1882.] 



MICKOSCOPICAL JOUKNAL. 



63 



Let us now look for a moment at 

 the difference between the telescopic 

 and microscopic fields and at the dif- 

 ferent ways of regarding them. Let 

 //', in fig. 23, be a lens through which 

 the rays from a microscopic object 

 {a b) form an image of this object 

 [a' a) at the conjugate aplanatic fo- 



c and d. It is also evident that as o' 

 approaches the lens, as when the tube 

 is shortened, its conjugate focus o re- 

 cedes from it and the angle cod be- 

 comes smaller. Leaving out of con- 

 sideration, for the present, any other 

 cause of variation, it is clear that the 

 angle of the telescopic field diminishes 



Fig. 23. 



cus."jThis enlarged image is, of course, 

 examined by means of the microscope 

 eye-piece. But remove the ocular 

 and apply^the naked eye to a small 

 hole at o' (or substitute a telescope 

 eye-piece) and we see, not a b, but 

 objects remote and in the telescopic 

 field c ^,*by" means of the image of 

 that field which is formed behind the 

 objective, but quite close to it, and at 

 the aplanatic conjugate focus of c d, 

 viz. c d' . This image is a real im- 

 age, and its size and distance from 

 the back of the lens depend upon the 

 distance oi c d from the front of the 

 lens, but it is^ bounded, nevertheless, 

 by the marginal rays of the cone lo' I'. 

 It will, in fact, be found where the 

 rays c I and d I' cut / 0' and /' 0' 

 after refraction. This follows strictly 



with the shortening of the tube. 

 Another fact is also important. 

 Viewed with reference to the image 

 c' d', the ray c o /', is marginal to the 

 cone Ic I' and the xzy do I is marginal 

 to the cone I d I'. A pin-hole diaph- 

 ragm at 0, only large enough to allow 

 a minute pencil of rays to pass from 

 c and d respectively, will still suffice 

 for the formation of the image c' d'; 

 but if farther from the lens than o, 

 the field will be rapidly cut down and 

 the apparent angle diminished, for no 

 ray from <r or ^ can reach the lens 

 through the diaphragm after the latter 

 has passed beyond the^intersection of 

 c I' and d I. The limitations under 

 which this will be found true, in prac- 

 tice, will be examined hereafter; it is 

 now referred to for the purpose of 



Fi&. 24. 



from the principle of conjugate foci 

 already stated, and if be coincident 

 with the centre of the disc of the 

 apertometer, or with the pivot of the 

 swinging arm connected with the 

 traverse lens, the angle cod will 

 generally be correctly measured by 

 the degrees upon the sector between 



emphasizing the fact, that the angk 

 of aperture of the instrument when 

 used as a telescope, is measured by 

 the rays passing from the margin of 

 the field c d, through 0, to the margin 

 of the available front of the lens, and 

 thence to the margin of the image 

 c' d'. Starting from the image, under 



