increasing, in other words the orbital motion of Jupiter must be increasing, or Jupiter must be receding from the sun. To this extent therefore, the sun-Jupiter system is analogous to the earthmoon system. As the tides on the earth are driving away the moon, so the tides in Jupiter and the sun are gradually driving the two bodies apart. But there is a profound difference between the two cases. It can be proved that the tides produced in Jupiter by the sun are more effective than those produced in the sun by Jupiter. The contribution of the sun may, therefore, be at present omitted; so that, practically, the augmentations of the orbital moment of momentum of Jupiter are achieved at the expense of that stored up by Jupiter's rotation. But what is 12 compared with 600,000. Even when the whole of Jupiter's rotational moment of momentum and that of his satellites has become absorbed into the orbital motion, there will hardly be an appreciable difference in the latter. In ancient days we may indeed suppose that Jupiter being hotter was larger than at present, and that he, therefore, had more rotational moment of momentum. But it is hardly credible that Jupiter can ever have had one hundred times the moment of momentum that he has at present. Yet even if 1,200 units of rotational momentum had been transferred to the orbital motion it would only correspond with the most trivial difference in the distance of Jupiter from the sun. We are hence assured that the tides have not appreciably altered the dimensions of the orbit of Jupiter, or of the other great planets. The time will however, come, when the rotation of Jupiter on his axis will be gradually abated by the influence of the tides. It will then be found that the moment of momentum of the sun's rotation will be gradually expended in increasing the orbits of the planets, but as this reserve only holds about two per cent. of the whole amount in our system, it cannot produce any considerable effect. And now we must draw this chapter to a close, though there are many other subjects that might be included. The theory of tidal evolution is, indeed, one of quite exceptional interest. The earlier mathematicians expended their labour on the determination of the dynamics of a system which consisted of rigid bodies. We are indebted to contemporary mathematicians for opening up celestial mechanics on the more real supposition that the bodies are not rigid; in other words, that they are subject to tides. The mathematical difficulties are enormously enhanced, but the problem is more true to nature, and has already led to some of the most remarkable astronomical discoveries made in modern times. Our Story of the Heavens has now been told. We commenced this work with some account of the mechanical and optical aids to astronomy; we have ended it with a brief description of an intellectual method of research which reveals some of the celestial phenomena that occurred ages before the human race existed. We have spoken of those objects which are comparatively near to us, and then step by step we have advanced to the distant nebulæ and clusters which seem to lie on the confines of the visible universe. Yet, after all, how little is all we can see even with our greatest telescopes, when compared with the whole extent of infinite space! No matter how vast may be the depth which our instruments have sounded, there is yet a beyond of infinite extent. Imagine a mighty globe described in space, a globe of such stupendous dimensions that it shall include the sun and his system, all the stars and nebulæ, and even all the objects which our finite capacities can imagine. Yet, after all, what must be the relation of even this great globe to the whole extent of infinite space. The globe will bear to that a ratio infinitely less than that which the water in a single drop of dew bears to the water in the whole Atlantic Ocean. THE END. APPENDIX. ASTRONOMICAL QUANTITIES. THE SUN. THE sun's mean distance from the earth is 92,700,000 miles; his diameter is 865,000 miles; his density, as compared with water, is 14; his ellipticity is insensible; he rotates on his axis in a period between 25 and 26 days. THE MOON. The moon's mean distance from the earth is 238,000 miles. The least possible distance is 221,000 miles; the greatest is 260,000 miles. The diameter of the moon is 2,160 miles; and her density, as compared with water, is 3-5. The time of a revolution around the earth is 27-322 days. m. secs. Mercury 35.9 28.6 43.3 Venus Earth 87-969 2,992 24 5 (1) 6.85 4.81 5.66 |