J 68 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. 



necessary to a given focal length of an object-lens or speculum ; and that a failure 

 in this point might probably bring on that indistinctness which had been ascribed 

 to the smallness of the pencils. In order therefore to put this to a trial, I used 

 now an object-lens of l.'io focal length, with an aperture confined to .01; the 

 rest of the apparatus being as in the 3d, 4th, and 5th experiments. The pencil 

 in this case was about the lOOOdth part of an inch; and though by a different 

 construction I had already seen very well with a pencil of not half that diameter, 

 I found this to give me, as now I had reason to expect, a very indistinct picture, 

 so much so indeed, that it could hardly be called a representation of the object. 



Eccper. 1 1 . Increasing the aperture of the object-lens to .0124, I had a pencil 

 of the 758th part of an inch, but could see no better with it. 



Exper. 1 2. Proceeding in the track now pointed out to me, I admitted an 

 aperture of .017, which gave a pencil of the 550th part of an inch, but could 

 see not much better with it than before. 



Exper. 13. On a further increase of the aperture to .0231, and a pencil of 

 the 406th part of an inch, I saw a little better ; but still had not distinctness 

 enough even to see the bristles before-mentioned at all. Hence we may con- 

 clude that, in such constructions as the present one, the aperture of tlie object- 

 glass must bear a considerable proportion to its focal length; since the 54th part 

 (for .0231 : 1.25 :: 1 : 54) is here not nearly sufficient. 



Exper. 14. To the same apparatus I applied a higher power, by an exchange 

 of the eye-glass; but the indistinctness remained as before. 



Exper. 15. Returning again to the former construction, I admitted an aper- 

 ture of about .037 ; and having now a pencil of nearly the 250th part of an 

 inch, I could but just perceive some of the large bristles; which shows that even 

 the 34th part (for .037 : 1 .25 :: 1 : 34) of the focal length is not a sufficient aper- 

 ture for object-lenses that act under such circumstances as the present. 



So far I have only related experiments that were made in the year 1778; and 

 my opinion that the smallness of the optic pencils could be no objection to seeing 

 well being thus supported by evident facts, I hesitated not, in a paper on the 

 Parallax of the Fixed Stars (Phil. Trans, vol. 72, p. 96) to affirm, that we might 

 see distinctly with pencils much smaller than the 40th or 50th part of an inch. 

 It did not appear to be necessary, nor would the subject of that paper permit me 

 to enter into a detail of experiments; but having, in the course of my reading 

 about that time, met with an account of some very small globules made for mi- 

 croscopic uses, I contented myself with an instance of small pencils taken from 

 them. I shall however now proceed just to hint at a few inferences that may be 

 drawn from these related experiments; as, on a mature consideration, we may 

 find reason to believe they point out a cause of indistinctness of vision hitherto 

 never noticed by optical writers; and which, when properly investigated, cannot 



