the same time. This follows, because, as Newton has shown, in such a case, the compound force which tends to the centre of the sphere would be everywhere proportional to the distance from the centre; and under the action of such a force, ellipses about the centre would be described, all the periods being of the same amount. This kind of symmetrical and simple systematic motion, presented by Newton as a mere exemplification of the results of his mechanical principles, is perhaps realized, approximately at least, in some of the globular clusters. The motions will be swift or slow, according to the total mass of the groups. If, for instance, our Sun were thus broken into fragments, so as to fill the sphere girdled by the earth's orbit, all the fragments would revolve round the centre in a year. Now, there is no symptom, in any cluster, of its parts moving nearly so fast as this; and therefore we have, it would seem, evidence that the groups are much less dense than would be the space so filled with fragments of the sun. The slowness of the motions, in this case, as in the nebulæ, is evidence of the weakness of the forces, and therefore, of the rarity of the mass; and till we have some gyratory motion discovered in these groups, we have nothing to limit our supposition of the extreme tenuity of their total substance. 3. Let us then go on to the cases in which we have proof of such gyratory motions in the stars; for such are not wanting. Fifty years ago, Herschel the father, had already ascertained that there are certain pairs of stars, very near each other (so near, indeed, that to the unassisted eye they are seen as single stars only,) and which revolve about each other. These Binary Sidereal Systems have since been examined with immense diligence and profound skill by Herschel the son, and others; and the number of such binary systems has been found, by such observers, to be very considerable. The periods of their revolutions are of various lengths, from 30 or 40 years to several hundreds of years. Some of those pairs which have the shortest periods, have already, since the nature of their movements was discovered, performed more than a complete revolution;[3] thus leaving no room for doubting that their motions are really of this gyratory kind. Not only the fact, but the law of this orbital motion, has been investigated; and the investigations, which naturally were commenced on the hypothesis that these distant bodies were governed by that Law of universal Gravitation, which prevails throughout the solar system, and so completely explains the minutest features of its motions, have ended in establishing the reality of that Law, for several Binary Systems, with as complete evidence as that which carries its operations to the orbits of Uranus and Neptune.