HALLEY versus DELISLE : THE COMING TRANSIT OF
FROM the tone of Mr. Goschen's reply to a question of Sir John Lubbock's respecting the approaching Transit of Venus, many have been led to imagine that Halley's method of observing a transit is an obsolete and almost useless contrivance, while Delisle's is a new and more scientific process, leading to a much greater degree of accuracy. A brief explanation will remove this erroneous impression.
In the first place, it is to be noticed that Halley and Delisle were contemporaries, Delisle being only some twenty-five years the younger ; and both died before the famous Transit of 1769, when England so nobly acquitted herself of her duties as the chief Naval country in the world.
There is no simpler way of comparing the processes suggested by these two astronomers, than by considering the actual applica- tion of the processes in two typical cases. We begin with Delisle's method. The stations we consider are Honolulu (Sand- wich Islands) and Rodriguez.
On the morning of December 9, at about five minutes past two, Greenwich time, the planet Venus will just have made her com- plete entrance on the San's face, as seen from Honolulu. At this moment the local time at Hoaolulu will be about 33 minutes past 3 on the afternoon of December 8. The observers stationed there will have to determine as nearly as they can the true moment when Venus just touches the sun's edge on the inside. This coin-
pleted, they will have little left to do as the sun draws towards the horizon, and sunset will occur before the transit is half over.
Now about 21 minutes later the observers stationed at Rodriguez will have their turn. With them, however, it will be about 38 minutes past 6 on the morning of December 9, when Venus is just seen fully upon the Sun's disc. They must determine the true moment when this happens, and then they can watch the rest of the transit (if they care to do so, and are not afraid of incurring the displeasure of the Astronomer-Royal by a kind of observa- tion which he has not seen fit to sanction). Their business at Rodriguez, however, is solely to time the moment of Venus's ingress on the disc.
And now let us consider in what way the results obtained at Honolulu and Rodriguez are to be utilised, and on what their value depends.
If the observer at Honolulu knows the exact longitude of his station, he can at once convert the observed time into Greenwich time. The determination of longitude is, however, so difficult a matter, that some error will necessarily accrue in this process. The Astronomer-Royal believes that this error can be reduced to a single second, which, considering some recent instances in which the longitudes of well-known stations have been found to be two or three seconds in error, indicates a well-marked confidence in the observational processes to be employed at these distant stations. Next it is to be noted that to make the time-observation correct, the clock should show true time, and it does not seem altogether impossible that the clock may be a second or two in error. It is, at any rate, in our opinion, a rather bold assumption on Sir G. Airy's part that the error due to this cause, combined with the last named, will probably amount but to i single second. Lastly, the observer is likely to make some slight mistake in estimating the true moment when Venus will be in contact with the sun's edge. Mr. Stone, recently First Assistant at Greenwich, from his examination of the corresponding errors made in 1769, sets four- and-a-quarter seconds as the probable error on this account. (See vol. xxix. of the "Monthly Notices" of the Astronomical Society, p. 252.) It is barely possible that if an effort were being made by the Astronomer-Royal to minimise this probable error, instead of the reverse, the idea would present itself that, owing to improve- ments in observational- means and experience, the error made in this way is likely to be appreciably less in 1874, than we should infer from the work of the old observers in 1769. Let this pass, however, with the rest.
The same remarks being applicable to the case of Rodriguez, we see that the comparison of epochs at this pair of stations will be affected by four errors, two of which will probably amount to one second, while the other two will probably amount to four-and-a- quarter seconds, according to the Astronomer-Royal's view.
Subject to these errors, the observations will have established the absolute difference in point of time between the moments of Venus's ingress as seen at Honolulu and at Rodriguez, this
difference being about 21 minutes. Of course, the whole aim of the observers is to determine this interval exactly, and their success depends on the smallness of the error, not in itself, but as compared with the total interval.
Now let us take a case of the application of Halley's method. And fortunately, notwithstanding all that has been said, there are northern stations actually to be occupied where the whole transit can be seen, and where, therefore, Halley's method can be applied. We take Tchefoo, not by any means the most suitable northern station, but because it is to be occupied by a German observing-party ; and as a southern station, we take Kerguelen's Island, where an English observing-party will be stationed (bat presumably with careful instructions not to attempt to apply Halley's method, lest by so doing they should seem to reflect on the Astronomer-Royal).
