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are so nearly equal in size that we cannot give one the preference in this way; and in all cases it is more correct to regard both stars as revolving round some point in between them than to regard one as fixed and the other as revolving round it.

These double stars are often beautifully coloured; one of them being of a different colour from the other. But our chief concern to-day is not with the colours, but with the movements of the two partners. They are waltzing round one another just like a pair of dancers in a ballroom: the idea of waltzing will help us very much, because the dancers not only turn round one another but move down the room at the same time. At the corners of the room they have to turn, and it is possible that our waltzing double stars may have to turn at some corner or other in the future: at present we cannot say because we have not been watching them waltz long enough; we have only had about a century to watch them since they were discovered, and even a century is but a short time in the life of a double star. Some of them take as long as that to make a single waltz-turn, and others take much longer—so much longer that in the century since they have been watched they have scarcely turned at all. You may ask how we know that they are partners in that case. Well, sometimes you see a pair of partners in a ballroom not waltzing round at all, but going down the room without turning. We know that they are partners because they keep together as they move down the room; and so it is with these double stars which do not seem to be turning they are nevertheless moving together