Rapid as the course of these objects is, the distances which we have described are such that, in the great majority of cases, all the observations yet made on the positions of the stars fail to show any well-established motion. It is only in the case of the nearer of these objects that we can expect any motion to be perceptible during the period, in no case exceeding one hundred and fifty years, through which accurate observations extend. The efforts of all the observatories which engage in such work are, up to the present time, unequal to the task of grappling with the motions of all the stars that can be seen with the instruments, and reaching a decision as to the proper motion in each particular case. As the question now stands, the aim of the astronomer is to determine what stars have proper motions large enough to be well established. To make our statement on this subject clear, it must be understood that by this term the astronomer does not mean the speed of a star in space, but its angular motion as he observes it on the celestial sphere. A star moving forward with a given speed will have a greater proper motion according as it is nearer to us. To avoid all ambiguity, we shall use the term "speed" to express the velocity in miles per second with which such a body moves through space, and the term "proper motion" to express the apparent angular motion which the astronomer measures upon the celestial sphere. Up to the present time, two stars have been found whose proper motions are so large that, if continued, the bodies would make a complete circuit of the heavens in less than 200,000 years. One of these would require about 160,000; the other about 180,000 years for the circuit. Of other stars having a rapid motion only about one hundred would complete their course in less than a million of years. Quite recently a system of observations upon stars to the ninth magnitude has been nearly carried through by an international combination of observatories. The most important conclusion from these observations relates to the distribution of the stars with reference to the Milky Way, which we have already described. We have shown that stars of every magnitude, bright and faint, show a tendency to crowd towards this belt. It is, therefore, remarkable that no such tendency is seen in the case of those stars which have proper motions large enough to be accurately determined. So far as yet appears, such stars are equally scattered over the heavens, without reference to the course of the Milky Way. The conclusion is obvious. These stars are all inside the girdle of the Milky Way, and within the sphere which contains them the distribution in space is approximately uniform. At least there is no well-marked condensation in the direction of the galaxy nor any marked thinning out towards its poles. What can we say as to the extent of this sphere?