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718 THE PHOTOGRAPHIC NEWS. [October 16, 1891. PHOTOGRAPHIC MAGNITUDES OF STARS. The character of the image of a star photographed on a sensitised film ; the relation between the intensity of the fight photographed, and the blackened disk produced ; the influence of the time of exposure on the image—are ques tions now receiving much attention. For this reason, Dr. Scheiner’s contribution to the subject, embracing, as it does, the latest results of the Potsdam Observatory, is especially welcome ; but these results will not be accepted without great reserve, contravening, as they do, a theory, or at least an assertion, that has been very generally accepted, viz., that increasing the intensity of light is exactly equivalent to increasing the time of photographic exposure. A consequence of such a law would be that an additional magnitude would be impressed on the film by increasing the time of exposure two and a half times the length. Such a law cannot be rigorously exact, and its stoutest supporters have been careful to confine its application “ within limits.” But Dr. Scheiner’s contention is that, owing to the complex character of the disk produced on the film, such a principle is a very unsafe guide, either as a rule for the determination of the feeblest magnitude impressed on the negative, or as offering a satisfactory explanation of the growth of the diameter or area. In the first place, there is evidence of want of uniformity of actinic action throughout the whole extent of the stellar disk. A mean intensity (i) may be assumed at a certain distance (r) from the centre of the image, where the intensity is I. The centre will not be a geometrical point, but, owing to atmospheric and other disturbances, will occupy a small area of radius (). The intensity (i) at distance (r) will depend materially on the increase of the area (), which may be represented by vp). Consequently, the simplest expresssion for i = Iv(p)e", where a is the coefficient of absorption of the sensitive film. On com paring two stellar disks, formed on the same emulsion, and treated by the same developer, this expression becomes— t _ I,Vp,),a(r;—, ro), b Io (Po) and, if the disks be on the same plate, Pl = Po and q = t„, so that the formula can be simplified to— , 110-4, \ a(ro—") = log- i = d (m, — ma) lo mod. In order to derive the relation between diameters and exposure, put I = I, and then— log. to = a(r, — r 0 ). It is not likely that such an expression has any other value than to serve as a convenient formula for interpola tion. The variable character of a under different con ¬ ditions, but always depending on the time of exposure, is Another well-known formula in which magnitude is made shown by the following table :— Exposure, m. s. Instrument. a. Instrument. a. 1 0 ... Reflector 4-99 ... 5-in. refractor 4'12 2 0 ... 4-57 5-09 4 0 ... 4-67 5-47 8 0 ... 4-89 • •• a 5'89 16 0 ... 5'39 • •• 33 7-51 0 24 ... 13-in. refractor 3-18 ... 13-in. refractor 2-67 1 0 ... 3-16 2-20 2 30 ... 3-33 2-48 6 15 ... 3-33 3-00 15 38 ... 33 4-48 ••• 33 — to depend on diameter is m — a - b log. D, and in this case b is shown, notwithstanding Dr. Charlier’s results to the contrary, to be a function of the time of exposure. The results are as follows :— Time of b Time of b exposure. Charlier. exposure. Scheiner. h. m. m. s. 0 13 6-719 0 24 5-17 1 30 6-779 10 6-35 2 0 6-683 2 30 7-06 3 0 6-814 6 15 8-08 The disagreement is conspicuous, but the explanation offered by Dr. Scheiner is scarcely satisfactory. He would ascribe the constancy in the value of b, found by Dr. Charlier, to the fact that in his experiments there is always a large absolute value of the time coefficient. It will, however, be observed that the ratio between Dr. Charlier’s extreme exposures is not greatly different from that which obtains in Dr. Scheiner’s experiments. If it be admitted that the product of intensity by the time is not a constant quantity, it becomes a matter of great practical importance to determine what is gained on a photographic plate by prolonged exposure. This question forms the real investigation of Dr. Scheiner’s two papers, and though some of his results may be questioned, yet the general issue is so grave and disquiet ing that it may not be utterly ignored. Passing over the details of his method of examination, and the precautions taken to ensure accurate results, for which the reputation of the Potsdam Observatory is a sufficient guarantee, Dr. Scheiner presents the following table, in which is exhibited the faintest magnitude which, under certain varied circumstances, can be detected on a photographic plate :— Time of exposure. Faintest Magnitude. m. s. Plate I. Plate II. Plate IIf. Plate IV. 0 24 . .. 9-0 ... 6-4 ... 7-7 ... 8'2 1 0 ... 9-4 ... 7-25 ... 8-3 ... 8-75 2 30 . .. 9-9 ... 7-7 ... 8-55 ... 9-3 6 15 . .. 10-6 ... 8-45 ... 9-3 ... 9-65 15 38 ... — ... 8-85 ... 9-7 — It will be noticed that, while each successive exposure is 2-5 that of the preceding, the corresponding gain in light is considerably less than one magnitude. From each of the four plates the gain is as follows : — Gain in mag. Plate 1 0-53 „ II 0-61 „ III 0-50 „ IV. 0.48 The mean is 0-53—that is to say, instead of one mag nitude being gained by continued exposure through each successive interval, the actual gain is only half a magni tude. The exception that might be taken to these ex periments is, that the detection of the feeblest stars on a plate is a matter of doubt and great practical difficulty. Dr. Scheiner has, however, availed himself of a second test by counting the stars on a plate after various exposures. With this view two plates were taken of the region round e Orionis, one with an exposure of one hour, the other with eight hours’ exposure. Therefore, if 2’5 times the exposure produced stars a magnitude fainter, there ought to be a gain of more than two magnitudes on the second plate, and it may be assumed that the number of stars impressed would follow the known law. On the one-hour plate were found 1,174 stars, on the eight-hour 5,689.