If the stars which really bestrew the heavens beyond the sun could be seen, the case would be different, for they would serve as index points, by means of which to estimate the sun's displacement. But although stars not lying near the sun's place on the heavens can be seen by day with powerful telescopes, those close around him are quite invisible. This method failing, the astronomer has to look for other means of solving the problem. The planet Venus, which comes at times much nearer to the earth than the sun is, and in fact nearer than any celestial body except the moon, naturally claims attention as a suitable object for the astronomer's purpose. For it is to be remembered that the proportions of the solar system have long been accurately determined; so that as soon as the distance of any one planet is ascertained, the scale of the whole solar system becomes also known.

1 Only observations of the mid-day sun would avail, because the only instruments having the requisite delicacy of adjustment are meridional. There is an instrument suitable for observing the moon when she is not on the meridian; but it is quite unfit for the purpose we are considering.

Venus, however, when at her nearest, is lost in the sun's light, and, though discernible in powerful telescopes, is quite unsuitably placed for the delicate observations which would alone avail to determine her distance.

This brings us at once to the recognition of the importance of a transit of Venus. When Venus passes between the sun and earth, in such a way as not to cross the sun's face,-that is, when she passes above or below the long and almost linear portion of space lying actually between the earth and sun,she cannot be well observed; but when, in making the passage, she comes so close to the line joining the earth and sun as actually to be seen on the sun's face, she can be observed to great advantage. For she is then seen as a round black spot on the sun's face; this face is thus as a sort of dial-plate on which the black disc of Venus is as an index. The sharply-defined edge of this black disc presents the same advantage which a neatly-cut index possesses, enabling the observer to measure satisfactorily the place of the planet. All the circumstances are favourable, except two :- first, the index,that is, the black disc,- is not even for an instant at rest; and, secondly, the index-plate,-that is, the sun's disc, is itself displaced by any difference in the position of the terrestrial observers.

Nothing can be done to remedy the latter circumstance. Its effects are easily seen. Suppose an observer at some northern station sees Venus in reality depressed by a third of a minute of arc, which is about the hundredth part of the sun's apparent diameter. Then the sun, being farther away in the proportion of about ten to three, is depressed by about the tenth of a minute. Accordingly, Venus only seems to be depressed by the difference of these amounts, or by little more than a quarter of a minute. Nevertheless it is far easier to measure this reduced displacement on the sun's face, than to measure the larger displacement without his face as an index-plate.

The other circumstance has been dealt with in two ways.

First, in accordance with a suggestion of Halley's, instead of attempting to measure the position of Venus on the sun's face, the astronomer may simply time her as she crosses that face, and so judge how long the chord is which she has traversed. This shows how nearly the chord approaches the sun's centre, and thus gives a determination as satisfactory as an actual measurement. Of course, there are many details to be taken into account: for instance, the apparent path of Venus is not a straight line in reality, because the observer's station is not at rest, but carried round the axis of the rotating: earth. But the mathematician finds no difficulty in taking such considerations fully into account.

Secondly, Delisle proposed that astronomers should note the actual moment (of absolute, not local time) when Venus seems to enter or leave the sun's face, as seen from different stations on the earth. It will be manifest, on a moment's consideration of the actual circumstances of the case, that the transit will not seem to begin or end at the same instant, as seen from different parts of the earth. There is the great globe of the sun at one side, and the smaller globe of the earth on the other; and Venus passes between. Now, in order to show more clearly what must happen, let us take an illustrative case drawn from an event which in a few weeks from the present time will interest a large proportion of our population. Suppose that on one side of the river Thames there is a long building whose extremeties we call A and B. Suppose that just opposite there is a barge whose corresponding extreme-ties we call a and b. Now suppose the winning boat to be coming along so as to pass between the house and the barge (coming first between the ends A, a). And for simplicity of description let us confine our remarks to the little flag carried at the bow of the boat. It is manifest that an observer at a will see the little flag cross his line of vision towards A before an observer at b; sees the like. And the observer at a will in like manner see the light blue flag (I beg pardon, I should say the blue flag simply) crossing his line of vision towards B before an observer at b sees the like. The flag will traverse the range A B as seen both from a and from 6, but both its ingress on this range and its egress from it will be earlier as seen from a than as seen from b. Now our earth may be compared to the barge; the sun to the building A B.; and Venus to the boat. There is one spot on the earth at which Venus will seem to enter earliest on the sun's face, and another spot (on the opposite side, just as b is farthest away from a) where Venus will seem to enter latest; and in like manner there is one spot at which Venus will seem to leave the sun's face earliest, and another (on the opposite side) at which Venus will seem to leave the sun's face latest.