On this point all doubts should have been very quickly removed. For, almost simultaneously with able for applying Halley's method as the transit of 1874. So the Astronomer Royal concluded. He did not enter into details, but after summing up the evidence much as we have done above, he said "the observable difference of duration in 1874 will probably not be half of that in 1882." It was in 1857 that he thus spoke; and he has never said a word or written a line since that time implying that he had gone into the details of the matter. When he next touched on the subject (in 1864) he referred to the lecture of 1857 as showing the suitability of Halley's method in 1882, and he left the transit of 1874 wholly unnoticed. Again, in December 1868, he touched on the matter, simply saying that Halley's method fails totally in 1874. That fatal lecture, or rather the error suggested in the process of popularising the subject for that occasion, led to so established a conviction as to the uselessness of Halley's method in 1874, that it had never seemed worth while to re-examine the matter. But now let us consider details a little, and see how the matter will then appear.
'In the first place, the transit of 1882 at once loses its apparent superiority. The southern observer must have the sun moving from west to east during the transit,-or in other words, he must have the sun on the night side (so to speak) of the sky. There is, of course, no night near the Antarctic Pole on December 6, but at nominal midnight the sun is at its lowest; and the sun must be towards this part of his diurnal course, if the observer is to get the advantage we are considering. There is no known Antarctic station where this can be, the sun being also fairly high at the beginning and end of the transit. This at once disposes of the superiority of the transit of 1882. If an Antarctic station is sought at all, there will be a hastening instead of a retarding of the planet's transit,-or an unfavourable point, as in the case of the earlier transit. In reality, the loss thus accruing is found to be much more serious in 1882 than the corresponding loss in 1874, when we inquire into actual details.
'But in 1874, as we have seen, there must be an unfavourable hastening of Venus's motion as seen from a northern station; and this hastening seems to cancel the effect due to the lengthened transit-path. When we inquire, however, to what extent this cancelling takes place, we at once see that the Astronomer Royal was frightened away from Halley's method without sufficient reason. He manifestly (see the italicised remark quoted above) supposed that the duration would scarcely be increased at all at the northern station. Let us see, however, whether Mr. Proctor has been right or not in saying that the duration is conthe announcement of my result, the news arrived that the French astronomer, Puiseux, had obtained almost siderably increased at a suitable northern station, notwithstanding the undoubted partial cancelling which takes place from the cause indicated. Not to favour one side or the other, we go direct to the Nautical Almanack for 1874. We take Nertchinsk, the place pointed to by Mr. Proctor so far back as March 1869; and we note that he then assigned to this station a lengthening of the duration of transit by 15 1/2 minutes (a very considerable amount, much more in fact than at the most favourable station in 1882). Now, what says the Nautical Almanack for 1874? At page 434, it states that the mean duration of transit is 3 hours 42 min. 2 sec. At page 20 of the appendix, it states that at Nertchinsk the duration is 3 hours 57 min. 6 sec, exceeding the former duration by 15 min. 4 see. This is very close indeed to Mr. Proctor's result, and shows how nearly the values obtained by his graphic constructions accord with those deduced by rigid calculation. (Moreover, a part even of the slight difference is due to a difference in the adopted value of Venus's diameter.) Here, then, instead of that complete cancelling of the value of the northern station which Sir G. Airy too hastily assumed, we have a lengthening of the transit period by more than 15 minutes, which in this problem is an unusually large amount. To show that this is so, and how slightly the northern station is affected by the peculiarity which Sir G. Airy had hastily regarded as introducing a fatal objection, we have only to remark that at Possession Island, the most favourable southern station (where the two conditions conspire, instead of opposing each other), the shortening of the transit amounts only to 17 1/2 minutes. Combining this shortening with the lengthening at Nertchinsk, we have a difference of duration of fully 32 1/2 minutes. And now observe how greatly this result differs from Sir G. Airy's anticipation ! He thought the difference of duration would probably "not be half of that in 1882 "; but his own estimate of the greatest difference of duration in 1882 (to be obtained only by seeking an inaccessible station, where the sun will be but four degrees high at egress) amounts only to 28 minutes. Instead of being less than half, the difference of duration in 1874 is greater in the proportion of about 7 to 6. Add to this that in 1874 the solar elevation, both at ingress and egress will exceed twenty degrees, and the importance of having a station at Possession Island becomes manifest. Russia has occupied Nertchinsk, and it is Great Britain's duty (and that of no other country) to occupy Possession Island. If she shrinks from this duty, it will be no answer to the reproach which she will hereafter incur, that she occupied stations in other respects advantageous. Other countries are occupying these stations, the Papelotte exactly the same conclusion. The sole difference between his result and mine was, that he simply announced that Halley's method was advantageously applicable, whereas I showed that it was more advantageously applicable than Delisle's. Even this differ-ance, however, is readily accounted for, since, in Puiseux's investigation, several of the niceties to which I had attended were neglected as unimportant.1