begins (or ends) nearly at the earliest, and that another should obtain a favourable view of the same phase at some place where the transit begins (or ends as the case may be) nearly at the latest. Both observers must time the commencement (or end) of the transit most carefully. Then to compare the two observations, in order to tell the absolute interval of time between the two, we must know the exact longitude of the two places; for the observations will of course be referred to local time, so that in order to compare them, we must refer them to some standard time, as that of Greenwich or Paris.

Here, then, are the difficulties in Delisle's method: unless the longitude of each station is accurately known, and furthermore, the exact local time at which transit begins or ends, the determination of the Sun's distance will be inexact. As respects the former point there is little difficulty, only the observers must stay some time at their respective stations, making suitable observations to determine the longitude of the station. This can be done either before or after the transit as may be convenient. But as respects the determination of the local time at which the transit begins (or ends as the case may be), there will be a difficulty if bad weather precede and follow the epoch at which the phase occurs. For we can only determine local time exactly when the weather is clear, so that we can make suitable observations on the stars; and during a few days of cloudy weather, the best astronomical time-pieces will get a second or two wrong.

In

Halley's method the clock may be altogether wrong, yet if its rate be fairly good, the duration of the transit. will be accurately determined; but in Delisle's the clock must show absolutely correct time.

Here again, however, the difficulties, so far from being insuperable, are only such as astronomers are in the habit of dealing with and mastering.

Both methods were applied during the two transits of the eighteenth century. Of these one took place in June 1761, and the other in June 1769. Both occurring during the summer of the northern hemisphere, the Earth's northern pole was bowed towards the Sun; and in this respect the circumstances of the transits differed importantly from those of the transits which are to occur in 1874 and 1882, for both these will take place in December, when the southern pole of the Earth is bowed towards the Sun.

The transit of 1761 was not observed in a very satisfactory manner. It was a transit for the observation of which Delisle's method was somewhat better suited than Halley's,* and the astronomers of the eighteenth

*It is worthy of notice that in the case of two transits separated by an interval of eight years, the former is commonly best suited for Delisle's method, the latter for Halley's. Both the transits will occur at the same season, that is, Venus will either be near her ascending node at both transits, or near her descending node at both. For an interval of eight years corresponds almost exactly to thirteen revolutions of Venus, so that, supposing Venus near a node when in inferior conjunction, she will be near her node at the conjunction occurring eight years later (or after five synodical revolutions). Now, it so happens, that the line of these successive conjunctions in the same neighbourhood continually regrades round the ecliptic, one interval being in fact about 2 days less than eight years. Thus the latitude of Venus at successive eight

century were not so well prepared to deal with the difficulties of that method as those of our time will

yearly conjunctions near a node differs by the amount of Venus's motion in latitude (near a node) in the course of 24 days. Thus the apparent path of Venus across the Sun's disc would (as supposed to be seen from the Earth's centre) be as 1 1, 2 2, fig. 13 (1), when she is near her FIG. 13.

rising node or when both the transits are December ones; and as 3 3, 4 4, fig. 13 (1), when she is at a descending node, or when both the transits are June ones. [The distance between 1, 1 and 2, 2-and between 3, 3 and 4, 4, would be about that shown in the figure, and the slope with reference to the ecliptic is of course the same (approximately) in all transits. But the pair of lines may have any position whatever as respects distance from the Sun's centre. Now, if either line in either figure falls very near the centre of the Sun's disc the other will not fall on the Sun, and there will be only one transit during those years when this conjunction is travelling past the node. This will happen in no inconsiderable proportion of these passages-a circumstance requiring notice because our treatises on astronomy commonly assert that transits of Venus occur at successive intervals of 8, 121, 8, 105, 8, 121, &c. years, which is far from being strictly correct. In fact, instead of two transits occurring at every such passage, very nearly half the passages would supply only one transit. The list in Lalande's astronomy is wholly untrustworthy in this respect, as any one will find who will calculate the distances of Venus from her nodes at the conjunctions referred to in that list.] To resume;-Taking the case of December transits illustrated by fig. 13, we see that at the first transit when the path is as 1, 1, the northern station from which the path will appear lowest down on the Sun's disc, will give the longest interval; and the advantage of applying Halley's method will depend on the greatness of this interval as compared with the shorter interval during which the transit lasts as seen from some southern station. Now the Earth is rotating, and the effect of the Earth's rotation considered alone is to give Venus a continual slight westerly displacement in all places where the Sun is

prove themselves.

