Mr. B. S. Proctor on the Focal Adjustment of the Eye. 295 



" Following/' it is said, t( an analogous method to that pursued 

 by Mr. Jerrard, we might dispute the validity of any mathema- 

 tical proposition whatever on such grounds as these : 

 &'=%, .'. %—cc=(l—l)x = 0, 







—> 



1-1 



and all formulae into which x enters are illusory/' The alleged 

 analogy, however, does not exist. Instead of a similitude, I 

 discern a contrast. The presumed objection (which, if applicable, 

 would be instantly fatal to my researches) is unsupported by any 

 proof. It seems to have sprung up in the mind of the writer 

 from the delusive idea that Lagrange's theory is capable of fur- 

 nishing us with some equation or other which, unlike (e x ) *, shall 

 not conduct us to an illusory result when v = u b . But whatever 

 doubt there may be respecting the grounds on which he pro- 

 ceeds, one thing is certain — that his objection is nugatory f. 

 What difficulty can there be, I would ask, in accepting the 

 conclusion that when v = u b we cannot by Lagrange's method, 

 or indeed by any conceivable method, superadd a second rational 

 relation between v and u which shall be independent of the one 

 with which we set out ? I leave the reader to reflect on this. 

 September 1863. 



XLII. On the Focal Adjustment of the Eye. 



By Barnard S. Proctor, Esq.% 



[With a Plate]. 



TflERE is considerable difficulty in accumulating statistical 

 evidence regarding the powers of the eye ; and, as far as I 

 am aware, there has not been anything published upon precisely 

 the same subject as that which forms the material of this com- 

 munication. These considerations, I hope, will justify me in 

 bringing forward the subject in its present crude condition. 



In March 1860 Mr. Wharton Jones read a paper before the 

 Royal Society § giving an analysis of his own sight ; the present 

 paper was designed to show how far his observations coincide 

 with general experience, and to afford answers to the following 

 questions : — 



Is it occasionally, generally, or universally that the human 

 eye has distinct foci for vertical and horizontal lines ? 



* For an explanation of the symbols (e{), v, u see my paper in the Phil. 

 Mag. for December 1862. 



f See art. 4 (note) of the paper just referred to. 



>% Communicated by the Author, having been read before the British 

 Association at Newcastle-upon-Tyne, August 1863. 



§ See Phil. Mag. S. 4. vol. xx. p. 480. 