Now, in this case, we shall not weary our readers by naming the hours, either of Greenwich or local time, when the transit will begin and end. The observers, indeed, if they were satisfied with Halley's method, would have no occasion to trouble themselves about Greenwich time,—that is, about their longitude. All the expense of that three months' stay which the Astronomer-Royal insists on (very properly) as necessary to determine the longitude could be dispensed with. The observers would only require a clock going at true rate during the four hours or so that the transit will last. It would not matter even though the clock were an hour wrong, so that it went at the true rate. If they arrived at these stations in sufficient time to set up their instruments, &c., that would be all they would require. But let us see what they have to observe. Each must time the duration of the transit from ingress to egress, and it is by comparing the observed durations that their
observations are to be utilised. Therefore each has to note two contacts of Venus. According to the Astronomer-Royal's opinion, that the instruments and observers of our day are about equal to those of 1769, each of the four observations is likely to be about 41 seconds in error. In Delisle's case, it will be remembered, only two of the errors were likely to be so great, the other two each amounting (according to the sanguine views of the Astronomer- Royal) to about one second only. But the actual difference of duration at Tchefoo and Kerguelen Island will amount to about 30 minutes. In the former case, it will be remembered, the time interval to be measured amounted to about 21 minutes. So that Delisle's method has the advantage in one respect, Halley's in the other. Which advantage prevails? We do not trouble our readers with the comparison of the probable effects of the four errors in each case, because in point of fact it depends on mathematical considerations not altogether elementary. We simply give results. Mr. Proctor adopting, for the sake of argument, the Astronomer- Royal's figures, showed in 1869 (and the Astronomer-Royal, having gone over the calculations, admits the accuracy of the result) that the advantage of Delisle's method, in the comparative smallness of two out of the four probable errors, corresponds to an increase of the time-interval in the proportion of 1,377 to 1,000. Now if we increase 21 min. in this degree we obtain a time-interval of 29 min. But we have seen that the difference of the duration of the transit as seen at Tchefoo and Kerguelen Island amounts to 30 min. It follows, therefore, by the Astronomer-Royal's own test, that Halley's method. even as applied at these stations (which, be it observed, are not merely accessible, but are actually to be occupied), has a measurable superiority. By selecting other stations, a difference of duration of 33 min. can readily be obtained ; and if Nertchinsk and Enderby Land were occupied, the difference would amount to more than 353- min. Over and above this calculated superiority, Halley's method is very much simpler, is much less costly in application, it would spread the observers (and so reduce the chances of failure through bad weather), and lastly, it is an independent method, and, as the Astronomer-Royal once said, every independent method should be applied.
Either, then, Mr. Goschen was misinformed, or he misappre- hended what had been stated to him, when he said that little reliance could be placed on Halley's method ; and that "Delisle's would be greatly superior." For in the above discussion we have applied to unquestionable actual values, the tests not of an up- holder of Halley's method (like Mr. Proctor at present and Sir G. Airy until his recent sudden change of view), but those insisted on by Sir G. Airy himself in the full ardour of his new zeal for Delisle's method.
But there is a new method, probably superior to both Delisle's and Halley's, which has been advocated by the German and American astronomers of late. It was first suggested, we believe (we are not quite sure, however, as to his priority), by Mr. Proctor, and is referred to in the first edition of "The Sun," p. 450. It requires the actual determination of Venus's place on the sun's face at successive epochs throughout the transit. In the days of Halley and Delisle, the application of such a process was out of the question ; for whatever Sir George Airy and Mr. Stone may say, astronomers have improved a little since those days. The Germans are going to apply it at Tchefoo and Macdonald Island (one of Mr. Proctor's suggested stations, and altogether overlooked till he noted its advantages). Now we beg to invite the close attention of our readers to one very remarkable fact. England is going to occupy Alexandria, because there the transit will end about ten minutes late. This phase will be observed soon after sunrise, the sun being only 14 degrees above the horizon, and of course when the sun rises the transit will be already more than half over. Now at stations in North India, and therefore pecu- liarly calling for British occupation, the transit will end quite as late as at Alexandria, and instead of being but partially seen, the whole transit will be visible, the critical phase (egress) occurring with a well elevated sun. So that here, —(1) Delisle's method can be applied with a high sun, which is not the case at Alexandria ; and (2) Halley's method can also be applied, which is not the case at Alexandria ; and (3) the new method above referred to can be applied in North India, and not at Alexandria. Yet because by an oversight (and some very peculiar mapping processes) these North Indian stations were completely overlooked by the Astronomer-Royal (see "Monthly Notices " of the Astronomical Society for December, 1868, p. 37), he has declined as definitely to sanction an observing station in this region, as to correct that other mistake according to which Halley's method "fails totally" in 1874. We would ask whether the Astronomer-Royal thinks his fame so weakly
established that he cannot afford to correct demonstrated mistakes. If so, we venture to say he is the only person living who has formed so low an estimate of the esteem and honour in which Sir George Airy is justly held.