46 Transactions of the Society.. 



and this accords with such trials as I have made ; for although 

 to carry power further may show a wider separation on some such 

 objects as bright double stars (see pp. 35, 45), I have found the 

 same effect, without much increase, from softening their light with 

 a bluish-green glass.* 



In telescopes limited to a single magnifying power (/«) for day 

 objects, taking a pencil of 0"1 in. to give in daylight all the dis- 

 tinctness that the eye can appreciate (see p. 39), the utmost a'perture 



oil/ 

 required for the object-glass will be r-r in., and it may be made 



rather less than this with little disadvantage. 



It is observable that whether the pencil entering the eye is 

 contracted to a certain size at the object-glass or by a " stop " at 

 the eye-piece, no difference appears to be produced in the size of 

 the rings before-mentioned or in the defining-power. 



For ascertaining the limit to de lining-power in the Microscope 



wdiich had been peculiarly the purpose of this investigation, it 



was necessary, the vanishing distance {d) being limited to the 



front conjugate focal length of the object-glass, to vary the size of 



the object instead of its distance till it should be sufficiently small 



for the pattern to disappear. This was accomplished by forming, 



with a fine microscopic object-glass of short focus, an image of 



the former patterns at a variable distance (c) from them, which 



image was then to be viewed as an object in the Microscope ; the 



separation of its parts (s) being to that in the original object (s') 



as the focal length (h) of the tjlass forming the image to its distance 



sh 

 {c) from the original pattern, i.e. — = s. It was thus that s 



was obtained in the observations given in the third table. 



Several circumstances had here to be attended to which it may 

 be well to mention, if only to show that they were not neglected. . 



1. It was requisite that the glass forming the image should be 

 capable of giving a picture at least as sharp as the glass with 

 which it was viewed had power to define, and that the adjustment 

 of both glasses for the rays entering them should be so complete 

 tliat no part should form an imperfect or partial image beyond the 

 general focus — for want of guarding which point some discrepancy 

 at first appeared in the observations. 



2. The focal lengths of the different object-glasses had to be 

 determined with an accuracy difficult to attain in such small 

 measurements. The method adopted was, to begin with, a single 

 plain convex achromatic glass, which (§ of its thickness, or 0'12 



* Note by A. E. C. — It is very remarkable that Lister deduced from his ex- 

 periments, made eighty years ago, figures coming so very near to those now 

 generally accepted on the basis of much later work, viz. the resolving-power of 

 telescopes as about 4 J seconds of arc divided by aperture in inches, and the highest 

 ordinarily useful magnification as 50 per in. of aperture. 



