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among the other stars hand-in-hand so to speak; so that we may safely regard them as partners. Thus a ballroom helps us in several ways to think of the movements of the stars, but now I come to a point where it ceases to help us. Partners in a ballroom are always in pairs; I have seen three people waltzing together for fun, but you would not see it often; and I doubt whether you would ever see four or five together, let alone twenty or thirty. But with the stars it is different. The general rule is for a pair of stars to waltz together, but we often have three or four, and lately we have been finding groups of thirty or forty together, or even more. We detect the partnership because they move together in the ballroom: when there are only three or four, we can sometimes see them also turning round one another, but the movements are apt to be complicated when there are more than two, because it is difficult to know which of the several partners you are to pay attention to at any one time. All the partners in the group are pulling at one another, and though we know the exact law of the pulls (which is simply that great Law of Gravitation which Newton found out for us), it is quite impossible for mathematicians, with all their present skill, to trace out the consequences of the law. Perhaps they may have better success in the future, but meantime we need not trouble so much about the treatment of one partner or another because what I want you to notice chiefly is that the whole group moves together. Look (Fig. 90) at the picture of the group called the Pleiades, in which arrows are drawn to represent