Limit to Defining-poivcr. By J. J. Lister. 41 



This limitation, although the pencil admitted ])y the pu])il may 

 average in moderate light 0'15in., and in some eyes extend to 

 • 3 in., gives us abundant defining-power for the usual purposes of 

 life, and appears wisely ordered to provide against the i)erplexity 

 that must otherwise have attended the dilatation and contraction 

 of tlie pupil — an action so necessary and not subject to our 

 control. 



The curves in the accompanying diagram are an attempt to 

 show the progressive approach to the above limit with different 

 eyes, the middle curve representing my own (which I found to be 

 nearly an average one), the upper that of a person of very acute 

 sight, and the lower of one slightly myopic ; the horizontal line 

 gives the diameters of the apertures, and the ordinates are the 

 relative vanishincj-distances. 



There was a near accordance between the eyes of the several 

 observers when the smaller openings were used, but between 

 • 020d and * 094 in. the form of the curves, which represented 

 their defining-powers, varied considerably, owing to differences in 

 the figure of different eyes ; the power, too, in the same eye is not 

 at all times entirely the same, which renders the register of the 

 extreme limit rather uncertain. The smallest angle at which my 

 eye detects any indication of separation in a series of stripes or 

 checquers is, according to the table, 30^9 of radius, or 1 min. 7 sees. ; 

 that of the most penetrating eye that was tried, 1 min. 4 sees., or, 

 taking into account the refraction of the humour of the eye, the 

 smallest perceptible separation in the picture formed on the retina 

 would appear to be about 4 oVo ^^- -^^^^ ^ should remark that two 

 stripes only appear, through contracted apertures, to show separ- 

 tion at a greater distance by about ^J^ than a series ; this, how- 

 ever, would seem to proceed not from genuine definition, but from 

 an optical illusion produced by contrast, and which does not 

 authorize the extension of the limit,* for at the vanishing-distances 

 of the series, three stripes on a white ground give (apparently 

 from the same cause) a faint impression of but two with a tliin 

 grey line in the light-space between them, and at -^^ in. farther the 

 plane where the two stripes would appear as one shade, the three 

 will be pronounced to be two only. 



SLx glass tubes filled with mercury, each 0*16 in. diam., their 

 sides coated with black paper, and placed side by side so as to 

 reflect narrow stripes from a bright sky, were found to have, 

 under the most favourable circumstances, similar vanishing- 

 distances to the stripes on glass, and two tubes only appeared as 

 separated at a rather greater distance than those ; but it was more 

 difficult to obtain a suitable light for showing such results. 



* Note by A. E. C— The fact that two, or, generally, a small number of lines 

 are more easily resolved than a large number, has in recent times been shown to 

 be easily deducible from the undulatory theory of light. 



