Limit to Dejining-poiver. By J. J. Lister. .'>0 



Some following columns contain similar observations of otlier 

 persons for the sake of comparison. The last column but one, 



— , refers the separation of each pattern to 1 in., showing tliat tlie 



vanishing -distance varies as the size of the pattern, and furnishing 

 a comparative measure of the defining-power of the pencils admitted 

 tlirough the several apertures. It may be seen in this column that 

 even when the breadth of the black stripes was to that of the white 

 as 3 to 1, the ratio of the vanishing-distance to the separation is 

 the same as when the breadths are equal, and the small difference 

 when the white stripes were as much in excess appeared to me to 

 proceed only from greater difficulty in detecting the limit. I 

 referred to the same cause a slight deficiency in the average 

 distance at which checquers vanished compared with stripes, which 

 indeed would have been scarcely perceptible had not the observa- 

 tions set down been in all cases the extreme ones — a circumstance 

 that makes the mean of all probably the nearest approach to 

 truth. The squares and rhombs formed by crossing patterns of 

 stripes w^ere found to vanish on an average at the same distances 

 as the stripes that produced them. 



The last column, — , the mean numbers of the preceding one 

 d 



being taken as -, refers the diameter of the apertures also to 1 in., 



s 

 and, on the supposition that the vanishing -distance, or, in other 

 words, the linear defining-power, varies as the aperture, should give 

 a constant number, as the measure of the angle of a separation of 

 1 in., seen through an aperture of 1 in. in terms of radius as unity. 

 On ascending the column, beginning from the aperture * 0094 in., 

 \ve find the result will be seen to accord with the supposition 



till we have passed 0-0206 in., y being on an average 0-0000219, 



or, taking the pattern of stripes only, • 0000217, within this range. 

 As we descend from • 0094 it becomes progressively rather greater, 

 but not more so than may be attributed to the effect upon the 

 pencil of the coats of the eye or the lamina of the crystalline lens, 

 which produce with very small openings the impression of looking 

 through a partially obstructing medium. 



Thus it appears that up to an opening of 0-02 in. the intrinsic 

 distinctness of the pencil increases as the aperture, and it will 

 shortly be seen by observations with the telescope and Microscope 

 that the same law continues to prevail with i-egard to larger open- 

 ings, although as we proceed up the column the defining-power of 

 the eye no'longer increases in the same ratio; the difference, 

 indeed, which is at first small, accelerates so rapidly that in day- 

 light, with an opening of 0-095, nearly the utmost definition is 

 attained of which the ordinary eye is capable. 



