And as our illustrative case explains the nature of Delisle's method, so also it illustrates the rationale of the method. Of course, the two cases are not exactly similar; but they are sufficiently so to make the illustration instructive. Suppose that the length of the barge a b is known (as the dimensions of the earth are known); thus, say that it is 24 yards in length. Now suppose that the course of the boat is known to be in midstream, or exactly midway between the house and the barge. Then a moment's consideration will show that the boat traverses 12 yards between the moments when the spectators at a and b severally see it towards A. Now suppose that the observer at a indicates by a call or other signal the moment when the flag is thus seen by him, and that the observer at b, provided with a stop-watch, notes that two seconds elapse before he sees the flag towards A. This, then, is the time occupied by the boat in traversing 12 yards; so that she is moving at the rate of six yards per second. Similar remarks apply to the apparent transit of the flag past B as seen from a and b, In like manner, the astronomer can gather from observations by Delisle's method the rate at which Venus is moving in her orbit,-that is, the exact number of miles over which she moves per minute. So that, since he knows exactly how long she is in completing the circuit of her orbit, he learns, in fact, the exact circumference of her orbit in miles, whence its radius (or her distance from the sun) follows at once.

It is manifest that Delisle's method can be applied with equal advantage either to the ingress or to the egress of Venus. The comparison of two observations-in one of which her ingress happens as early as possible, while in the other it happens as late as possible-is quite sufficient to determine the sun's distance. So also the comparison of two observations of egress (most accelerated and most retarded) is separately sufficient to determine the sun's distance. This is an important advantage of the method. Because while, as in Halley's method, two stations are absolutely necessary, there is but a single observation to be made at each, whereas in Halley's the beginning and end of the transit must be observed at both stations. This introduces a double difficulty. For first, there is the necessity for a longer continuance of clear sky, since the transit may last several hours; and, secondly, there is the difficulty of securing a station where the sun is well placed on the sky, both at the beginning and end of the transit. It will not suffice, in applying Halley's method, to have the sun well above the horizon at the moment of ingress if he is low down at the moment of egress, or to have the sun high at egress if he is low at ingress. Accordingly, the condition has to be secured that at stations where the day is short (that is, in December, at northerly stations) the middle of the transit shall occur nearly at mid-day. This limits the choice for northern stations considerably.

On the other hand, Delisle's method has this disadvantage, that the exact moment at which ingress or egress occurs must be known. A mistake, even of a second or two, would be of serious moment. So that the clocks made use of at each station where this method is applied, must not only have good rates, but must show absolutely true time at the moment of the observed phenomenon. Moreover, the latitude and longitude of the place of observation must be known, the latter (the only difficult point) with especial accuracy, since on its determination depends the change of local time into (say) Greenwich time; and this change must be accurately effected before two observations made in different longitudes can be compared as respects the absolute time of their occurrence. On the contrary, Halley's method, while only requiring a relatively rough determination of the longitude, can be satisfactorily applied when the clocks employed are simply well rated; for it depends only on the duration of the transit as seen at different stations. A clock must be badly rated indeed-utterly unfit, in fact, for any astronomical use whatever-which should lose a single second in four or five hours.

But the most important point to be noticed is, that both methods ought to be employed, if possible, apart from all nice considerations of their relative value. It is certain that astronomers will place much more confidence in closely concordant results obtained by the application of these two methods, differing wholly as they do in principle, than in as many and equally concordant results all obtained by one method. A third method is indeed to be applied,viz., a method based on the ingenious use of photography. But as yet too little is known respecting the chances of success by this method to warrant too implicit reliance upon it.

Let us inquire what preparations are being made by astronomers, and especially by the astronomers of England, to make adequate use of the opportunities presented by the coming transit.

It has first, unfortunately, to be noted, that, so far as this country is concerned, no provision whatever has been hitherto made for the employment of Halley's method. If this resulted from the simple preference of Delisle's method, there would be little to say. Most assuredly, speaking for myself, I should be very loth to urge the advantages of Halley's method, if I found against such a view the practical experience of those astronomers who are continually testing the value of various methods of observation. But the rejection of Halley's method for the transit of 1874 was not originally, and is not now, based on any objection to the principle of the method, but on certain mathematical considerations, which appeared to prove that the method could not be advantageously applied in 1874, while it could be applied successfully in 1882. It was accordingly reserved for the latter transit, and all the stations for observing the transit of 1874 were selected with special reference to the method of Delisle.