Now it happened that early in 1869 I was attracted to the examination of the subject of the coming transits, by the circumstance that the investigation applied to the matter by the Astronomer Royal had struck me as imperfect in method. I was interested, viewing the matter merely as a mathematical problem, to inquire what corrections might occur if all the niceties of research of which the question admitted were applied throughout the investigation. Working with this sole object in view, I analysed the whole matter in two independent ways, viz., first as a problem of calculation, and secondly as a geometrical problem. The results, perfectly concordant, differed so remarkably from those published by the Astronomer Royal, that I was constrained (in mere fealty to the cause of science) to submit them to the examination of the scientific world.

To begin with : Halley's method, of which,-in 1857, and again in 1864, and yet again in 1868,the Astronomer Royal had said that it is totally inapplicable in 1874, was found to be applicable under circumstances altogether more favourable than those which will exist in 1882.1 It was found not only to be applicable with 'To this last question the reply is easy. It chanced unfortunately that in 1857 the Astronomer Royal delivered a lecture on the subject of the now approaching Transits. In that lecture his great mistake had its origin. Intent on presenting the more striking and popular features of his subject, and in a way which would be clear and convincing to everyone, he was led to adopt a method of reasoning which on the face of it seems convincing enough (and which, indeed, is sound in itself); but the conclusions derived from which may be, and in the actual case are, dependent on certain details into which the Astronomer Royal neither then entered nor has ever entered since. It is the palpably convincing nature of the evidence at a first view which led to all the mischief. We will endeavour to give a brief but sufficient sketch of the line of argument.

1 The origin of this mistake on the Astronomer Royal's part is thus explained in an article in the 'Spectator' for March 1, 1873: 'Everyone is asking whether it is possible that an astronomer so eminent and so skilful as Sir George Airy-for the time is past when names need be concealed-can have made any serious mistake in a matter of this importance. And again, everyone is anxious to know precisely what mistake is imputed, and how it arose (granting that a mistake has been made).

'Let it be premised that, for applying Halley's method-or the English method, as it is often called-with advantage, what is wanted is that at some station the transit shall last as long as possible, while at another it shall last as short a time as possible. It matters nothing whether the increase or reduction of the time be obtained by a seeming change in the length of the line traversed by Venus, or by a change in the rate at which she seems to move during transit. So much premised, let it be noted that in 1874 Venus will cross the sun's face on a line placed somewhat as a line from the figure X to the figure I on a clock-face. As seen from northern stations, the line of transit will be advantage, but even more advantageously than De-lisle's.

lowered, and therefore manifestly will be lengthened. From southern stations, the line will be raised, and therefore shortened. We therefore set an observer at as northerly a station as we can, to get as great a lengthening as we can, and that is one point gained. We set an observer at as southerly a station as we can, and so get as great a shortening as possible, and that is a second point gained. But it is easily shown (we do not trouble our readers with the proof) that our northerly observer is so shifted by the earth's rotation while the transit is in progress that Venus is seemingly hastened on her course in transit. This shortens the time of transit at the northern station, and is discordant with the lengthening obtained by setting an observer as far north as possible. Here, then, is one point against us. Lastly, the southern station can be taken so as to give either a hastening or a retarding of Venus's motion, simply because the transit occurs in the southern summer, when places far south have no night, so that we can set the observer either where he will have the sun moving from east to west during the transit. or where he will have the sun moving from west to east. We set our observer so that Venus is hastened (which is secured by taking a station where, during the transit, the sun moves from east to west). This hastening is manifestly accordant with the shortening of her path at southern stations, and thus we get a third point in our favour. We have, then, three points in our favour and one against us, or a balance of only two favourable points.

'Now, in 1882, Venus crosses the lower part of the sun's face, or somewhat as from figure VII to figure IV on a clock-face. In this case, the northern station gives the lowest or shortest course, while the southern gives the highest or longest course. As before, we get two points in our favour by setting an observer far to the north and another far to the south. As before, the northern observer sees Venus hastened on her course; but now this is a favourable point, since it manifestly accords with the shortening of the northern line of transit. This makes point three in our favour. And again, as before, we can set our southern observer where the motion of Venus can be hastened or retarded as we please. We assign him a station where she will be retarded (which is secured when the sun moves from west to east during the transit): this manifestly accords with the lengthening of her path. Thus we have four favourable points in all in 1882; whereas in 1874 we can secure only three or (one being unfavourable), a majority of only two favourable points.

'It seems manifest, then, that the transit of 1882 is twice as favour-