254 



NATURE 



[July i6, 1891 



ponents of a close double point will overlap ; and if the 

 distance between the centres do not exceed the diameter 

 of the representative patches of light, there can be no 

 distinct resolution. Now their diameter varies inversely 

 as the aperture ; and thus the resolving power is directly 

 as the aperture. 



My object to-night is to show you by actual examples 

 that this is so. I have prepared a series of photographs 

 of a grating consisting of parallel copper wires separated 

 by intervals equal to their own diameter, and such that 

 the distance from centre to centre is -^^ inch. The grating 

 was backed by a parafifin lamp and large condensing lens ; 

 and the photographs were taken in the usual way, except 

 that the lens employed was a telescopic object-glass, and 

 was stopped by a screen perforated with a narrow adjust- 

 able slit, parallel to the wires.^ In each case the exposure 

 was inversely As the aperture employed. The first [thrown 

 upon the screen] is a picture done by an aperture of 

 eight hundredths of an inch, and the definition is toler- 

 ably good. The next, with six hundredths, is rather 

 worse. In the third case, I think that everyone can see 

 that the definition is deteriorating ; that was done by an 

 aperture of four hundredths of an inch. The next is one 

 done by an aperture of three hundredths of an inch, and 

 you can see that the lines are getting washed out. In 

 focussing the plate for this photograph I saw that the 

 lines had entirely disappeared, and I was surprised, on 

 developing the plate, to find them still visible. That was 

 in virtue of the shorter wave-length of the light operative 

 in photography as compared with vision. In the last 

 example, the aperture was only two-and-a-half hundredths 

 of an inch, and the effect of the contraction has been 

 to wash away the image altogether, although, so far as 

 ordinary optical imperfections are concerned, the lens 

 was acting more favourably with the smaller aperture 

 than with the larger ones. 



This experiment may be easily made with very simple 

 apparatus ; and I have arranged that each one of my 

 audience may be able to repeat it by means of the piece 

 of gauze and perforated card which have been distri- 

 buted. The piece of gauze should be placed against the 

 window so as to be backed by the sky, or in front of a 

 lamp provided with a ground-glass or opal globe. You 

 then look at the gauze through the pin-holes. Using the 

 smaller hole, and gradually drawing back from the gauze, 

 you will find that you lose definition and ultimately all 

 sight of the wires. That will happen at a distance of 

 about 44 feet from the gauze. If, when looking through 

 the smaller hole, you have just lost the wires, you shift 

 the card so as to bring the larger hole into operation, 

 you will see the wires again perfectly. 



That is one side of the question. However perfect 

 your lens may be, you cannot get good definition if the 

 aperture is too much restricted. On the other 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. [Experi- 

 ment.] 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 will 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 



' The distance between the grating and the telescope lens was 12 feet 

 3 inches. 



NO. I 133, VOL. 44] 



in the faintness 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 suffi- 

 ciently small, the image is no worse without a lens than 

 with one. . 



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

 the important question in dealing with pin-hole photo- 

 graphy. It was first considered by Prof. Petzval, of 

 Vienna, and he arrived at the result indicated by the 

 formula, ir- = /X, where ir is the diameter of the 

 aperture, A the wave-length of light, and / the focal 

 length, or rather simply the distance between the aper- 

 ture 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 mathe- 

 matical problem of the diffraction of light by a circular 

 hole has been sufficiently worked out to enable the ques- 

 tion to be solved. The mathematician to whom we owe 

 this achievement is Prof. Lommel. I have adapted his 

 results to the problem of pin-hole photography. [A 

 series of curves [Philosophical Magazine^ February 1891), 

 were shown, exhibiting to the eye the distribution of 

 illumination in the images obtainable with various aper- 

 tures.] The general conclusion is that the hole may 

 advantageously be enlarged beyond that given by Petzval's 

 rule. A suitable radius is r = VC/X). 



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

 application of pin-hole photography on a different scale 

 from the usual. The definition improves as the aper- 

 ture increases ; but in the absence of a lens the 

 augmented aperture entails a greatly extended focal 

 length. The limits of an ordinary portable camera are 

 thus soon passed. The original of the transparency now 

 to be thrown upon the screen was taken in an ordinary 

 room, carefully darkened. The aperture (in the shutter) 

 was o"07 inch, and the distance of the 12 x 10 plate from 

 the aperture was 7 feet. The resulting picture of a group 

 of cedars shows nearly as much detail as could be seen 

 direct from the place in question. 



THE SMITHSONIAN ASTRO-PHYSICAL 

 OBSERVATORY. 



T^HE Smithsonian Institution, as we have already 

 -^ announced, has established as one of its depart- 

 ments a Physical Observatory which, with the instru- 

 ments, has been supplied from the Smithsonian Fund. 

 It occupies at present a temporary structure, though 

 funds have been subscribed for a permanent building 

 when Congress shall provide a suitable site. For the 

 maintenance of the Observatory an appropriation has 

 been made by Congress which became available on 

 July I. The actual instrumental work of the new 

 Observatory will necessarily devolve largely upon a 

 senior and a junior assistant, who can devote their 

 entire time to research, and it is hoped that with the 

 improved apparatus it will be possible to prosecute ad- 

 vantageously investigations in telluric and astro-physics, 

 and particularly those with the bolometer in radiant 

 energy. 



In accepting the position of assistant secretary of the 

 Smithsonian Institution in 1887, Mr. Langley retained 

 the Directorship of the Observatory at Allegheny for the 

 purpose of completing the researches begun there, and 

 after his appointment as Secretary of the Institution, he 

 still continued the titular Directorship, though but a 

 limited amount of time could be spared from his official 



