OF ARTS AND SCIENCES. 275 



companions is far too great to sensibly affect tlie variables, but other 

 nearer objects may lie in the same plane. The approximate position 

 ani^le of the companion was computed from its Durchmusterung 

 jilace. The position angle of the pole of the variable stars was meas- 

 ured by a protractor, laid upon the globe over the position of the 

 variable star, and stretching a thread to the pole. Each of these 

 determinations is liable to an error of some degrees, but the results 

 which are given in column seven are sufficiently exact for our present 

 purposes. Some of these stars are red, and when they are contained 

 in the Catalogue of Birmingham * their numbers are given in the last 

 column. 



The numbers of the third column show that the stars of the fifth 

 class are not concentrated in the assumed plane. If uniformly dis- 

 tributed all over the heavens, their average distance should be about 

 30°, since one half of each hemisphere is contained in a zone of this 

 width. In the short-period stars of the fourth class, however, the 

 agreement is most remarkable. None have yet been found more 

 distant than 16° from the circle, and with two exceptions none are 

 more distant than 10^. There is only one chance in four that a given 

 star should lie within 15° of a given great circle, and about one in six 

 that it should lie within 9° of it. Evidently the chances would be 

 many millions to one against the observed arrangement being acci- 

 dental. As an argument in favor of the parallelisms of the axes, this 

 distribution of the stars fails by proving too much. We should ex- 

 pect, if the axes were jjarallel, to find nearly as many stars between, 

 10° and 20°, as between 0° and 10°, since the variation would be a 

 function of the cosines of these angles. If the axes were not exactly 

 coincident, we should find the stars still more widely distributed. 



Of course it is possible that the distribution of these stars may be 

 partly due to the parallelism of their axes of rotation. But we have 

 shown that the latter cause is insufficient. Since then we must assume 

 an arrangement of the stars approximately in a plane, we cannot be 

 sure that their apparent distribution is not wholly due to it, and 

 the evidence in favor of parallelism of their axes is much weakened. 



It is a little singular that this plane appears to pass through the 

 Sun. We should expect that while the more distant stars mi^ht lie 

 upon a great circle, the nearer, and therefore presumably the brighter, 

 stars, would lie on the opposite side of it from the Sun. As, however, 

 the positive and negative signs are nearly equally distributed, we must 



* Trans. Roy. Inst. Acad., x.xvi. 24y. 



