chouria, Japan, and North China, whose names are shown in both maps.

Now, as regards the southern stations where the shortest duration is to be observed, we have in some respects a wider selection, for the obvious reason that day lasts longer at these southern stations in December (a relation corresponding, of course, to the longer portions of southern latitude-parallels shown in both maps).

We require to find a southern station where the transit will begin as late and end as early as possible.

All the stations by the place of most retarded ingress in Plate IX. are shown also in Plate X., but in the latter plate they are seen to be very far from the place of most accelerated egress. On the other hand, the stations near the latter place in Plate X., though all visible in Plate IX., are seen in the latter plate to be very far from the place of most retarded ingress.

The best stations as respects proximity to both the place of retarded ingress and that of accelerated egress are Kemp Island, Enderby Land, Sabrina Land, and those in the neighbourhood of these spots. All are in very unsatisfactory and almost inaccessible regions of the Earth's surface.

It happens, however, that Crozet Island, Kerguelen Land, Royal Co. Island, and Macquarie Island give sufficiently shortened transit-periods to afford very satisfactory means of comparison, by Halley's method, with the lengthened transit-periods at Nertchinsk and other neighbouring northern stations.

As regards the elevation of the Sun the difficulty is of course greater at the northern than at the southern stations. But at all the northern stations marked in the maps the Sun will have an elevation exceeding ten degrees at the epochs of internal

contact.

On the whole, as will be inferred from the tables at the end of this Appendix, Halley's method will be applicable under very favourable conditions during the transit of 1874.*

*It will be seen that I express in the above paragraphs the opinion that Halley's method, which had been pronounced' wholly inapplicable'

Before proceeding to consider certain other matters belonging to the general subject, I will briefly discuss the transit of 1882.

to the transit of 1874, can be applied under very favourable conditions. In vol. xxix. of the Monthly Notices of the Royal Astronomical Society, I have exhibited the calculations requisite to indicate the probable relative values of Delisle's and Halley's method in 1874; and the conclusion to which these calculations point is that Halley's method is on the whole superior to Delisle's. Somewhat before my papers appeared, the French astronomer Puiseux had published a paper expressing his belief that Halley's method could be applied under conditions sufficiently favourable to render it advisable that that method, as well as Delisle's, should be employed. The actual results obtained by Puiseux gave, however, a slightly inferior position to Halley's method. The difference is due to the fact that M. Puiseux employed approximate instead of exact modes, considering the passage of Venus's centre, for example, instead of internal contacts, and taking no account of the equation of time. My results, not only as relates to the several methods, but as respects those cases in which I deduce different relative values for certain stations suitable for applying either Delisle's and Halley's method, have been now abundantly confirmed by the calculations of Peters, Hansen, and others. They were never indeed seriously questioned, because I was able to point to the exact places where my processes diverged from former and less exact computations, and to show how differences of considerable importance came thus to be discernible in the results. But I must disavow all desire to dwell upon or to magnify errors either of computation or of plan in the work of the eminent astronomer who preceded me in dealing with this problem. The work was not undertaken by me, as I fear the Astronomer Royal judged at the time, in any spirit of captious criticism. Deeply imbued with a sense of the extreme interest and importance of the problem of determining the Sun's distance, and attracted to it also by the exceedingly beautiful nature of the geometrical considerations it involves, I worked at it without any reference in the first place to the labours of others. Only when I found that my results differed in many respects (which seemed to me, and still seem, important) from the Astronomer Royal's, was I led to compare his processes with my own, and to trace out the causes which led to the difference in the results. I was prepared to find I had fallen into some error. As the reverse appeared, and as his results had been made widely public, and were, as I believed, to be made the basis of the choice of stations and methods for English observers in 1874, I should have been wanting in my allegiance to the cause of science had I failed to

In the first place it is well to have a picture indicating the relations which Plates IX. and X. indicate for the transit of 1874. The time has not yet come, perhaps, when so carefullyconstructed a drawing is needed; but a drawing of a somewhat similar nature is essential to the adequate illustration of the subject. I might avail myself here of the Astronomer Royal's two drawings, which will be found in Guillemin's 'Heavens' (and are repeated, with Mr. Airy's statements, in Mr. Lockyer's 'Elementary Lessons of Astronomy'); for the corrections involved by the considerations I have attended to in the case of the transit of 1874, have (for reasons which need not be entered into) a far less important effect in the case of the later transit. But I do not find myself on the whole content to adopt this course, partly because the differences (as anyone will see by comparing figs. 104 and 105 with the Astronomer Royal's drawings) are quite appreciable; secondly, because the cross-lines which indicate the passage of the boundary of Venus's shadow-cone over the face of the Earth have not been separated by minute intervals, as in my maps (but by tenths of the total interval of passage), and are not quite correctly placed; and, thirdly, because I think it on the whole more worthy of the student of science to give his own work in such instances.

Figs. 104 and 105 show the exact presentation of the Earth

publish the results of my researches. One thing alone would have forced me to publish my results-namely, the fact that it had been widely announced that in 1882 Halley's method could be applied if certain Antarctic stations were reached, whereas my calculations serve to prove that there is absolutely no station where Halley's method can be applied in 1882 under conditions sufficiently favourable to warrant the dangerous expeditions and the protracted stay in Antarctic stations by which alone the requisite observations could be made. I repeat here, and urge as the main reason for the earnestness with which I have pressed my views, that to send expeditions to survey the neighbourhood of the proposed stations near Victoria Land and Repulse Bay, and to select either of these neighbourhoods for wintering, in anticipation of the summer (Antarctic) transit of 1882, would be to risk the lives of British seamen and men of science without any prospect of adequate return.

at the beginning 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 Antarctic regions. Kerguelen's TRANSIT OF 1882. (INGRESS.)

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

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

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 (fourteen years at least) that Halley's method is only