310 Hastings — Error of Collimation in the Human Eye. 



Art. XXIX. — The Error of Collimation in the Human Eye ; 

 by C. S. Hastings. 



[The references H in the following pages are to the HandbTich der Physi- 

 ologischen Optik von H. von Helmholtz. Zweite Auflage, 1896.] 



One of the most curious imperfections of the human eye, 

 of the many discovered or investigated by Helmholtz, is that of 

 an'unf ailing inclination of the line of sight to the axis of sym- 

 metry of the cornea (H. p. IT), or, what appears to be essen- 

 tially the same thing, to the geometrical axis of symmetry of 

 the whole eye (H. pp. 108, 109). There is, it is true, no reason 

 for surprise that such an error should exist, since, if we sup- 

 pose, as we are obliged to do, that the present structure of the 

 eye is the result of a long process of evolution, we ought to 

 expect the survival of imperfections which, too minute to 

 impair the effectiveness of the eye as a sense organ, would 

 therefore be too minute to serve as incentives to farther 

 development. Such surviving imperfections would be called 

 errors when we regard the eye as an optical instrument; and 

 Helmholtz has shown that no error which can be named by 

 the optician is absent from the eye. On the other hand, this 

 eminent investigator has shown that these errors are always 

 so small, in a normally formed eye, as not to impair the pre- 

 cision or visual perceptions with the eye of its present size. 

 This point may be emphasized by the following consideration. 

 If it were required to remodel the eye so as to double its pres- 

 ent power, it can easily be shown that this would necessitate an 

 increase of volume to fifteen or twenty times its present value. 

 In view of the enormous difficulties to be met in nourishing 

 and protecting such an organ with a retention of its transpar- 

 ency, we may well conclude that the balance between physio- 

 logical cost and utility has already been attained, in short, that 

 the closest approach to practical perfection has been reached 

 long ago, even in the protracted history of evolution. 



The particular error, however, which is the subject of our 

 consideration and which would be known to opticians as an 

 error of collimation, is distinguished from nearly all others in 

 two peculiarities ; first, it is the easiest of all errors in an ordi- 

 nary optical instrument to eliminate, and second, it is systematic, 

 i. e. it is of such a character that the axis of vision always lies 

 on the nasal side of the geometrical axis outside of the eye. 

 It is this systematic character of the error which gives it its 

 particular interest and for which we feel ourselves prompted 

 to seek a reason. 



The first step in an investigation with this end in view is to 

 find the average value of the error. Helmholtz himself (H. p. 



