centre as seen at that instant from any point of the Earth's sunlit hemisphere.

The chart itself shows clearly the relation between the strip of the Sun's disk (divided into three portions in the chart) and the outline of that disk. Moreover, the circles marked, and

- indicate by their intersection with the various transit chords, where external contact and internal contact respectively take place; for, manifestly, when Venus's centre, as seen from any station, is on the circle marked + (that is, is at a distance from the Sun's centre equal to the sum of his radius and Venus's) Venus must be at the moment, and as seen from that station, in external contact; and similarly she must be in internal contact when her centre, as seen from any station, is on the circle marked 0-19.

But Plate XIX. serves to show more clearly how the illustrative chart is to be interpreted. It shows the northern half of the Sun's disk, and indicates the relative dimensions of the disk of Venus and the Sun, as well as the maximum parallactic displacement of Venus.

I apprehend that it has been demonstrated that (i.) the Astronomer Royal's first and only discussion of the suitability of Halley's method in 1874 was based on insufficient evidence, was in itself incomplete, and led him to an erroneous opinion; (ii) that not only is the method more advantageously applicable in 1874 than in 1882, as regards time-difference, but that the objection of low solar altitude at a critical phase in 1882 has no existence in 1874; (iii) that the Astronomer Royal himself warmly advocated the equipment of Antarctic expeditions for viewing the transit of 1882 by Halley's method, notwithstanding the known difficulties; and (iv) that the best naval authorities on this special subject concur in regarding Antarctic expeditions for viewing a transit early in December as altogether practicable.

The conclusion directly deducible from these results cannot be mistaken. England's duty is more than manifest; it has been to all intents and purposes admitted by her astronomical and nautical official representatives. And I cannot but express my conviction that it will be little less than a national calamity, as assuredly it will be scientifically most regrettable if any considerations, either of convenience or of personal dignity on the one hand, or of false courtesy on the other, should lead to the loss of opportunities which will not be again available for many years to come.

From the Monthly Notices of the Astronomical Society for March 1873.

THE DIRECT METHOD OF OBSERVING

TRANSITS.

VERY early during my examination of the subject of the approaching transits, I was led to adopt and state the opinion that the parallactic displacement of Venus and thence the Sun's parallax, might, in the present state of instrumental astronomy, be determined at least as accurately by direct measurement of Venus's position at successive epochs of her transit as by either Delisle's or Halley's method. It appears impossible to eliminate the error resulting from the clinging of Venus to the Sun's limb, after ingress and before egress; and although several contrivances have been suggested for reducing this error, it is doubtful whether any of them will prove successful. It remains to be shown, moreover, whether photography can be successfully applied to determine the parallactic displacement of Venus.

I find that the German astronomers have for some time recognised the advantages which would probably result from such processes of measurement as I have mentioned; and their selection of Tchefoo, where the whole transit will be observable, indicates in a marked manner their preference for the direct method, since Tchefoo is not an exceptionally advantageous station for observing the accelerated ingress, and still less for observing the retarded egress. It is also inferior to other Northern stations for applying Halley's method; and indeed German astronomers have definitely indicated their preference for the direct method.

The American astronomers have also adopted a favourable opinion as to the direct method.

It appears to me that if English astronomers are to base their methods of procedure on foreign opinions (a growing fashion which I myself am far from urging as desirable), attention might not disadvantageously be directed to the considerations resulting from the above-mentioned opinions of German and American astronomers. It is easy to perceive what these considerations are.

In the first place, it is manifest that, cæteris paribus, those

stations will be most advantageous which show the whole transit under the most favourable conditions; and in comparing these stations, we should regard that station as the better which shows the greater proportion of the transit favourably. So that, so far as this method of observation is concerned, our selected stations at Woahoo and Alexandria would be altogether inferior to such a station as Tchefoo, since at Woahoo the Sun sets before half the transit has taken place, and at Alexandria more than half the transit is already over when the Sun rises.

It is probable, however, that few would be disposed to sacrifice such a station as Woahoo, where Delisle's method is applicable under conditions exceptionally advantageous. But it may be worth while to inquire whether so much can be said in favour of Alexandria in fact, it appears to me that but one answer can be made to this question, so far as it relates to the action called for on England's part.

To begin with, it seems not wholly unreasonable to expect that either Italy or Greece should occupy the only really advantageous Mediterranean station. Moreover, France is to occupy Suez, and the circumstances of the transit at Suez and Alexandria will be very nearly identical, as can be seen at once from Plate XVIII. which illustrates the present essay.

But it is when we compare the circumstances of the transit at Alexandria with those which will be presented at North Indian stations, such as Peshawur, Delhi, and so on, that we find most occasion to regret the unfortunate accident by which these North Indian stations came to be so long and so completely overlooked.

As respects the application of Delisle's method, the advantage of Peshawur is sufficiently marked. The retardation is indeed but a third of a minute greater at Peshawur than at Alexandria. But the Sun is unfortunately very low at Alexandria-only 14° above the horizon-when egress occurs, whereas at Peshawur the Sun will be more than 31° above the horizon.

The main point, however, and I conceive it to be an extremely important point-is that at Peshawur, at Delhi, and at many stations over the region between these places, the whole transit will be visible, and therefore processes of direct measurement can be most effectively applied. When we add to these considerations the circumstance that it is much more manifestly the duty of Great Britain to occupy this advantageous region in her own territory than to occupy Alexandria, but one opinion can be formed.

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