It would be natural, at the conclusion of this brief review of some types of astronomical discovery, to summarise the lessons indicated: but there is the important difficulty that there appear to be none. It has been pointed out as we proceeded that what seemed to be a safe deduction from one piece of history has been flatly contradicted by another; no sooner have we learnt that important results may be obtained by pursuing steadily a line of work in spite of the fact that it seems to have become tedious and unprofitable (as in the search for minor planets) than we are confronted with the possibility that by such simple devotion to the day's work we may be losing a great opportunity, as Challis did. We can scarcely go wrong in following up the study of residual phenomena in the wake of Bradley; but there is the important difficulty that we may be wholly unable to find a clue for the arrangement of our residuals, as is at present largely the case in meteorology. And, in general, human expectations are likely to be quite misleading, as has been shown in the last two chapters; the discoveries we desire may lie in the direction precisely opposite to that indicated by the best opinion at present available. There is no royal road to discovery, and though this statement may meet with such ready acceptance that it seems scarcely worth making, it is hoped that there may be sufficient of interest in the illustrations of its truth. The one positive conclusion which we may derive from the examples studied is that discoveries are seldom made without both hard work and conspicuous ability. A new planet, even as large as Uranus, does not reveal itself to a passive observer: thirteen times it may appear to such a one without fear of detection, until at last it encounters an alert Herschel, who suspects, tests, and verifies, and even then announces a comet--so little did he realise the whole truth. Fifteen years of unrequited labour before Astræa was found, nineteen years of observation before the discovery of nutation could be announced: how seldom do these years of toil present themselves to our imaginations when we glibly say that "Bradley discovered nutation," or "Hencke discovered Astræa"! That the necessary labour is so often forgotten must be my excuse for recalling attention to it somewhat persistently in these examples. But beyond the fact that he must work hard, it would seem as though there were little of value to tell the would-be discoverer. The situation has been well summarised by Jevons in his chapter on Induction in the "Principles of Science;" and his words will form a fitting conclusion to these chapters:--