October 3, 1907] 



NATURE 



567 



Four have proper motions greater than i"o : 



Procyon ... 

 Sirius 

 Arcturus 

 a Centauri 



Mean 



213 



036 



P^- 



It is clear from the first group that low magnitude 

 alone has no very close association with large parallax, 

 and in the other groups Arcturus is the only star with 

 considerable proper motion that has not a considerable 

 parallax, as parallaxes go. 



I think that in forming his low estimate of the estab- 

 lished relation between parallax and proper motion Prof. 

 Pearson must have been misled by Miss 

 Ciibson's results. She has calculated the 

 correlation between parallax and the 

 separate components of the proper motion 

 in right ascension and declination, and 

 <o has naturally obtained a smaller result 

 than if she had used the whole proper 

 motion in seconds of arc on a great circle, 

 as is usually done. 



I have plotted the material used by Miss 

 Gibson in two ways, parallax against 

 magnitude and parallax against proper 

 motion on a great circle, and it seems to 

 me that the second diagram .shows con- 

 siderable correlation. 



Some of the parallaxes are marked by 

 Newcomb as doubtful ; these I have shown 

 by smaller dots. Five which depend on 

 absolute right ascensions observed with 

 the meridian circle may be considered too 

 doubtful for use in this discussion ; I have 

 struck them through with a cross. 



The seventy-two parallaxes grouped in 

 means by whole magnitudes give a 

 " curve of regression " with three peaks 

 and two valleys, to which Miss Gibson 

 thinks that it might be possible to fit a 

 quartic curve. I suggested a simpler 

 explanation, and Prof. Pearson asks for 

 details of the reason why this curve of 

 regression has such a switchback form if 

 it is not real. It is easy to answer this 

 question. Consider, for example, the 

 second-magnitude group ; it contains 

 si.x stars, only one of which has a 

 moderately large proper motion. Four of 

 the stars were observed in the early days 

 of photography as part of the late Prof. 

 Pritchard's scheme to determine the 

 paralla.xes of all second-magnitude stars. 

 One of the stars is Polaris, of small 

 proper motion, observed just because it 

 is Polaris ; the sixth is a Gruis, of small 

 proper motion and parallax. The group 

 contains no star specially selected in 

 anticipation of finding a large parallax, 

 and naturally the mean of the group is 

 small, because it is more or less representative of the 

 second-magnitude stars in general. 



On the other hand, the fourth-magnitude group includes 

 several stars observed because of large proper motion, 

 7) Cassiopeia, t Ceti, 70 Ophiuchi, and is helped out by 

 a large parallax assigned to tj Herculis which is certainly 

 spurious. Hence the mean parallax of the group is 

 large. 



.''md so on. It would be tedious to examine each group 

 in detail, but the almost fortuitous value of the mean 

 parallax for each of these small magnitude groups is 

 amusingly illustrated by the first two. The first contains 

 two stars, parallaxes o"-37 and o"-oo ; mean, o"'ig. The 

 second contains five stars ; four have parallaxes of o"o9, 

 o"oo, o"-03, and o".ii, but the group is translated from 

 the valley to the peak because the fifth parallax is o".75. 

 This, the largest known parallax, belongs to the double 



NO. 1979, VOL. 76] 



star a Centauri, the components of which have magnitudes 

 04 and i-g. We might add the fainter component to the 

 second-magnitude group discussed above ; this would bring 

 the mean parallax of the group up with a bound from 

 o"-o8 to o"-i8, make a new peak, and remove one of 

 Prof. Pearson's difficulties. 



Probably there is no need to justify more minutely my 

 remark at Leicester that a statistician who attacks astro- 

 nomical problems must be as intimately acquainted with 

 technical astronomy as with the use of his modern statis- 

 tical tools. If any doubt remains, it will be dispelled by 

 reading further in Miss Gibson's paper. " The next stage 

 in the work was to inquire whether magnitude was more 

 markedly correlated with any other character than 

 parallax. Colour suggested itself as a character for which 

 definite data were available. In vol. ix. of the ' Annals 



« 



(J 70 



C'bc 

 0-5C 



0-y. 

 02c 



0-10 



o-sc 

 p 



O-jo 

 0-t>c 

 0-5C 

 04tx 

 0-X ' 

 02c ■ 



J- 



0" 



'3 4 



3 



4 



7' 



Correlation between (i) parallax and magnitude ; (2) parallax an 

 great circle, for the seventy-two stars in Newco 



of the Cape Observatory ' will be found a catalogue from 

 which the colour of 159 stars can be extracted. ..." 

 Prof. Pearson quotes in his letter one of the results of 

 this section, " that colour and magnitude are related at 

 least as closely as parallax or proper motion and magni- 

 tude." And Miss Gibson concludes "that we have a 

 suggestion, even if it be only of the vaguest kind, that 

 the bulk of the lucid stars may belong to a separate 

 universe within which magnitude is not mainly determined 

 by parallax or distance, but is more closely associated 

 with colour, and thus probably with chemical or physical 

 conditions." On examining the basis of this far-reaching 

 suggestion about the " bulk of the lucid stars," one is 

 struck with the remarkable fact that " white had no 

 frequency in the record " ! ,\ search in the Cape volume 

 shows that the list in question is entitled " Coloured 

 Stars observed during the Revision of the ' Cape Photo- 



