THE 



AMERICAN JOURNAL OF SCIENCE 



[FOURTH SERIES.] 



Art. XLII. — On a Group of Visual Phenomena depending 

 upon Optical Errors of the Human Eye • by Charles S. 

 Hastings. 



In two preceding articles* the writer has contributed meas- 

 urements which serve to define the average human eye, both 

 with respect to its color error and its error of collimation, to a 

 closer degree of approximation than that of Helmholtz and his 

 successors as embodied in the well known schematic eye. The 

 aim of this paper is to discuss certain consequences which may 

 be based upon these more exactly determined data and to 

 describe, and explain as far as practicable, a number of visual 

 phenomena not thoroughly studied heretofore, or, perhaps, 

 wholly known. For this purpose we require, in addition to 

 the elements established in the papers cited, a knowledge of 

 the positions of the external and internal pupils of the model 

 eye. By the former term is meant the virtual image of the 

 real pupil as formed by refraction at the cornea ; and by the 

 latter, the virtual image of the real pupil as formed by succes- 

 sive refractions at the anterior and posterior surfaces of the 

 lens. These are evidently so related to each other that a ray 

 from an object outside to a point in the exterior pupil will 

 correspond to a ray from the corresponding point in the inte- 

 rior pupil to the image of the object. If we take, as in the 

 preceding articles, the vertex of the cornea as the origin of 

 coordinates, together with the place of the center of the real 

 pupil as established in the second paper, a simple calculation 

 shows that the centers of the pupils are at 0*304:6 cm and 

 0*3705 cm , respectively, both lying on the nasal side of the axis 



* This Journal, vol. xix, p. 205 and p. 310. 



Am. Jour. Sci.— Fourth Series, Vol. XIX, No. 114.— June, 1905. 

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