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at the begining and end of the transit of 1882. The general relations indicated correspond precisely to those dealt with already.

As regards the application of Delisle's method at ingress, we have for the accelerated phase few convenient stations, those best situated being very near the Antartic regions. Kerguelen's TRANSIT OF 1882. (INGRESS.)

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Illuminated side of the Earth at ingress, Dec. 6, 2h. 15m. 56s

(Greenwich mean time.)

Land, parts of Madagascar, and the Cape of Good Hope seem the best. The retarded phase can be viewed under singularly favourable circumstances, however, since the whole seaboard of the United States and many inland towns there and in Canada fall close by the place of most retarded ingress. Many West Indian stations also seem not unsuitable.

As regards egress, we also find a number of well-suited

stations, many of which are identical with those just referred to as well suited for observing the retarded ingress. It is well that these doubly fortunate stations are American, since our American brethren in science are far more warmly supported by their Government than ours are (or perhaps I

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Illuminated side of the Earth at egress, Dec. 6, 8h. Om. 32s.
(Greenwich mean time.)

should say their cause is far more warmly advocated before their Government).

Retarded egress can be observed favourably in New Zealand, and parts of Australia.

Now, as respects the application of Halley's method, I find myself approaching a delicate subject. It has been so long asserted (thirteen years at least) that Halley's method is only

applicable in 1882, that many will be disposed to ridicule the notion that there can have been any mistake in the matter. Yet, confident in the simple mathematical relations dealt with (and confirmed also by the view of the matter now steadily growing among mathematicians), I point to figs. 95 and 96, and ask where the stations are to be placed? So far as the shortened transit observed in northern stations is concerned, there is no difficulty; since, as we have seen, the commencement of the transit will be most retarded at the very stations where the end will be most accelerated-that is, in the United States, Bermuda, the West Indies, and so on. But as regards a southern station where the transit shall be most lengthened, the case is not so simple. The Astronomer Royal has pointed to two southern stations-one at Repulse Bay, near Sabrina Land, and one near Victoria Land. These are shown on the map. There is a double objection to Repulse Bay. First, the Sun will have an elevation of but about 4 degrees both at ingress and egress; and, secondly, there is no known station there. The suggested station' marked in Mr. Airy's maps (December number of Monthly Notices of Royal Astronomical Society' for 1868-69) at Victoria Land, occupies a spot on a shore line (explored by Captain Sir J. C. Ross) so precipitous that Ross could not approach it, though he would readily have given his right arm' for an anchorage there. At Possession Island near by, a place where his men landed but were compelled to leave by the fearful odour of the accumulated penguin guano, the Sun would have the totally insufficient elevation of but about 5 degrees at ingress.

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Now, remembering that it has been shown by skilful Arctic and Antarctic seamen that to make observations at these socalled stations on December 6, 1882, astronomers would have to winter there (making their way to them in February or March, 1882, at latest), it surely will not be thought that the poor observations which could alone be made on a Sun but 4 or 5 degrees above the horizon are worth the expense and great risk which must needs be involved. But even if they were, then à fortiori would the application of Halley's method in

1874 be called for; since I have been able to demonstrate that without seeking such dismal regions, a more favourable opportunity will be afforded in 1874 than in 1882, even on the supposition that the selected stations were visited during the latter transit. And this result has been confirmed by mathematicians of eminence.

As regards other southern stations in 1882, it needs but a brief study of figs. 95 and 96, to see that none are available. All the stations on the right of the arrow-line in fig. 95, ard close by the arrow-feather, are unseen in fig. 96—that is, the Sun has set at those stations. The barren Antarctic land south of Cape Horn (Graham Land) is not very favourably situated in fig. 95, but in fig. 97 has passed over to the wrong side of the central cross-line; in other words, there is acceleration of egress instead of the needed retardation. Similar remarks apply to the southern parts of South America.*

So far, then, is it from being true that Halley's method is wholly inapplicable in 1874 but is applicable under favourable circumstances in 1882, that the exact reverse is the case. Halley's method is even better than Delisle's in 1874, and is wholly inapplicable in 1882.†

The reasoning in the note beginning on p. 37 will be found to be well illustrated by a comparison of Plates IX. and X. with figs. 95 and 96. It will be seen that in the transit of 1874 the rotation of the Earth carries the northern stations the wrong way as regards that lengthening which is required; while in the transit of 1882 the northern stations are carried the right way for the shortening which is required. As to the southern stations, it will be seen how, according as they lie above or below the pole (as shown in the maps), the lengthening or shortening can be increased or diminished. It is the fact that no stations below the pole are suitable in 1882, which spoils the otherwise sound reasoning of the Astronomer Royal.

It will be seen from fig. 93 that the path of the Earth crosses the surface of the shadow-cone much more obliquely in 1874 than in 1882; and, as this path is as it were the reflexion of the apparent path of Venus over the Sun's disc, Venus crosses the limb much more obliquely in 1874 than in 1882. Thus the actual progress of ingress and egress must take place much more slowly. Mr. Stone believes that all time-errors will be correspondingly increased. The comparison above referred to is founded G G

And now I propose to indicate, in conclusion, considerations which lead me to believe that the direct method of determining the actual parallactic displacement of Venus on the Sun's disc can be applied under very favourable circumstances during the approaching transits.

Let us first consider if we cannot in part diminish the difficulties which seem inherent in this method.

Suppose an observer at one station sees Venus at a given epoch as at a (fig. 97, I.), while at the same epoch another observer sees her at B. Then it is perfectly obvious that in such a case as is illustrated by I., when the two observations

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Illustrating the displacement of Venus as seen from different
terrestrial stations during transit.

are brought into comparison, any error affecting the bearing of B or A from C will tend to produce its full effect in increas ing or diminishing the parallactic displacement separating A and B. But now suppose that a and b in II. represent the

on this opinion, very unfavourable to my views. I must, however, express my own conviction that though the time-errors will be larger in 1874 they will not be proportionately increased. The slowness of ingress and egress will give the observer an opportunity of observing the features of ingress and egress more satisfactorily. Especially if my suggestion is attended to as regards the breadth of the ligament at the moment of breaking or forming (see p. 63) will this be the case. Apart from this, as all the time-differences are increased precisely in proportion to the slowness of ingress or egress, a very slanting passage is cæteris paribus as favourable as a more direct one.

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