;6o 



NATURE 



[April i i, 1895 



come, however, to actual facts, it is recorded in the latest 

 published catalogue of magnitudes, that of Potsdam, 

 that the probable error of the concluded magnitude is 

 0"04 mag. This amounts to the same thing, practically, 

 as decidmg between the illuminating power of 25 and 

 26-candle gas. It is not known whether such a problem 

 would offer any ditYiculty to gas e.\perts, but even they 

 sometimes fail to gain full credence from the public. 



Bat the record of photometric research is by no means 

 exhausted by this catalogue of work, limited to the 

 application of specially devised photometers to the stars 

 directly. Another and entirely different method of in- 

 vestigation has been actively prosecuted in the last few 

 years, and apparently with the greatest success. This 

 method avails itself of the refinements and the results 

 of photography. Every one knows the appearance of a 

 photographic plate on developing it after it has been 

 exposed in the focal plane of a telescope for a longer or 

 shorter time. It is seen that the circular images of the 

 stars impressed differ greatly in size, and it may be in 

 depth of deposit, according to the magnitude of the stars 

 impinging on the plate. Consequently, by appropriate 

 means of discussion we are able to determine the rela- 

 tive magnitudes of the stars themselves. And since we 

 have here to contemplate the measurement of a sensible 

 area, it miy not be unwise to recall the fact that the term 

 " magnitude '' of a star is strictly limited to its brilliancy. 

 Magnitude, therefore, in its accurate astronomical sense, 

 is not easy of definition ; difference of magnitude, in- 

 volving as it does difference of brilliancy, is, however, 

 easily apprehended, and it is a difference of magnitude 

 that IS sought to be determined by measurement of the 

 blackened area corresponding to the star images on the 

 sensitised film. 



The problem here offered for solution is not precisely 

 the same as that in the direct application of a photo- 

 meter to the light of the stars. The eye ceases to be the 

 actual photometer employed. For the impression on the 

 retina we have substituted the impression recorded on 

 the photographic film. This film may be more or less 

 sensitive 10 some of the rays that go to make up the 

 whole of the light of a star than is the ordinary retina, 

 and consequently the record will differ in mdividual 

 cases from ihat obtained by photometric means in the 

 more ordinary sense of the word. Leaving out of the 

 question orlhochromatic plates, which are not usually 

 employed in recording the positions of stars, the films 

 are prepared so as to be most sensitive for the violet 

 light of a star, whereas the eye is generally most sensi- 

 tive to the yellow. If object-glasses arc employed, this 

 ditterence is usually aggravated again, for the optician 

 seeks to make this coloured light most operative, ac- 

 cording to the direction in which the telescope is to be 

 employed. In the case of a photographic telescope, the 

 rays about G in the spectrum are most important ; in 

 the visual telescope, those rays about D. In whatever 

 svay the photographic observations are discussed, with 

 the view of ensuring a general agreement with photo- 

 metric results, it must be anticipated that exceptional 

 cases will differ, especially when the star light is rich in 

 violet rays. Speaking generally, while a photometer, as 

 usually employed, seeks to arrange the stars according 

 to their appearance to a normal eye, a photographic 

 determination of relative brilliancy exhibits the stars as 

 they would appear to an eye most keenly sensitive to 

 chemical rays. 



The method of deriving the photographic magnitude 

 will differ according to the manner in which the observa- 

 tions have been made. In the ftr^l place the ordinary 

 plate, whether it be taken with the view of producing a 

 general chart of the heavens, or the accurate representa- 

 tion of any small selected area on the sky, will contain 

 implicitly the magnitudes of the stars impressed. Con- 

 sequently, if we measure the diameter of the circular 



N J. 1328, VOL. 51 ] 



images produced by the stars of known magnitude, we 

 have a relation between diameter and stellar magnitude. 

 Such attempts end in the derivation of a convenient 

 formula of interpolation. We may find that an expres- 

 sion of the form m = a~ bd or /// = a-h log d (where m and 

 d are respectively magnitude and diameter and a and b 

 constants applicable only to that plate, and available 

 only through a small range of magnitudes) is serviceable 

 practically, but has no physical meaning. The determ- 

 ination of the constants a and b is troublesome, and 

 demands a previous knowledge of the photometric mag- 

 nitudes of some of the stars on the plate — information 

 not always at hand. 1-or these reasons attempts, more 

 or less successful, have been made to assign the magnitude 

 of a star from a knowledge of the diameter of the image 

 and the duration of exposure. To be completely success- 

 ful such an inquiry demands an acquaintance with the 

 manner in which the image grows on the sensitised film, 

 and this inquiry has progressed but slowly, and is still 

 incomplete. In the early <iays of photography, it was 

 supposed that the diameter varied as the square root of 

 the time of exposure ; later, with the modern dry plate, 

 the fourth root of the time was thought by some to mote 

 nearly express the rate of growth ; but I'rof. Turner and 

 the Astronomer Royal have both shown that neither of 

 the suggestions is satisfactory. The character of the plate, 

 the steadiness of the image, and the accuracyof "driving " 

 (that is, the successful removal of the effects of the earth 

 rotation), all enter as perplexing variables in a research of 

 this character. The Astronomer Royal has suggested 

 that the square root of the diameter of the photographic 

 image increases as the logarithm of the time of exposure. 

 This may be applicable to a particular telescope and 

 through a definite range of magnitudes, but is scarcely 

 likely to express a physical law. But, accepting such .1 

 result as a working hypothesis, we cannot pass directly to 

 the magnitude of stars without making another assump- 

 tion with regard to the diameters. This is usually 

 summed up in the expression that for equal diameters- - 



Exposure x brightness = constant. 



That is to say, in order to get equal diameters of the 

 images of two stars, one of which has four times the light 

 ot the other, we must expose the plate to the fainter star 

 four time? as long as to the brighter. This sounds 

 almost axiomatic, and was for a long lime accepted as a 

 demonstrated fact. So much so, that at the Paris Con- 

 ference in iSSy it was decided that the proper time of 

 exposure to photograph eleventh magnitude stars was 

 six and a quarter times that required for a ninth magni- 

 tude star. This decision of six and a quarter was 

 adopted because this number expresses the ratio of the 

 light in a ninth magnitude star to that in the eleventh. 

 Probably no great harm will come from the adoption of 

 such a resolution, but Captain Abney has given good 

 reasons for doubting the assumption that length of 

 exposure and intrinsic brightness are equally operative 

 in producing the same photographic effect. All this goes 

 to show that the determination of magnitude from an 

 examination of the small circular dots on a " star plate" 

 is not at all a simple problem. There is, too, anothci 

 fact which should be borne in mind. All the discs are 

 small, and yet in a range of five magnitudes, one hundred 

 times more light has gone to make up the l.iiger than the 

 smaller of the two discs. This means th.it the scale is 

 much contracted, and will probably interfere with final 

 accuracy, quite as much as a want of dcrtnilcness at the 

 edge of the disc, or distortion from a circular shape by 

 being photographed at a distance from the optical axi^. 

 or other c.iuscs which make the measurement of tliu 

 exact size of the blackened area, uncert.iin. 



It is a question If the problem be materially simplified 

 when the plates are photographed with the direct 

 purpose of determining magnitude. We should then 



