than fidelity, diligence, and a moderate skill in astronomy. For there is no need that the latitude of the place should be scrupulously observed, nor that the hours themselves should be accurately determined with respect to the meridian: it is sufficient that the clocks be regulated according to the motion of the heavens, if the times be well reckoned from the total ingress of Venus into the Sun's disc, to the beginning of her egress from it; that is, when the dark globe of Venus first begins to touch the bright limb of the Sun within; which moments, I know, by my own experience, may be observed within a second of time.

But on account of the very strict laws by which the motions of the planets are regulated, Venus is seldom seen within the Sun's disc; and during the course of more than 120 years, it could not be seen once; namely, from the year 1639 (when this most pleasing sight happened to that excellent youth, Horrox, our countryman, and to him only, since the creation) to the year 1761; in which year, according to the theories which we have hitherto found agreeable to the celestial motions, Venus will again pass over the Sun on the* 26th of May, in the morning; so that at London, about six o'clock in the morning, we may expect to see it near the middle of the Sun's disc, and not above four minutes of a degree south of the Sun's centre. But the duration of this transit will be almost eight hours; namely, from two o'clock in the morning till almost ten. Hence the ingress will not be visible in England; but as the Sun will at that time be in the 16th degree of Gemini, having almost 23 degrees north declination, it will be seen without setting at all in almost all parts of the north frigid zone: and therefore the inhabitants of the coast of Norway, beyond the city of Nidrosia, which is called Drontheim, as far as the North Cape, will be able to observe Venus entering the Sun's disc; and perhaps

The sixth of June, according to the new style.

the ingress of Venus upon the Sun, when rising, will be seen by the Scotch, in the northern parts of the kingdom, and by the inhabitants of the Shetland Isles, formerly called Thule. But at the time when Venus will be nearest the Sun's centre, the Sun will be vertical to the northern shores of the bay of Bengal, or rather over the kingdom of Pegu; and therefore in the adjacent regions, as the Sun, when Venus enters his disc, will be almost four hours towards the east, and as many toward the west when she leaves him, the apparent motion of Venus on the Sun will be accelerated by almost double the horizontal parallax of Venus from the Sun; because Venus at that time is carried with a retrograde motion from east to west, while an eye placed upon the Earth's surface is whirled the contrary way, from west to east*.

* This has been already taken notice of in § 24; but I shall here endeavour to explain it more at large, together with some of the following part of the Doctor's Essay, by a figure.

In Fig. 1. of Plate XV let C be the centre of the Earth, and Z the centre of the Sun. In the right line CvZ, make «Z to CZ as 726 is to 1015 (§ 12). Let achd be the Earth, Venus's place in her orbit at the time of her conjunction with the Sun; and let TSU be the Sun, whose diameter is 31′ 42′′.

The motion of Venus in her orbit is in the direction Non, and the Earth's motion on its axis is according to the order of the 24 hours placed around it in the figure. Therefore, supposing the mouth of the Ganges to be at G, when Venus is at E in her orbit, and to be carried from G to g by the Earth's motion on its axis, while Venus moves from E toe in her orbit; it is plain that the motions of Venus and the Ganges are contrary to each other.

The true motion of Venus in her orbit, and consequently the space she seems to run over on the Sun's disc in any given time, could be seen only from the Earth's centre C, which is at rest with respect to its surface. And as seen from C, her path on the Sun would be in the right line TU; and her motion therein at the rate of four minutes of a degree in an hour. Tis the point of the Sun's eastern limb which Venus seems to touch at the moment of her total ingress on the Sun, as seen from C, when Venus is at E in her orbit; and U is the point of the Sun's western limb which she seems to touch at the moment of her beginning of egress from the Sun, as seen from G, when she is at e in her orbit.

Supposing the Sun's parallax (as we have said) to be 124", the parallax of Venus will be 43"; from which subtracting the parallax of the Sun, there will remain 30" at least for the horizontal parallax of Venus from the Sun; and therefore the motion of Venus will be increased 45′′ at least by that parallax, while she passes over the Sun's disc, in those elevations of the pole which are in places near the tropic, and yet more in the neighbourhood of the equator. Now Venus at that time will move on the sun's disc, very nearly at the rate of four minutes of a degree in an hour; and therefore 11 minutes of time at least are to be allowed for 45", or three fourths of a minute of

are

When the mouth of the Ganges is at m (in revolving through the arc Gmg) the Sun is on its meridian. Therefore, since & and equally distant from m at the beginning and ending of the transit, it is plain that the Sun will be as far east of the meridian of the Ganges (at G) when the transit begins, as it will be west of the meridian of the same place (revolving from G to g) when the transit ends.

But although the beginning of the transit, or rather the moment of Venus's total ingress upon the Sun at T, as seen from the Earth's centre, must be when Venus is at E in her orbit, because she is then seen in the direction of the right line CET; yet at the same instant of time, as seen from the Ganges at G, she will be short of her ingress on the Sun, being then seen eastward of him, in the right line GEK, which makes the angle KET (equal to the opposite angle GEC), with the right line CET. This angle is called the angle of Venus's parallax from the Sun, which retards the beginning of the transit as seen from the banks of the Ganges; so that the Ganges G, must advance "a little farther toward m, and Venus must move on in her orbit from E to R, before she can be seen from G (in the right line GRT) wholly within the Sun's disc at T.

