Li7nit to Defining -poiucr. By J. J. Lister. 47 



iu., being added to the space, l-o5 in., between its front surface 

 and a finely divided glass micrometer in its focus) gave 1*4:7 in. 

 as its front conjugate focal length ; the divisions of the micrometer 

 M-ere then thrown upon paper by the camera-lucida, and tlie same 

 eye-piece being retained, other object-glasses of more complex 

 structure were applied to the Microscope ; the divisions as shown 

 by them were thrown on tlie same paper, and their relative focal 

 lengtlis were taken to be as the number of divisions respectivelv 

 projected from them on a given length of the paper, corrections 

 being afterwards made for any small differences in the back con- 

 jugate foci. 



To obtain a minute object for ascertaining the defining-power 

 of microscopic object-glasses of difterent apertures and focal lengths. 



An original object, chequers or stripes (black on glass), is set 

 up before a mirror reflecting light from the sky (call distance of 

 their middle s, 1st column). 



Of this object {s) a diminished image (s) is formed by an object- 

 glass of any short focal length (b, 2nd column) and of sufficient 

 pencil to ensure a distinctness in the image that will employ the 

 full defining-power of another object-glass of such aperture (a, 4th 

 column) and focal length {d, 3rd column) as is to be tried upon 

 it. The Microscope with the latter object-glass a being fixed 

 before the form h so as to view the image, they are brouglit to 

 that distance of h from the original object s at which the pattern 

 vanishes (call this distance c, 5th column), then the measure rf 

 the separation of the middles of stripes or squares in the image to 



be viewed is — = s (6th column). 

 c 



Now, from the observations made, it appears that the distances 



(d) at which patterns of stripes or chequers of different sizes will 



vanish when viewed through one and the same aj^erture, varies 



directly as the linear size of the pattern, so that whatever be the 



s 

 measure of s or of d, a remaining unchanged, ^ will be a constant 



number and will represent the arc subtended by s in terms of 

 radius d taken as unity. 



Then, on the supposition that this arc varies inversely as the 



S Cb 



aperture a is varied, , , the arc of the separation of the pattern 



for an aperture of 1 in. (see 7th column) will also be a constant 

 number (oj), and its proving such will botli show the correctness 

 of the supposition, and give an expression for the limit of definition 

 with any aperture and distance or size of pattern ; for 



dx dx , , as 



s = — ; a = — ; and d — - 

 as X 



