We may look upon Lexell's as the first discovered comet of short period; for although it was never seen after its first visit, yet nothing can be more certain than that it did actually return once, and that it went twice round its new orbit. Indeed, if it has not been absorbed by Jupiter - a very unlikely contingency - it must still be revolving in space with an orbit which brings it, once in each revolution, to the scene of its former encounters. The figure of its orbit may be altered again and again by encounters with Jupiter; but each new orbit must traverse this dangerous point. This follows directly from the laws of orbital motion around an attracting centre. A body will continue to revolve in any orbit along which it has once begun to move, unless it is acted upon by some extraneous force. Accordingly, if at any point of its path an extraneous force suddenly disturb its motion, the disturbed orbit cannot fail to pass through the point of disturbance. Thus the body may again fall under the influence of the disturbing agent, and be caused to move in yet another orbit through the same point. And in the course of millions of years, a body might thus travel in a hundred different orbits, all passing through a common point. There is, indeed, one way in which Lexell's comet might have escaped from Jupiter's control. If after one of its encounters with Jupiter, it happened to pursue a path which brought it very nearly into contact with Saturn or some other large planet, it might be compelled thenceforth to abandon its allegiance to Jupiter. But the probability of this happening to a comet which had once got into the toils, may be reckoned 'almost at naked nothing.'

We have been careful to dwell on this point for a reason which will appear presently.

The search for Lexell's comet led to the discovery of a considerable number of nebulae; and the discovery of nebulae led in turn to the discovery of another comet of small period. In 1786 Mechain announced to Messier (who had constructed a list of 103 nebulae) that he had discovered a nebulous object. This turned out to be a telescopic comet. It was again seen by Miss Caroline Herschel in 1795, by Thulis in 1805, and by Pons in 1818. All this time no suspicion had arisen that these observers had seen the same object. But in 1818 the comet remained in view so long that it became possible to calculate its orbit. This was done by the German mathematician Encke, who found that the orbit is an ellipse, and the period of revolution about three years and four months. He found, after a laborious process of calculation, that it could be no other than the object that attracted attention in 1786, 1795, and 1805. Encke then applied himself to calculate the next return of the comet, which he did so successfully that astronomers have continued to call by his name the object whose motions he had been the first to interpret.

Encke's comet was seen by one observer only in 1822, as it was not favourably situated for observation in the northern hemisphere-that observer was M. Rumker, who followed the comet for three weeks at the private observatory of Sir T. M. Brisbane at Paramatta. In 1825, the comet was detected by several independent observers. It was seen again in 1828, being detected by two observers - Harding at Gottin--gen, and Gambart at Marseilles. In 1832 and 1835, it was seen from the observatory at the Cape of (rood Hope.

At the next return of the comet, which took place on December 9, it was visible to the naked eye for the first time since its discovery. At this passage, also, a very noteworthy peculiarity was remarked-or rather a peculiarity which had been remarked by Encke in 1818, was now, for the first time, placed beyond a doubt. Encke had suspected that the comet's period was slowly diminishing. Each return to perihelion occurred about two and a half hours before the calculated time. Such a discrepancy may appear very trifling, and in fact it might seem that no certainty could be felt respecting it; and this is the case so far as one or two revolutions are concerned. But when each successive revolution shows the same discrepancy, the deficiency soon mounts up to a period respecting which no doubt can be entertained. For example, between the perihelion passage in 1789 and that of 1865, the comet has made twenty-three revolutions, and each has been less than the preceding by two and a half hours (on the average). Hence, the last revolution of the series occupied two days and a half less than the first. But even this does not express the full effect of the change; for the comet having gained two and a half hours in the first revolution, five in the next, seven and a half in the next, and so on-it is the sum of all these gains (and not the gain made in the last revolution) which expresses the total gain of the comet in point of time. Hence the last perihelion passage occurred twenty-nine days before the time at which it would have taken place, but for some unknown cause which has interfered with the comet's motion. What that cause may be, has not yet been certainly determined; but it is at least highly probable that Encke has assigned the true cause in suggesting that so light a substance as the comet may be retarded in its passage through the interplanetary spaces by the existence of 'a thin ethereal medium,' incapable of perceptibly retarding the motion of the planets.

At first sight, it may seem strange that we should speak of the acceleration of the comet as being caused by the retarding influence of such a medium as has been conceived to occupy the interplanetary spaces. Yet it is strictly the case that, if a planet or comet be continually checked in its onward course, its velocity will continually grow greater and greater. For instance, if our earth were so checked, it would move in a spiral which would gradually bring its orbit to that of Venus, by which time its motion would be as rapid as that of Venus (which moves one-third faster than the earth); then it would continue revolving in a spiral till it reached the orbit of Mercury, when it would be moving as fast as this the swiftest of all the planets. And so the earth would continue to approach the sun with continually increasing velocity.