Hastings — Error 1 of Collimation in the Human Eye. 311 



19) measured this angle for three eyes only, but Dr. Uhthoff 

 (H. p. 22) adds four, and H. Knapp (H. p. 109) gives data from 

 which we may deduce, with considerable confidence, four more. 

 We thus have eleven cases of which the average value of the 

 angle (a) is 5°*36. This is an insufficient number to serve as 

 the basis of any important conclusions, especially in view of 

 their great irregularity of values ; it seemed desirable, there- 

 fore, to collect a larger number of instances. In this work 

 Professor F. E. Beach kindly aided me with great skill, and to 

 him is due more than half of all the measurements of which 

 the results follow. 



The method employed was quite like that devised by Helm- 

 holtz (H. pp. 15-19), except that we used a filar micrometer 

 instead of an ophthalmometer. Both methods were tried, but, 

 notwithstanding the obvious advantages of the double image 

 instrument, the former was found quite as accurate and mate- 

 rially more rapid. With this arrangement we found for 52 

 eyes the following results : 



I. There was no case of reversal in sign of a, that is, the 

 axis of vision, extended outwards, always lies on the nasal side 

 of the axis of symmetry of the cornea. 



II. The value of a varies greatly. The smallest value 

 which we found was 1°'25 and the largest Y 0, 76. There was 

 no evidence of a systematic difference in the numerical values 

 of the angle for the right and the left eye. 



III. The mean value for the 52 eyes examined was 3°'98. 

 The mean value is much less than that of the German 



measures ; this may be owing to racial differences — it is well 

 known that the average separation of the eyes is less for 

 Americans than for Germans — or it may be owing simply to 

 the small number of cases in the earlier group. However 

 this may be, it seems that the best attainable value at present 

 is the weighted mean of these two averages, namely : 



a = 4°-2 



We shall assume in our further studies, therefore, that a line 

 drawn from the second nodal point in the normal eye to the 

 center of that small region of the retina to which the sharpest 

 visual perceptions are confined — the fovea centralis — lies 

 wholly on the temporal side of the geometrical axis of the eye 

 and inclined to it at an angle of 4°*2 ; moreover, as neces- 

 sarily involved with this assumption, that a line drawn outwards 

 from the first nodal point to the point of fixation lies wholly 

 on the nasal side of the axis at the same angle of inclination. 

 This angle we may call, for convenience, the constant of col- 

 limation for the normal or schematic eye (H. p. 140). 



Closely connected with the constant of collimation in the 

 discussion of a variety of optical phenomena which I shall con- 



