l6d PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. 



The first opportunity I had of making the proposed experiments was in the 

 year 1778, and the result of them proved so decisive tiiat 1 have never since 

 resumed the subject; and had it not been for a late conversation with some of 

 my highly esteemed and learned friends, I might probably have left the papers on 

 which these experiments were recorded, among the rest of those that are laid 

 aside when they have afforded me the information I want. But a doubt seeming 

 still to be entertained on the subject of the smallness of the optic pencils, it may 

 now be proper to comnmnicate these experiments, that it may appear how far 

 the conclusions I have drawn from them are warranted by the facts on which I 

 suppose them to rest. 



Experiments with the naked eye. — Exper, 1. Through a very thin plate of 

 brass I made a minute hole with the fine point of a needle; its magnified dia- 

 meter, very accurately measured under a double microscope, I found to be .465 

 of an inch, while under the same apparatus a line of .05 in length gave a mag- 

 nified image of 3.545 inches. Hence I concluded, that the real diameter of the 

 perforation was about the 152d part of an inch. Through this small opening, 

 held close to the eye, I could very distinctly read any printed letters on which I 

 made the trial. Proper allowance must be made for the very inconvenient situ- 

 ation of the eye, which by the unusual closeness to the paper cannot be expected 

 to see with its common facility. Besides, the continual motion of the letters, 

 which is required on account of the smallness of the field of view, must needs 

 take up a considerable time. 



Exper. 1. In some other pieces of brass I made smaller holes; and among 

 many, that were measured with the same accuracy as in the former experiment, 

 I found one whose magnified diameter was .29 : hence the real diameter could 

 not exceed the 244th part of an inch. Through this opening I could also read 

 the same letters ; but the difficulty of managing so as not to intercept all the in- 

 cident light, as well as the very uneasy situation of the eye, were sufficient rea- 

 sons for not carrying the intended experiments any further under this form. Be- 

 sides, I should hardly have allowed them to be fair, if, on a further contraction 

 of the hole in the brass plate, an indistinctness had come on ; as we might well 

 have suspected at least 2 other causes, besides the smallness of the pencils, to 

 contribute to such an imperfection, viz. want of light, and a deflection of it on 

 the contracted edges of the hole. 



Microscopic experiments. — Exper. 3. I had now recourse to a double micro- 

 scope, consisting, for simplicity's sake, of only 2 lenses. The focal length of 

 the eye-glass, carefully ascertained by an object half a mile off, being .9 ; the 

 distance of the object-glass from the eye-glass 9.36; and the aperture of the 

 object-glass .0405. Hence we compute that the diameter of the optic pencil, 

 when it entered the eye, could not exceed the 232d part of an inch ; yet with 