When Venus comes to e in her orbit, she will appear at U, as seen from the Earth's centre C, just beginning to leave the Sun; that is, at the beginning of her egress from his western limb but at the same instant of time, as seen from the Ganges, which is then at g, she will be quite clear of the Sun toward the west; being then seen from g in the right line geL, which makes an angle, as UeL (equal to the opposite angle Ceg), with the right line CeU: and this is the angle of Venus's

a degree; and by this space of time, the duration of this eclipse caused by Venus will, on account of the parallax, be shortened. And from this

shortening of the time only, we might safely enough draw a conclusion concerning the parallax which we are in search of, provided the diameter of the Sun, and the latitude of Venus, were accurately known. But we cannot expect an exact computation in a matter of such subtilty.

We must endeavour therefore to obtain, if possible, another observation, to be taken in those places where Venus will be in the middle of the Sun's disc at midnight; that is, in places under the opposite meridian to the former, or about 6 hours or 90 degrees west of London; and where Venus enters upon the Sun a little before its set

parallax from the Sun, as seen from the Ganges at g, when she is but just beginning to leave the Sun at U, as seen from the Earth's

centre C.

Here it is plain, that the duration of the transit about the mouth of the Ganges (and also in the neighbouring places) will be diminished by about double the quantity of Venus's parallax from the Sun at the beginning and ending of the transit. For Venus must be at E in her orbit when she is wholly upon the Sun at 7, as seen from the Earth's centre C: but at that time she is short of the Sun, as seen from the Ganges at G, by the whole quantity of her eastern parallax from the Sun at that time, which is the angle KET. [This angle, in fact, is only 23"; though it is represented much larger in the figure, because the Earth therein is a vast deal too big.] Now, as Venus moves at the rate of 4' in an hour, she will move 23" in 5 minutes 45 seconds: and therefore, the transit will begin later by 5 minutes 45 seconds at the banks of the Ganges than at the Earth's centre.—When the transit is ending at U, as seen from the Earth's centre at C, Venus will be quite clear of the Sun (by the whole quantity of her western parallax from him) as seen from the Ganges, which is then at g: and this parallax will be 22′′, equal to the space through which Venus moves in 5 minutes 30 seconds of time: so that the transit will end 51 minutes sooner as seen from the Ganges, than as seen from the Earth's centre.

Here the whole contraction of the duration of the transit at the mouth of the Ganges will be 11 minutes 15 seconds of time: for it is 5 minutes 45 seconds at the beginning, and 5 minutes 30 seconds at the end.

ting, and goes off a little after its rising. And this will happen under the above-mentioned meridian, and where the elevation of the north pole is about 56 degrees; that is, in a part of Hudson's Bay, near a place called Port-Nelson. For, in this and the adjacent places, the parallax of Venus will increase the duration of the transit by at least six minutes of time; because, while the Sun, from its setting to its rising, seems to pass under the pole, those places on the Earth's disc will be carried with a motion from east to west, contrary to the motion of the Ganges; that is, with a motion conspiring with the motion of Venus; and therefore Venus will seem to move more slowly on the Sun, and to be longer in passing over his disc.**

*In Fig. 1. of Plate XV. let aC' be the meridian of the eastern mouth of the Ganges; and 6C the meridian of Port-Nelson at the mouth of York River in Hudson's Bay, 56° north latitude. As the meridian of the Ganges revolves from a to c, the meridian of Port-Nelson will revolve from 6 to d: therefore, while the Ganges revolves from G to g, through the arc Gmg, Port-Nelson revolves the contrary way (as seen from the Sun or Venus) from P to f through the arc Pnp.Now, as the motion of Venus is from E to e in her orbit, while she seems to pass over the Sun's disc in the right line TU, as seen from the Earth's centre C, it is plain that while the motion of the Ganges is contrary to the motion of Venus in her orbit, and thereby shortens the duration of the transit at that place, the motion of Port-Nelson is the same way as the motion of Venus, and will therefore increase the duration of the transit: which may in some degree be illustrated by supposing, that while a ship is under sail, if two birds fly along the side of the ship in contrary directions to each other, the bird which flies contrary to the motion of the ship will pass by it sooner than the bird will, which flies the same way that the ship moves.

In fine, it is plain by the figure, that the duration of the transit must be longer as seen from Port-Nelson, than as seen from the Earth's centre; and longer as seen from the Earth's centre, than as seen from the mouth of the Ganges For Port-Nelson must be at P, and Venus at Nin her orbit, when she appears wholly within the Sun at T: and the same place must be at , and Venus at n, when she appears at U beginning to leave the Sun.-The Ganges must be at G, and Venus at R, when she is seen from G upon