are adequate to deal with the problem. They point out how much is due to Mercury, how much is due to Jupiter; and the wanderings of Encke's comet can thus be made to disclose the mass of Jupiter as well as that of Mercury. Here we have a means of testing the precision of our weighing appliances. The mass of Jupiter can be measured by his moons, in the way mentioned in a previous chapter. As the satellites revolve round and round the planet, they furnish a method of measuring his weight by the rapidity of their motion. They tell us that if the sun were placed in one scale of the celestial balance, it would take 1,047 bodies equal to Jupiter in the other to weigh him down. Hardly a trace of uncertainty clings to this determination, and it is therefore of great interest to test the theory of Encke's comet by seeing whether it gives an accordant result. The comparison has been made by Von Asten. Encke's comet tells us that the sun is 1,050 times as heavy as Jupiter; so the results are practically identical, and the accuracy of the indications of the comet are confirmed. But the calculation of the perturbations of Encke's comet is so extremely intricate that Asten's result is not of great value. From the motion of Winnecke's periodic comet, Haerdtl has found that the sun is 1,047.17 times as heavy as Jupiter, in perfect accordance with the best results derived from the attraction of Jupiter on his satellites and the other planets. We have hitherto discussed the adventures of Encke's comet in cases where they throw light on questions otherwise more or less known to us. We now approach a celebrated problem, on which Encke's comet is our only authority. Every 1,210 days that comet revolves completely around its orbit, and returns again to the neighbourhood of the sun. The movements of the comet are, however, somewhat irregular. We have already explained how perturbations arise from Mercury and from Jupiter. Further disturbances arise from the attraction of the earth and of the other remaining planets; but all these can be allowed for, and then we are entitled to expect, if the law of gravitation be universally true, that the comet shall obey the calculations of mathematics. Encke's comet has not justified this anticipation; at each revolution the period is getting steadily shorter! Each time the comet comes back to perihelion in two and a half hours less than on the former occasion. Two and a half hours is, no doubt, a small period in comparison with that of an entire revolution; but in the region of its path visible to us the comet is moving so quickly that its motion in two and a half hours is considerable. This irregularity cannot be overlooked, inasmuch as it has been confirmed by the returns during about twenty revolutions. It has sometimes been thought that the discrepancies might be attributed to some planetary perturbations omitted or not fully accounted for. The masterly analysis of Von Asten and Backlund has, however, disposed of