The transit of 1761 (like that which will occur on December 6, 1882) was partially visible in England. It was observed at Greenwich by the Rev. Mr. Bliss, Astronomer Royal, and at Savile House, near London, by Mr. Short, "in presence," says the account, "of His Royal Highness the Duke of York, accompanied by their Royal Highnesses Prince William, Prince Henry, and Prince Frederick." A great number of observations* were made also in different parts of the world, and a sufficiently satisfactory determination of the sun's distance was deduced therefrom.

It was, however, in 1769 that the real attack was made. It was then that the famous expedition of Captain Cook, in the Endeavour, was made, England being the only country which had a station in the Pacific. The Arctic regions were visited also, a station being selected at Wardhus in North Lapland, where the following notable peculiarity was presented, the beginning of the transit was observed before sunset and the end after sunrise. There were also stations at Kola, Yakutsk in Siberia, Pekin, Manilla, Batavia, Hudson's Bay, St. Petersburg, St. Joseph in California, and many other places. In all there were no fewer than seventy-four observing stations, whereof fifty were in Europe.

The reader need hardly be reminded that the determination of the sun's distance which was until lately in use in our text-books of astronomy was based on the observations made during the transit of Venus in 1769. Nevertheless it has been shown that those observations, rightly interpreted, give a determination of the sun's distance according well with those which have been obtained by the best modern methods, whether these have depended on observations of the sun himself, or the moon, or Mars-or, lastly, of the swift flight of light.

And now let us briefly consider what is proposed to be done in the case of the transit which is approaching.

First, as to the methods named after Halley and Delisle, about which there has been so much said. Is it possible to indicate, in a way which non-mathematicians can readily understand, the principles on which these methods depend? It appears to me that it is. The point in which the explanations hitherto given have failed (when they have failed) is in this, that they have attempted to explain too much. It must be remembered that after all the general reader does

There were 63 observing stations in all, thus distributed :-13 in North Europe, 8 in England, 15 in France, 6 in Spain, Portugal, and Italy, 16 in Germany, and 3 in other places.

not want to know the details of the matter; he only requires general results. He does not need, for example, to be told precisely how the sun's distance is to be determined from observations of Venus; and probably has no time to follow an explanation, however lucid, which necessarily covers a good deal of ground, and requires throughout his close attention.

It seems to me that it is to the following points that the general reader's thoughts should be alone or at least primarily directed.

First, as to Delisle's method. The earth having size, it necessarily happens that as Venus crosses between the earth and the sun, she must appear to enter earlier on the sun's face as seen from some stations on the earth than as seen from others; and the same holds when she is leaving the sun's face. The larger the earth in proportion to the sun's distance the greater will these differences necessarily be. So that if we can tell exactly how great they are, for stations occupying known places on the earth, we can infer how large the earth is compared with the sun's distance,—which, of course, is precisely what astronomers want to know.

Now let us see how it

This is the principle of Delisle's method. is to be applied, and what difficulties it presents.

It is, of course, desirable to choose places where the difference in point of time is greatest. Theoretically, then, I should like to set an observer at that point of the earth's surface where the transit will begin earliest, and another at the point (almost exactly opposite) where the transit will begin latest. These two would (theoretically) be able to tell us all we want to know. To make assurance doubly sure, we might set an observer where the transit will end earliest, and another where it will end latest. Then their result could be compared with that obtained by the others, the two results agreeing, of course, perfectly, if all the observations were exactly made.

Practically, we cannot set observers on the exact spots here named, because they would see the sun on the horizon (for reasons which we need not enter into) just at the very time when they wanted to see him most distinctly, and no astronomer in his senses expects to see the sun distinctly in the telescope (however distinct he may seem to ordinary vision) when near the horizon. Observers, however, can be set at suitable places near the spots referred to.

But now let us consider what such a pair of observers as we have mentioned would have to do. Suppose both were observing the beginning of transit, and that each had a good chronometer showing Greenwich time, and could trust his chronometer implicitly. Then, if each entered in his note-book the time when

the transit began, the difference of these epochs would at once show all that astronomers want to know. But unfortunately this is impracticable. Chronometers are made, indeed, which keep wonderfully good time, even on long voyages. But no chronometer could be trusted to convey the true time from one place to its antipodes, correct within a few seconds; and this is a case where seconds are all important. This will be manifest when the actual circumstances of the case are considered. Thus, in the transit of 1874, two selected stations are Honolulu (in Woahoo) and Rodriguez, near the Mauritius. The transit begins about twenty-one minutes earlier at the former than at the latter station, and everything depends on the exact determination of that period of twenty-one minutes. We know already that the period will be about twentyone minutes; but what the observers are to find out is how much exactly it exceeds or falls short of twenty-one minutes. Just as accurately as they ascertain this, just so accurately will the sun's distance be ascertained. Now, in twenty-one minutes there are 1,260 seconds, and an error of twelve seconds will therefore correspond to nearly the hundredth part of the interval. The mistake in the estimate of the sun's distance would be, therefore, about one hundreth part of that distance, or upwards of 900,000 miles. Astronomers hope to do much better than this.

