to draw lines of direction from 

 the extreme ends of the object and solve the similar triangles thus formed 

 (see page 511). By such a construction also we can calculate approximately 

 the distance from each other of the images of two luminous points which are 



b 



FIG. 214. Diagram showing the visual angle, i. e., the angle subtended by two lines of direction 

 a" a' and 6" b' through the first nodal point. 



just distinguishable, and can thus obtain a measure of the acuteness of vision. 

 For several reasons, however, this linear measure is not used, but instead the 

 angle which the two lines of direction subtend (Fig. 214) at the first or 

 second nodal point. This angle is called the visual angle. 



According to an old statement by Hooke, two stars whose apparent dis- 

 tance from one another is less than thirty celestial seconds always appear as 

 one star, and scarcely one person out of a hundred can distinguish the two 

 if their apparent distance is less than sixty seconds. Later observers have 

 obtained values varying all the way from fifty to ninety seconds. 



In Listing's schematic eye a visual angle of sixty seconds corresponds to a 

 distance on the retina of 0.00438 mm. Microscopical measurements find the 

 thickness of the cones in the yellow spot to be from 0.0054-0.0045 mm. (Kol- 

 liker) to 0.0036-0.002-0.0015 mm. Counts of the number of cones in the fovea 

 made by Salzer gave for the eyes of stillborn children 13,200-13,800 per square 

 millimeter. 



The limits of vision i. e., the ability to distinguish two points therefore 

 depend upon the diameter of the cones in the center of exact vision. To be 

 able to perceive points as distinct and separate, they must fall upon cones 

 which are separated by at least one resting cone. 



