1891.] on Some Applications of Photography. 271 



restricted. On the otlier hand if the aperture is much restricted, 

 then the lens is of no use, and you will get as good an image without 

 it as with it. 



I have not time to deal with this matter as I could wish, but I 

 will illustrate it by projecting on the screen the image of a piece of 

 gauze as formed by a narrow aperture parallel to one set of wires. 

 There is no lens whatever between the gauze and the screen. [Ex- 

 periment.] There is the image — if we can dignify it by such a 

 name — of the gauze as formed by an aperture which is somewhat 

 large. Now, as the aperture is gradually narrowed, we wdll trace the 

 effect upon the definition of the wires parallel to it. The definition 

 is improving ; and now it looks tolerably good. But I will go on, 

 and you will see that the definition will get bad again. Now, the 

 aperture has been further narrowed, and the lines are getting washed 

 out. Again, a little more, and they are gone. Perhaps you may 

 think that the explanation lies in the faintuess of the light. We 

 cannot avoid the loss of light which accompanies the contraction of 

 aperture, but to prove that the result is not so to be explained, I will 

 now put in a lens. This will bring the other set of wires into view, 

 and prove that there was plenty of light to enable us to see the first 

 set if the definition had been good enough. Too small an aperture, 

 then, is as bad as one which is too large ; and if the aperture is 

 sufficiently small, the image is no worse without a lens than with 

 one. 



What, then, is the best size of the aperture ? That is the im- 

 portant question in dealing with pin-hole photography. It was first 

 considered by Prof. Petzval, of Vienna, and he arrived at the result 

 indicated by the formula, 2 r^ = / A, where 2 r is the diameter of the 

 aperture, X. the wave-length of light, and / the focal length, or 

 rather simply the distance between the aperture and the screen 

 upon which the image is formed. 



His reasoning, however, though ingenious, is not sound, regarded 

 as an attempt at an accurate solution of the question. In fact it is 

 only lately that the mathematical problem of the diffraction of light 

 by circular holes has been sufficiently worked out to enable the ques- 

 tion to be solved. The mathematician to whom we owe this achieve- 

 ment is Prof. Lommel. I have adapted his results to the problem 

 of pin-hole photography. [A series of curves * were shown, exhibit- 

 ing to the eye the distribution of illumination in the images obtainable 

 with various apertures.] The general conclusion is that, the hole 

 may advantageously be enlarged beyond that given by Petzval's rule. 

 A suitable radius is r = V (f^)- 



I will not detain you further than just to show you one applica- 

 tion of pin-hole photography on a different scale from the usual. The 

 definition improves as the aperture increases ; but in the absence of a 

 lens the augmented aperture entails a greatly extended focal length. 



* ' Phil. Mag.' Feb. ISOl. 



T 2 



