surveying—the distance of our world from the centre of the solar system. That this will one day happen is rendered highly probable, in my opinion, by the successes next to be related. Besides the motions of the planets around the sun, there are their motions of rotation, and the rotation of the sun himself upon his axis. Some among these turning motions are sufficiently rapid to be dealt with by the new method. The most rapid rotational motion with which we are acquainted from actual observation is that of the planet Jupiter. The circuit of his equator amounts to about 267,000 miles, and he turns once on his axis in a few minutes less than ten hours, so that his equatorial surface travels at the rate of about 26,700 miles an hour, or nearly 7½ miles per second. Thus between the advancing and retreating sides of the equator there is a difference of motion in the line of sight amounting to nearly 15 miles. But this is not all. Jupiter shines by reflecting sunlight. Now it is easily seen that where his turning equator _meets_ the waves of light from the sun, these are shortened, in the same sense that waves are shortened for a swimmer travelling to meet them, while these waves, already shortened in this way, are further shortened when starting from the same advancing surface of Jupiter, on their journey to us after reflection. In this way the shortening of the waves is doubled, at least when the earth is so placed that Jupiter lies in the same direction from us as from the sun, the very time, in fact, when Jupiter is most favourably placed for ordinary observation, or is at his highest due south, when the sun is at his lowest below the northern horizon—that is, at midnight. The lengthening of the waves is similarly doubled at this most favourable time for observation; and the actual difference between the motion of the two sides of Jupiter’s equator being nearly 15 miles per second, the effect on the light-waves is equivalent to that due to a difference of nearly 30 miles per second. Thus the new method may fairly be expected to indicate Jupiter’s motion of rotation. The Greenwich observers have succeeded in applying it, though Jupiter has not been favourably situated for observation. Only on one occasion, says Sir G. Airy, was the spectrum of Jupiter “seen fairly well,” and on that occasion “measures were obtained which gave a result in remarkable agreement with the calculated value.” It may well be hoped that when in the course of a few years Jupiter returns to that part of his course where he rises high above the horizon, shining more brightly and through a less perturbed air, the new method will be still more successfully applied. We may even hope to see it extended to Saturn, not merely to confirm the measures already made of Saturn’s rotation, but to resolve the doubts which exist as to the rotation of Saturn’s ring-system.