Yet the result of the observations then made, which were interpreted as giving a solar

moving from east to west-that is, at all places save those close by the south pole, at which the Sun (being above the horizon all day, or nearly all day), moves through part of the day from west to east. Hence at northern stations, where Venus's path is longest, she is hastened on her path by this westerly displacement; and so the lengthening of her period of transit is diminished and the value of Halley's method pro tanto reduced. At southern stations the shortening will be increased at places where the transit occurs during the mid-day hours, and diminished where the transit occurs during the midnight (nominal) hours. But at the former stations the apparent path of Venus will not be thrown so far south as at the latter; so that at the southern stations also we find that the greatest possible shortening due to parallax cannot be combined with an additional shortening due to the Earth's motion of rotation. But at the second transit of this set-when Venus appears to follow such a path as 2, 2 (fig. 13), the reverse is the case. At the northern station Venus's path is thrown southwards and so shortened, while her motion across the Sun's disc is hastened (by the effects of the Earth's rotation) and therefore also shortened; whereas at the southern stations, where Venus's path is most lengthened, her motion across the Sun's face is retarded and so lengthened. Halley's method is then applicable under the most favourable conditions for securing a considerable time-difference. Similarly, it may be shown that at a June transit, when Venus's path is as 3, 3 (the first of a pair), Halley's method is not so favourably applicable as at a June transit when her path is as 4, 4 (the second of a pair).

Theoretically this is just, but practically, especially in December transits, the difficulty of securing suitable stations near the pole which is turned towards the Sun, may altogether change the conditions. As a matter of fact, indeed, the approaching transits of 1874 and 1882 are exceptions to the rule; and I have been able to demonstrate that, so far from Halley's method being most favourably applicable in 1882 (as the Astronomer-Royal had inferred from reasoning resembling the above), there is no reasonable chance of its being applied at all in 1882, the only two southern stations where it is possible to apply the method being such that the Sun will be barely 5° above the horizon, a state of things preventing all exact observation, and assuredly not justifying expeditions to stations so near the south pole that the observing parties would inevitably have to winter there. On the other hand, I have also been able to demonstrate that Halley's method, besides all the advantages

parallax of 8"-65, corresponding to a mean distance of about 94,500,000 miles,* was a great improvement on any before obtained—and better, in fact (though this was due to chance), than that deduced from the more complete and satisfactory observations made in 1769.

The transit of June 1769 attracted an amount of attention both in England and on the Continent which afforded very creditable evidence of the scientific enthusiasm of the men of the last century. The Royal Society presented a memorial to King George III., requesting that a vessel might be fitted out at Government expense to convey skilful observers to one of the stations which had been judged suitable for observing the phenomenon. The petition was complied with, and after some difficulty as to the choice of a leader,

arising from its simplicity, will be applicable under more favourable circumstances than Delisle's, in 1874. It is necessary to observe that there is nothing hypothetical about this conclusion. The difference between my conclusions and those before adopted arises simply from my having taken into consideration facts which had been (mistakenly) imagined to be such as might safely be neglected. Since my results were published, papers by Peters, of Altona, and by Hansen, the eminent German mathematician, have confirmed all the views I had insisted upon. See further, Appendix A.

It is convenient to notice that if the solar parallax were 10" the distance of the Sun would be 81,738,420; and the distance corresponding to any other value of the parallax can be deduced by simply dividing 817,384,200 by the number expressing such parallax. The table in Ferguson's Astronomy, complacently quoted in Chamber's Handbook, at p. 248, is incorrect, owing to the erroneous estimate of the Earth's mean diameter on which the table is based. Oddly enough, Mr. Chambers has combined the correct estimate for the parallax at present adopted, with Ferguson's incorrect values. It would almost appear as though the figures had been simply quoted without being tested in any way, were not such an idea incredible.