August 2, 1897.] 



KNOWLEDGE. 



193 



By C. J. T. 



BOOKS EECEIVED. 



Seform of Chemical and Phi/sical Calculations. 

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Electricitii and Magnetism for Beginners. By P. W. Sanderson, 

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The New Century Review. (The Unicorn Pre-s.) 6d. net. 



All About Animals. — Part II. To be completed in twelve fort- 

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A Primer of French Etymologi/. By B. Dalv Cocking. (Innes 

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Creation, with Development or Evolution. By J. Dudley R. Hewitt. 

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Aluminium. By A. Gr. Brown. (Aluminium Supply Company.) 

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British Marine Food Fishes. By Wm. C. Mclntosli and Arthur 

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Bureau of Ethnology. Fourteenth Annual Report to the Secre- 

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ASTRONOMICAL PHOTOGRAPHY.-I. 



The CoNDiTioys which Detekmise the Limiting Time oe Exposure. 



By F. L. 0. Wadswobth, 

 Astrophysicist, Yerkes Observatory. 



IN the April Number of Knowledge there is a paper 

 by Dr. Eoberts describing one of his fine photo- 

 graphs of the Orion nebula, taken with an 

 exposure of seven hours thirty-five minutes, 

 which " depicts, very probably, the maximum 

 of extent and detail that can be shown by aid 

 of photographic methods." This statement, as Dr. 

 Roberts points out, is a most important one; "for, if 

 correct, it proves that, as regards duration of exposure, we 

 have already reached the hmit of the available aid by this 

 method in astronomical researches." The reasons upon 

 which this conclusion is based are ; " (1) The film of the 

 negative is, in consequence of prolonged exposure to the 

 latent sky luminosity, darkened on development to a degree 

 that would obscure faint nebulosity and faint stars. (2) 

 Longer exposures of the plates would not reveal additional 

 details of nebulosity nor more faint star images." 



In spite of the well-known skill and long experience of 

 Dr. Roberts in this line of work, and the consequent 

 great weight of his opinion on such a subject, the point 

 involved is too important a one to allow it to pass without 

 question. Dr. Roberts has recognized that objections will 

 be raised to his conclusions, and has endeavoured to 

 answer some of them in advance. But there is one point 

 of great importance, which, strangely enough, seems to 

 have escaped the attention, not only of Dr. Roberts, but of 

 all other writers on the general subject of astronomical 

 photography (among others, Angot, 1877 ; Grubb, 1887 ; 

 Teunant, 1888; Schaeberle, Turner, 1889; Christie, 

 Charlier, 1891 ; Harkness, 1892 ; Abney, Searle, 1893 ; 

 Newall, Pickering, 1891 ; etc., etc.) whose papers are 

 accessible to the writer. 



Reference is made to the influence of the aperture of the 

 photographic instrument upon the brightness of the field 

 due to the general illumination of the sky. This general 

 illumination is produced by scattering of light in our own 

 atmosphere, by small particles (Rayleigh), and varies in 

 intensity inversely as the fourth power of the wave-length. 

 It is therefore of a character which affects a photographic 

 plate much more strongly than it does the eye. Moreover, 

 the great majority of the diffracting particles being at a 



relatively great distance from the instrument, the illumina- 

 tion is of the same character as u-ouhl be pruduced by a 

 uniformly luminous* area of infinite e.rtent. Now it follows 

 at once from the principle of the wave theory that the 

 intensity of illumination at the focal plane of an objective due 

 to such an illuminated area \cill be simply proportional to 

 the area of the objective — i.e., to the square of the linear 

 aperture (b) : and leill be entirely independent of the focal 

 length (/) of the instrument. Hence, for a given brightness of 

 sky (/,) (dependent upon the altitude of the observing station 

 and upon the condition of the atmosphere), the time of 

 e.rposure requisite to produce a given fogging or blackening of 

 the plate will, other things being equal, vary inversely as 

 the square of the linear aperture of the image-forming lens, 

 no matter what the focal length of the latter may be. 



In referring to the long-exposure photographs taken by 

 Dr. Gill at Cape Town (twenty-four hours fifty-three 

 minutes, on Eta Argus), and by Dr. ^Yolf, Dr. Roberts 

 says : " The reason why a refractor of focal distance to aper- 

 ture in the ratio of one to ten could not cause the darkening 

 of the film .... so rapidly as a reflector of the focal 

 ratio of one to five, is consequent upon the greater power 

 of the latter in the concentration of light upon the sensitive 

 film than is possessed by the refractor ; there is also loss 

 of hght by reflection from the surfaces of the lenses by 

 absorption, and by absence of perfect achromatism in the 

 lenses. Less sensitive plates may also have been used in 

 the refi-actor than were used in the reflector, and the 

 development of the plates may not have been carried or 

 the same degree of intensity. Therefore, on consideration 

 of all the relative conditions, twenty-five hours' exposure 

 of a plate in the refractor may not be so near the limit of 

 practical photographic eflect as seven and a half hours 

 would be with the twenty-inch reflector." From the pre- 

 ceding consideration it wUl readily be seen that this 

 explanation is not the true one. The fundamental cause 

 of the difference in exposure possible with the two instru- 

 ments under consideration lies in the difl'erence in linear 

 aperture. I assume (not having been able to find the 

 paper of Dr. Gill describing the plate m question) that the 

 photograph of Eta Argus referred to was taken with the 

 standard instrument prescribed by the Astrophotographic 

 Congress, which has a linear aperture of thirteen inches, 

 and a ratio of aperture to focal length of nearly one to ten. 

 If all the important conditions, save that of size of instru- 

 ment, which affect the general blackening or foggmg of 

 the film — i.e., the brightness of the sky, the efficiency of 

 the objective as regards optical form, transmitting (or 

 reflecting) power, etc., the sensitiveness of the film, the 

 manner and extent of development, etc., etc. — were the 

 same in the two cases, the instrument of thirteen inches 

 aperture would permit of an exposure nearly two and one- 

 half times as long as the one of twenty inches aperture. 

 If, then, we consider seven and one-half hours (more 

 exactly, seven hours thirty-five minutes) as the limiting 

 time of exposure for Dr. Roberts' instrument, the lirniting 

 exposure for a thirteen-inch under the same conditions 

 would be nearly nineteen hours, and fcr a six- inch at 

 least eighty hours. 



This, however, is not the most important conclusion to 

 be drawn from this relation between brightness of focal 

 field and aperture. The mere ability to lengthen the time 

 of exposure (at least beyond twenty-four hours) by de- 

 creasing the size of the photographic objective would not, 

 in itself, be of great importance, because there would be 



• Owing to the greater thickness of atmosphere traversed by the 

 liglit coining from the stars (and other luminous celestial bodies) 

 near the horizon, the general illumination of tliis portion of the sky 

 will be somewhat greater than of that portion near the zenith. 



