March 31, 192 1] 



NATURE 



145 



of visibility should be avoided by reserving them 

 for an instrument of larger aperture. A few causes 

 of error may be referred to briefly : (i) The 

 Purkinje phenomenon is well known ; if two lights 

 of different colours — say, a red and a green — 

 appear equally bright to the eye, then, if the in- 

 tensity of each is increased in the same ratio, the 

 red will appear the brighter; if reduced in the 

 same ratio, the green will appear the brighter. 

 Thus the relative magnitudes of two stars of dif- 

 ferent colours depend upon the aperture and 

 power with which they are observed, (ii) Con- 

 nected with this phenomenon is the difficulty of 

 comparing the brightness of two stars when their 

 colour is different with any type of photometer 

 which does not compensate for colour difference. 

 Some observers will estimate a red star as rela- 

 tively much brighter than will other observers — 

 errors of half a magnitude on this account are not 

 at all uncommon. The use of a red screen has 

 been suggested, but this and similar devices intro- 

 duce the Purkinje phenomenon. The most satis- 

 factory solution is to use the smallest aperture 

 which gives no perceptible colour, (iii) Errors are 

 possibly due to the two stars being observed on 

 different parts of the retina ; two stars which 

 appear equally bright when side by side will not 

 in general appear so when one is above the other. 

 It is advisable always to view the two stars side 

 by side and then to interchange their positions. 

 (iv) There are various errors possible owing to 

 varying accommodation of the eye, particularly 

 when the colours of the two stars differ. The 

 observer should therefore be screened by a dark 

 curtain, and all readings and settings performed 

 by a second observer outside the curtain. 



By the study of these and similar types of errors 

 and the best means of avoiding them, the influ- 

 ence of the human element has been reduced as 

 far as possible. With these precautions, the mag- 

 nitudes having been finally determined with the 

 photometer, it is necessary to apply a correction 

 for atmospheric absorption, which increases with 

 increase of zenith distance. Careful investigation 

 has been made, both at Harvard and at Potsdam, 

 of the amount of this correction at various alti- 

 tudes, and the effects of differential atmospheric 

 absorption have been allowed for with relatively 

 small uncertainty. But even after all precautions 

 have been taken it is found that there remain 

 systematic differences between different series of 

 observations, and that these occur not only in the 

 case of series made by different observers and 

 with different instruments, but even between dif- 

 ferent series made by the same observer with the 

 same instrument. In general, the errors are not 

 large, but they cannot be neglected in comparison 

 with the accidental error deduced from the inner 

 agreement between the observations in any one 

 series. The comparison of the brightness of two 

 images in a photometer is a subjective one, and 

 it seems impossible altogether to eliminate errors. 

 In the observations at Potsdam every star was 

 observed an equal number of times by the two 

 observers in order to make the whole series inter- 

 NO. 2683, VOL. 107] 



consistent; but another observer observing with 

 the same photometer would probably obtain results 

 diflering systematically according to colour. Dif- 

 ferent results are also obtained from different in- 

 struments. Thus MuUer and Kempf find, from a 

 comparison of the " Revised Harvard Photometry " 

 with the "Harvard Photometry," in which the 

 observations were made with different photo- 

 meters, the following relative dift'erences between 

 white and yellow stars in the two series : — 



The Potsdam observations made with the dif- 

 ferent photometers were intercompared, and cor- 

 rections derived by which all the observations were 

 reduced to a mean system. The differences, in 

 part, were probably due to differences in the ab- 

 sorptions in the several object glasses used. 



The comparison between the final Potsdam 

 results and the Harvard results reveals differences 

 which appear surprisingly large in view of the care 

 devoted to the observations themselves. The dif- 

 ferences are mainly dependent upon the colours of 

 the stars ; to a much less extent they vary with 

 their brightness. The following mean differences 

 in the sense Potsdam minus Harvard are found 

 for the Potsdam colour-classes W (white), GW 

 (yellowish-white), WG (whitish-yellow), G 

 (yellow) :■ — 



W, +o-2Sfn; GW, +o-22m ; WG, +oiom; G, o"oow. 



The differences show continuous variation with 

 brightness for the range 2m to 8m as follows : — 



W, -f-o"23w to +oTf7m ; GW, -f-o'20w to -t-o*30w ; 

 WG, -I-OI2W to +o'o'jm ; G, +o'ojm to -o*o8w. 



When it is recalled that a difference in magnitude' 

 of oirn corresponds to an error in apparent bright- 

 ness of nearly 10 per cent., the magnitude of these 

 errors can better be realised. It is also apparent 

 that there is much scope for improvement in the 

 accuracy of magnitude determinations. 



The Potsdam visual Durchmusterung, compris- 

 ing all stars in the " Bonn Durchmusterung " 

 down to a limit of 7-5m on the "Bonn Durch- 

 musterung " scale, is probably the most accurate 

 series so far as inner consistency is concerned, 

 the same two observers having observed every 

 star, and instrumental differences having been so 

 far as possible eliminated. If any series of visual 

 photometric observations can be regarded as 

 fundamental, it is this series ; but any other funda- 

 mental series may be expected to show slight 

 systematic discordances. There is a parallel in 

 the case of meridian observations, in which there 



