September 1, 1897. 



KNOWLEDGE. 



219 



increasing the contrast between sky and object in this case 

 is to increase the angular aperture. The larger the latter 

 the fainter the star that can be photographed. So far as 

 the delineation of faint stars is concerned, the size of the 

 objective — granting that the size does not affect the 

 question of optical efficiency — is a matter of indift'erence ; 

 with proper exposure an objective of one inch aperture will 

 show just as many and just as faint stars as one of ten 

 feet aperture — providing, of course, the image in the first 

 case is bright enough to start photographic action, and 

 providing also the law, that the photographic action is 

 constant when the light action (intensity x time) is con- 

 stant, holds throughout the range considered. Some recent 

 experiments of Abney seem to show that this law is 

 not always fulfilled in the case of very slow plates, 

 but these are never used in astronomical photography. 

 In practice the small lens would have an actual 

 optical advantage over the larger one, in that it is more 

 efficient optically — i.e., a larger percentage of the incident 

 light is transmitted, less being lost (at least in case of 

 lenses) by absorption, dispersion, etc. This advantage 

 will be treated more in detail a little later. The small 

 instrument has also, of course, a great advantage in 

 being very much less expensive both as to optical and 

 mechanical parts, in being more rigid, allowing better 

 following, and in being more conveniently handled. Its 

 disadvantages are the smaller scale of the photograph, and 

 the increase in exposure time necessary to show stars of a 

 given magnitude. With a given angular aperture such as 

 we have assumed in this case as a basis of comparison — 

 because upon this alone depends the contrast between sky 

 and star — the scale of the photograph varies directly as 

 the linear aperture, and the time of exposure (theoretically) 

 inversely as the square of the linear aperture. As a matter 

 of fact, the exposure time necessary with the larger lens 

 has been found to be longer than indicated by the above 

 comparison ; a fact which was long ago predicted by Sir 

 Howard Grubb,+ and which is undoubtedly due to the 

 greater optical efficiency (less loss by absorption, etc.), 

 already referred to, of the smaller size objectives. 



Since the available contrast between the field and the 

 star image depends simply and solely on the angular 

 aperture, and since for practical reasons an angular 

 aperture larger than that of Dr. Roberts' instrument 

 (one-fifth) can hardly be employed on account of the 

 practical optical difficulties of construction, it would 

 follow that the latter's conclusion as to the limiting 

 magnitude of stars photographically visible would hold 

 (although, as we have already seen, it does not hold 

 at all for nebulfe or extended objects), provided the time 

 of exposure which he sets is really the limiting time of 

 exposure for bis aperture— twenty inches. That it is, 

 however, is doubtful in view of the practical experiences of 

 many other observers. I have collected some evidence on 

 this important point, which is presented in the following 

 table. For comparison I have assumed that all secondary 

 conditions affecting time of exposure (such as condition of 



* The reason why a large aperture is necessary to render very faint 

 stars physiologicallif visible is that in the case of the eye a certain 

 minimum intensity of light is necessary to produce a retinal 

 impression. In the case of the photographic plate it is quanlitii of 

 light, not intensity, which is principally in question — although the 

 question may be raised whether there ie not a limit beyond which no 

 action at all will take place, no matter how long the light acts. Ou 

 this p lint Ciptain Abney is quoted by Russell • as saying : " I have 

 made experiments, and can say distinctly that there is, eo far as 

 I know, no light so feeble that an accumulation of it will not give an 

 image upon the photographic jilate." (" Popular Astronomy," Vol. II., 

 p. 4f>2.) 



t -'^O'"*'^' -Vo<ice», April, 1887, p. 303, 



sky, sensitiveness of plate, method of development, and 

 optical efficiency of instrument) are the same in the 

 different cases. The first column contains the name of the 

 observer ; the second, the reference to the paper containing 

 details respecting exposure, etc. ; the third, the linear 

 aperture of the instrument ; the fourth, the time of ex- 

 posure ; and the last, the time of exposure reduced to an 

 aperture of twenty inches (that of Roberts' instrument), by 

 multiplying the given time by the square of the ratio of 

 apertures. 



Cyrrespoiidiji^ 

 Liueiir Longest ' Exposui-o for 



Aperture. Esposure. ' 20-mcli 

 Aperture. 



(iill ... Roberts' Paper , !l3-iu. (?) 



Stratonoff A X,Vol. Ul, p. 104 ' 13-in. 



Stratonoff A.X., Vol. 142. p. 57 13.in. 



Pickering A.N., Vol. 113,p. 230 24-in. 



HR3. MIN.S. 



10 

 10 



8 

 8 



31 

 34 

 27 

 38 



No one of the three observers whose results are given in 

 the preceding table say anything about having reached 

 the limit of exposure time ou account of the darkening of 

 the plates, and all of them have given a considerably 

 longer (equivalent) exposure than Dr. Roberts. The 

 reason for the difference may lie either in the greater 

 sensitiveness of the plates used by Dr. Roberts ; to some 

 difference in development ; to greater brightness of sky 

 in England than at the other stations ; or, lastly, to a 

 greater optical efficiency of the refractor (all the instru- 

 ments whose performance is cited above were of this 

 class) as compared with the reflector. As regards the 

 first two reasons, it is equally fair to consider that on the 

 one hand Dr. Gill, Dr. Stratonoff, and Prof. Pickering's 

 plates were just as sensitive as Dr. Roberts', and that, on 

 the other hand, the latter's skill in development is fully 

 as great as that of any of the others. As regards the 

 third reason. Dr. Roberts holds that he has eliminated this 

 factor in the limiting time of exposure from consideration 

 by experiments extending over many nights of varying 

 quality. In passing it may be stated that it does not 

 appear to the writer just how this can be done. It is 

 certainly true that the darkening of the film will depend 

 directly on the brightness of the sky, and the darker the 

 latter the longer the possible time of exposure. The 

 limit set by Dr. Roberts as the result of his work 

 in England might therefore easily be exceeded with 

 the same instrument, same plates, and same development, 

 at another station more favourably situated. Finally, 

 as regards the last possible cause of difl'erence, I feel that 

 so much has already been said as to the relative advantages 

 of reflectors and refractors that an apology is almost 

 necessary for bringing up the question again. Neverthe- 

 less, I do not believe the question is by any means settled. 

 While practical experiment is certainly a valuable guide 

 to a conclusion, one is apt to fall into generalizations not 

 at all warranted by experiments made imder a limited 

 variation of conditions. It seems to me, for example, that 

 Dr. Roberts' conclusions as to the relative advantages 

 of the two classes of instruments have been too hastily 

 drawn. In his experiments with his reflector of twenty 

 inches linear aperture and ninety-eight inches focus 

 (angular aperture about one-fifth), and with two portrait 

 lenses, one of three and a half inches aperture, 9-56' 

 focus (angular aperture ^), and the other of five inches 

 aperture and iy-22" focus (angular aperture 5-5-;), he 



* " On the Relative Eilic eucy of a Reflector and of Portrait Lenses 

 for the Delinoationof Celestial 'Objects." J/ .V., April, iyu6, p. 372. 



