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want stations where the acceleration is greatest and where the retardation is greatest. The first lie at the point where accelerated ingress is written. We must not choose a station at this point, because there the Sun would be on the horizon, and therefore distorted; but taking the line representing the places where ingress is beginning a minute or so later we see that it passes near Woahoo and Hawaii. These, then, are good stations for observing this phase. Three or four minutes later the line passes Jeddo, Bonin, Marquesas, Otaheite, and so on; and these, therefore, though not such good stations as Hawaii or Woahoo, are still excellent. We may note, too, that at these stations the Sun will have a greater elevation, the actual elevation at different stations being indicated by the concentric circles marked with degrees.
As respects retarded ingress, we see that the best station is Crozet Island, close by the point marked retarded ingress. But Kerguelen's Island, Macdonald Island, Amsterdam Island, as also Rodriguez, Mauritius, and Bourbon, are all good stations for observing this phase.
Now let us turn to Plate X. to determine what stations are best for observing accelerated and retarded egress.
It will be seen that the place marked accelerated egress falls inconveniently near to the south pole. Only when we reach the cross-lines marked 1 lm. and 10m. do we come on places where stations could be conveniently taken. The lines marked 9m. and 8m. bring us past several excellent stations in New Zealand; and then we come to stations in South Australia; and on the other side of the arrow-line we find Kemp Island, and (inferior, but still serviceable) the Macdonald Islands, Kerguelen, and Crozet.
Lastly, as respects retarded egress, we find an abundance ot excellent stations, the best being in Siberia and Eastern European Russia; but there are several excellent stations in India; * while Alexandria will supply a very suitable place of observation.
* The very best Btation in English territory, namely Peshawar—far superior to Alexandria both as respects the amount of retardation and
Tables at the close of this Appendix exhibit the actual amount of acceleration and retardatiom at the several stations indicated in these maps, and at some others not named in either plate.
Now, as respects Halley's method, it will be remembered (see page 33) that we have to consider that the whole transit for at least the beginning and end)* should be visible. We want stations (these will obviously be northern ones) where the transit will last as long a time as possible, and other stations where the transit will last as short a time as possible. We should therefore naturally look for northern stations where the transit begins as early as possiole and ends as late as possible, and vice versa as respects southern stations.
But when we consider Hawaii and Woahoo, where the transit begins at the earliest, we find, on turning to Plate X., that these stations will not suit our purpose; for in Plate X. they are not visible; in other words, before the end of transit Hawaii and Woahoo pass to the un-illuminated side of the Earth,—the Sun sets, in fact, and the end of the phenomenon cannot be seen. In like manner, if we take those stations shown in Plate X. which are most suitable for observing the retarded egress, we find that at the epoch represented in Plate X. they are not visible; in other words, they are on the un-illuminated side of the Earth, or the Sun has not yet risen at these stations when transit begins.
It needs but a brief study of the two Plates to see that the stations which give the longest duration are those in Mansolar olevation—had wholly escaped notice until my construction of Plate X. (reduced from the sixth plate of the original series drawn by me lor the Royal Astronomical Society, and published in vol. xxix. of their Proceedings) exhibited the advantages of this station.
* This parenthetical remark may seem strange at first sight; but it must be remembered that there are southern stations (though I do not say any in this case are available) where the beginning of the transit can be seen before sunset and the end after sunrise. It is only necessary to study Plates IX. and X. thoughtfully in order to see that this is the case.
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 lo74.*
* 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 Puiseuz 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 tho 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, wag 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 bo 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 1 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 any one will see by comparing figs. 95 and 9C 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. 95 and 96 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 tho 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 requisito 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.