Kijiematics of the Eye. 



C05 



We must first integrate with respect to between the 



limits J7r + ^, where 



COS a . . 



cosv= , (21) 



A COS^' V J 



if we suppose i^ = in the primary position. The result is 

 1 



1 = 



27rsm 2 ^a , 



{ log tan (\it + \x) ~ sm X} ( fy' (--) 



Patting a = 40°, I find by a quadrature I = '0692, and the 

 •error of mean square is accordingly '26'3ds, as against 

 'HSds in the former case. The errors near the centre of 

 the field are about twice as great as on Listing's law (but 

 •differently distributed), and the maximum error is tan ads, 

 or -839 ds if* = 40°. 



The preceding argument of Helmholtz has been repro- 

 duced (in a simplified form) on account of its mathematical 

 interest. The question presents itself, however, whether the 

 cardinal advantage of the fact that the eye conforms to 

 Listing's law does not consist simply in this, that the test 

 of superposition is fulfilled for straight lines which pass 

 through the centre of the field of view, in the primary 

 position. If this view be adopted the above investiga- 

 tion still retains its value as showing a further consequent 

 advantage. 



