526 



NATURE 



[October i, 1891 



given for regarding that feature as an acquired one. If, 

 however, that view be incorrect, the presence of this 

 vacuity at once stultifies the statement that the Sivathere 

 can have no kinship with the giraffe and the deer, on 

 account of the absence of a similar vacuity ; and its 

 presence, so far as it goes, is also another argument 

 against the Sassabi theory. 



The last representative of the Giraffoid animals that 

 we have to mention is the recently discovered Samothe- 

 ritim, from the Pliocene of Samos, a figure of the skull 

 of which appeared in Nature, illustrating an article on 

 the extinct mammals of those deposits. In this animal, 

 the elongated form and straight profile characteristic of 

 the skull of the Giraffe are retained ; and the teeth are 

 almost indistinguishable from those of the latter. There 

 is, however, no development of air-cells in the bones of 

 the frontal region, so that the upper border of the orbit 

 is approximated to the plane of the face ; and the cranial 

 appendages take the form of upright compressed pro- 

 cesses rising immediately over the orbits. These ap- 

 pendages, which appear to have been inseparable from 

 the bones of the forehead, are, indeed, very similar, both 

 in form and position, to the horn-cores of certain extinct 

 antelopes, but we are, of course, unacquainted with the 

 nature of their covering. If, however, as seems to be 

 undoubtedly the case, the Samothere is a Girafibid, it 

 would seem that we must here again regard this super- 

 ficial resemblance to the antelopes as one independently 

 acquired. 



Finally, if the views expressed above are anywhere 

 near the truth, it would appear that, in the Pliocene 

 epoch, Giraffoid animals played a very important role 

 among the ruminants, and that they have undergone 

 modifications and developments fully as marked as those 

 which we observe among the antelopes at the present 

 day. Whether the circumstance that none of them, ex- 

 cept the giraffe (which is obviously an animal incapable 

 of further modification), appears to have obtained an 

 entrance into Africa has been the chief reason why only 

 a single representative of the group has survived to our 

 own times may be a fair subject of conjecture, since after 

 the Pliocene epoch both India and Europe seem to have 

 been unsuited to the maintenance of many forms of large 

 Artiodactyle Ungulates, as is proved by the disappear- 

 ance from those regions of the hippopotamus, the giraffe, 

 and a number of antelopes of African type. R. L. 



PHOTOGRAPHIC MAGNITUDES OF STARS. 



n^HE character of the image of a star photographed on 

 ■*■ a sensitized film ; the relation between the intensity 

 of the light photographed and the blackened disk pro- 

 duced ; the influence of the time of exposure on the 

 image — are questions 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. 



NO. I 144, VOL. 44] 



In the first place, there is evidence of want of uni- 

 formity of actinic action throughout the whole extent of 

 the stellar disk. A mean intensity (z) may be assumed 

 at a certain distance (r) from the centre of the image, 

 where the intensity is I. This centre will not be a geo- 

 metrical point, but, owing to atmospheric and other dis- 

 turbances, will occupy a small area of radius (p). The 

 intensity (z) at distance (r) will depend materially on the 

 increase of the area (p), which may be represented 

 by V'Cp)- Consequently, the simplest expression for 

 / = l^{p)e'^'' , where a is the coefficient of absorption 

 of the sensitive film. On comparing two stellar disks, 

 formed on the same emulsion, and treated by the same 

 developer, this expression becomes 



h Io^(Po) 

 and, if the disks be on the same plate, p^ = pQ and t^ = t^^i 

 so that the formula can be simplified to 



«(^o-^i) = log J- = -^- {in. 



m^ 



Iq . mod. 



In order to derive the relation between diameters and 

 exposure, put lo = I], and then 



log^ 



«(^i - ^o)- 



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 

 shown by the following table : — 



Exposure. Instrument. a. Instrument. a. 



m. s. 

 I o ... Reflector 4-99 ... 5-in. refractor 4'I2 



Another well-known formula in which magnitude is made 

 to depend on diameter 1% 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 : — 



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 7-iot 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 insure accurate results, for which the reputation 



