194 



KNOWLEDGE. 



[August 2, 1897. 



too much risk and difficulty in accurately following an 

 object for a much greater length of time than is done at 

 present. But in the case of nebulaj, planets, and other 

 celestial bodies (or phenomena) of finite though limited 

 size (/.('., of size lesa than the field of the camera), the 

 intensity of the image at the focal plane varies, as is well 

 known, as the square of the angular aperture of the 



objective — i.e., as ( ^r ) • Since the intensity of the field 



(due to the sky) varies, as already shown, as h- only, it at 

 once follows that for two instruments of the same ratio, 



-^j of aperture to focal length, but of different linear 



apertures, h^ and b^, the contrast between object and field 



win vary mversely as (^) ; or an objective of one inch 



aperture and (say) five inches focal length, will photo- 

 graphically reveal details only one-fourth as bright, as 

 compared with the sky, as can be revealed by one of two 

 inches aperture and ten inches focus. Or, assuminij that 

 till- development of the plate can lie pushed by proper methods 

 cor respondimjlij farther, the first lens will record given details 

 in one-fourth the time required Inj the second. In comparing 

 the rapidity of two lenses of differing aperture and focal 

 length, it has heretofore been customary to consider the 

 exposure time for a given object to vary simply as the 

 intensity of the image at the focal plane, i.e., as the square 

 of the angular aperture. Anyone who has tried photo- 

 graphing an object against a bright extended background, 

 such as the sky, knows that this law fails signally. Prof. 

 Barnard, in his experiments with the " lantern lens " at 

 the Lick Observatory," found that for very faint objects, 

 like the extended portions of the Orion nebula, the 

 Andromeda nebula, the earth-lit portion of the new moon, 

 etc., the time of exposure required with the " lantern 

 lens " was only one-twentieth to one-fortieth that required 

 with the Willard lens. The latter had an angular aperture 

 of one-fifth ; the former an angular aperture of about two- 

 sevenths. Hence, according to the usual rule, the time of 

 exposure required for the lantern lens would be a little less 

 than one-half that required by the Willard lens, or from ten to 

 twenty times what was actually required.! This difference 

 is very much greater than can be possibly explained by any 

 difference in the construction or transmissive power of the 

 two lenses, and proves conclusively that it is a question of 

 contrast between image and field, rather than of absolute 

 intensity of image alone, that determines the time of 

 exposure necessary to record photographically given details 

 of any object of finite angular extent. If we compare the 

 "lantern" and Willard lenses on this basis, we find that 

 there is no discrepancy remaining to be explained. For 

 the aperture of the Willard lens was six inches, while that 

 of the other was one and a half inches. Hence the squares 

 of the relative angular apertures being, as already stated, 

 about one to two, the ratio of the contrast between object 

 and field would be in the two cases — 



Lantern _ 2 / G V _ 32 



Millard ~ 1 Vl-5/ 1 



a value which agrees with the experimental results of 

 Prof. Barnard already referred to. Further evidence of the 

 correctness of this method of comparison is furnished by 

 the results of Pickering in photographing the Orion nebula. 

 Pickering used a Voightlilnder portrait lens of 2G inches 

 aperture and 86 inches equivalent focus, or of about ^.^ 

 angular aperture. J This is almost exactly the angular 



* Astronomif and Astrophysics, December, 1894, ]i. 811. 

 t It was Prof. Barnard's calling my attention to this great dis- 

 crepancy \yh!cli first led me to investigate this problem. 

 X Sid. Mess., Vol. IX., p. 2, January, 1890. 



aperture of the " lantern lens" (J^), and, according to usual 

 law, the time of exposure for a given object ought to be the 

 same for the two lenses (about eleven per cent, less for the 

 Voightlilnder lens). But the time of exposure required for 

 the Voightlilnder lens was three hours, while that required 

 for the " lantern lens " was only one hour fifteen minutes^ 

 about five to twelve as long. The ratio of contrast for 

 these two lenses is — 



Lantern ^ /H•B^ = , /2-6 . ^^ 13 j^^^^^^ ^, 12 . 



Voiglitlander V3-.5/ Vlo/ =5 5 



Here, again, the agreement between the ratio of theoretical 

 exposures and the ratio of actual exposures is very close. 

 It is, in fact, even closer than appears, because Pickering's 

 photograph with three hours' exposure did not show quite 

 as much as that of Barnard v^ith one hour fifteen minutes' 

 exposure. 



This law of variation of the brightness of the field 

 according to the inverse square of the aperture of the 

 camera objective, is also of great importance in indicating 

 the proper instruments for use in various fields of research 

 in astronomical photography. It will be quite evident 

 from the preceding considerations that the instrument 

 best suited for the photography of any faint extended 

 celestial body or phenomena, such as nebulas, comets, 

 meteor trails, the gegenschein, the zodiacal belt, etc., is 

 one of very small linear aperture — smaller even than any 

 that have so far been used. It should, of course, also have 

 as large an angular aperture (ratio of aperture to focal 

 length) as possible ; but this will be determined to a 

 certain extent by the angular extent of field sought after, 

 by the scale desired, and, in the superior limit, by optical 

 difficulties of construction. Because of these last an angular 

 aperture greater than one-fourth is hardly practicable when 

 any extent of field is to be covered at all sharply, and it is 

 better not to go below a ratio of one to five. So far as I 

 know, the smallest lens which has been used in astro- 

 nomical photography is the "lantern lens " of Prof. Barnard 

 already referred to, having a linear aperture of one and a 

 half inches. But I believe very much smaller apertures 

 than this even may be employed to advantage ; and I have 

 recently proposed to make use of two Zeiss microscope 

 objectives (for microphotography), having apertures of only 

 0"28 and 0-42 inch respectively, for photographing certain 

 very faint objects, particularly the gegenschein and the 

 fainter portions of the zodiacal band, and for searching 

 for faint nebulosity in portions of the sky in which it has 

 not previously been detected. These lenses, which have 

 an angular aperture of one to five — the same as the Willard 

 lens — would be respectively about four hundred and fifty 

 and two hundred times as efficient as the latter (granting 

 that they are as good from an optical point of view), either 

 as regards time of exposure (supposing the development 

 can be pushed far enough without foggini; the plate by 

 the action of the developer itself) or as regards extent of 

 detail, which can be obtained with long exposures (granting 

 that the scale of the photograph is sufficient to show this 

 detail). 



The difficulty mentioned in the last sentence of the 

 preceding paragraph is perhaps the most serious objection 

 to the use of very small apertures. Unfortunately, there 

 is no way of avoiding it, for looking at the relation between 

 intensity of image and of field in another way, we see that 

 the contrast between the two depends ultimately simply 

 on the absolute focal length (./').* To obtain four times the 



* Intensity of image varies as -, ; intensity of field as i= .". contrast 



image _ 1 

 field ~ f' 



f 