The observers are not going to trust, therefore, to so comparatively rough a process of determining how much sooner or later the transit begins. What they will have to do is to proceed scientifically to determine the longitude of their stations; that is, in reality, the difference of their time and Greenwich time. This will be done by observing the moon, and so difficult and delicate is the work where a great degree of accuracy is required, that the Astronomer Royal proposes to set his observers at work at their several stations three months before the transit begins. It will be seen, therefore, that whatever advantages Delisle's method may have, it requires very great care and much preliminary work. It is also necessarily very costly in its application. So that, supposing no mistake had been made, and that Delisle's method were the only available method, great credit would be due to this country for providing instruments and observers for no fewer than five stations at which the method is to be applied.

The difficulties do not end, however, with the determination of the longitude. The observer must not only know how much his local time differs from Greenwich time, but he must, at the epoch of observation, know what is his true local time. To explain this-if

his clock tells him the true time at which it is noon where he is stationed, then (if his longitude is determined) he knows the true time when it is noon at Greenwich; but, if his clock is wrong, the knowledge of his longitude will not help to set him right. Now the astronomer sets his clock right by observing the stars. It will therefore be desirable that for a few nights before and after the transit our observers at Woahoo and Rodriguez (and the rest, of course) should have clear nights, for otherwise their clocks are pretty certain to be a second or two wrong at the epoch of observation. It affords a gratifying proof of the confidence which the Astronomer Royal places in his plans, that he considers the probable error in the indication of time, on account of possible error in determining the longitude and possible clock-error combined, to be not more than a single second. In other words, the observer at Woahoo, say, will be able (according to the hopes of the Astronomer Royal) to decide certainly that the moment when he sees Venus just fully upon the sun is such and such a moment of Greenwich time, within one second either way; or, to put the matter more strikingly, if the observer at Woahoo, when he conceives Venus to have just made her entrance, calls out "now," then he will be able to say that that word was uttered while the pendulum beating seconds at Greenwich was making one particular double beat; so that, if observers were at Greenwich talking at the moment, and noting how the pendulum swung as their conversation progressed, the observer at Woahoo would know afterwards that he said "now" while some one of only four or five words had been uttered by his fellow astronomers at Greenwich. This is very marvellous, and I feel bound to add that -with full knowledge of the mastery attained by astronomers and horologists over all problems relating to the determination of timeit is in my opinion altogether improbable that this degree of accuracy will be secured.

I have said nothing of the difficulty which the observer will necessarily have to encounter in determining the exact moment when Venus has just fully entered upon the sun's face. Owing to a peculiar optical property, she appears slightly distorted when she is making her entrance (and correspondingly, of course, when she is making her exit). Thus, instead of the astronomer being able to determine the precise moment when a fine line of light appears between her black disc and the sun's edge, there is a clinging of the two outlines, and Venus appears at the last moment to leap from the sun's edge, so that in an instant there is a well-marked interval between the outlines. It is estimated that during the transit of 1769 the average error made

on this account amounted to about three seconds, and adopting this value it would follow (owing to the more slanting direction in which Venus will cross the sun's edge in 1874) that the probable error in 1874 will be about 44 seconds, supposing that there has been no improvement (since 1769) in observing skill and the construction of telescopes. Let it be remarked at this point that for the Astronomer Royal's present advocacy of Delisle's method to be maintained effectively this error, due to what is called "the clinging of Venus," must be assumed to be as large as possible, while the error arising in the determination of longitude and from clock-error must be assumed to be as small as possible. We have seen reason to believe that in setting this last-named error at probably less than a second, a somewhat bold assumption has been made. It seems permissible to remark that in estimating the error arising from the clinging of Venus on the supposition that there has been no improvement in observation since the year 1769, an equally daring (however effective) assumption has been made.

This leads us to the consideration of Halley's method, which is very much simpler than Delisle's and quite independent in principle. If two parallel lines be drawn across any part of a circle but its central zone, they will be unequal in length. So if Venus, as seen from two different stations on the earth, traverses two different paths across the sun's face, these paths will differ in length. They will differ so much the more as the stations are wider apart in a north and south direction. And the larger the earth (compared with the sun's distance) the farther apart relatively the stations can be put. Hence results a very obvious means of determining the sun's distance. For though two paths such as I have spoken of could not well be measured, nothing can be easier than to time Venus as she traverses them, and so to infer their relative length. The difference between the two intervals has to be ascertained, and thence can be deduced the distance of the sun as compared with the known dimensions of the earth.

Now here we have a process not requiring the knowledge of absolute time, that is, not requiring that the longitude should be accurately known, or the local time exactly ascertained. The longitude may be a minute or ten minutes in error, the clock may be an hour wrong, and yet the method can be applied effectively. For all that is wanted (besides, of course, such an approximation to the knowledge of the observer's geographical position as can be quite easily obtained) is that the length of time occupied by Venus in crossing the sun's face should be noted,-and for this it is only necessary