distances, their real diameters and bulks may be found.

15. The Earth's diameter, as seen from the Sun, subtends an angle of double the Sun's horizontal parallax, at the time of the Earth's mean distance from the Sun and the Sun's diameter, as seen from the Earth at that time, subtends an angle of 32′ 2′′, or 1922". Therefore the Sun's diameter is to the Earth's diameter, as 1922 is to 21.-And since the relative bulks of spherical bodies are as the cubes of their diameters, the Sun's bulk is to the Earth's bulk, as 756058 is to 1; supposing the Sun's mean horizontal parallax to be 10".5, as above.

16. It is plain by Fig. 4. that whether Venus be at U or V, or in any other part of the right line BVS, it will make no difference in the time of her total ingress on the Sun at S, as seen from B; but as seen from A it will. For, if Venus be at V, her horizontal parallax from the Sun is the arc Fe, which measures the angle FAe: but if she be nearer the Earth, as at U, her horizontal parallax from the Sun is the arc fe, which measures the angle fAe; and this angle is greater than the angle FAe, by the difference of their measures fF. So that, as the distance of the celestial object from the Earth is less, its parallax is the greater.

17. To find the parallax of Venus by the above method, it is necessary, 1. That the difference of meridians of the two places of observation be 90°. -2. That the time of Venus's total ingress on the Sun be when his eastern limb is either on the meridian of one of the places, or very near it.-And, 3. That each observer have his clock exactly regulated to the equal time at his place. But as it might, perhaps, be difficult to find two places on the Earth suited to the first and second of these requisites, we shall shew how this important problem may be solved by a single observer, if he be exact

as to his longitude, and have his clock truly adjusted to the equal time at his place.

18. That part of Venus's orbit in which she will move during her transit on the Sun, may be considered as a straight line; and therefore, a plane may be conceived to pass both through it and the Earth's centre. To every place on the Earth's surface cut by this plane, Venus will be seen on the Sun in the same path that she would describe as seen from the Earth's centre; and therefore she will have no parallax of latitude, either north or south; but will have a greater or less parallax of longitude, as she is more or less distant from the meridian, at any time during her transit.

Matura, a town and fort on the south coast of the island of Ceylon, will be in this plane at the time of Venus's total ingress on the Sun; and the Sun will then be 6210 east of the meridian of that place. Consequently to an observer at Matura, Venus will have a considerable parallax of longitude eastward from the Sun, when she would appear to touch the Sun's eastern limb as seen from the Earth's centre, at which the astronomical tables suppose the observer to be placed, and give the times as seen from thence.

19. According to these tables, Venus's total ingress on the Sun will be 50 minutes after VII in the morning, at Matura*, supposing that place to be 80° east longitude from the meridian of London, which is the observer's business to determine. Let us imagine that he finds it to be exactly so, but that to him the total ingress is at VII hours 55 minutes 46 seconds, which is 5 minutes 46 seconds later than the true calculated time of total ingress, as seen from the Earth's centre. Then, as Venus's motion on (or

* The time of total ingress at London, as seen from the Earth's cen tre, is at 30 minutes after II in the morning; and if Matura be just 80° (or 5 hours 20 minutes) east of London, when it is 30 minutes past II in the morning at London, it is 50 minutes past VII at Matura.

toward, or from) the Sun is at the rate of 4 minutes of a degree in an hour (by § 10.) her motion must be 23".1 of a degree in 5 minutes 46 seconds of time: and this 23".1 is her parallax eastward, from her total ingress as seen from Matura, when her ingress would be total if seen from the Earth's centre.

20. At VII hours 50 minutes in the morning, the Sun is 621° from the meridian; at VI in the morning he is 90° from it: therefore, as the sine of 621° is to the sine of 23".1 (which is Venus's parallax from her true place on the Sun at VII hours 50 minutes), so is radius or the sine of 90°, to the sine of 26", which is Venus's horizontal parallax from the Sun at VI. In logarithms thus:

As the logarithmic sine of 620 30'

Is to the logarithmic sine of 23′′.1

So is the logarithmic radius

To the logarithmic sine of 26" very nearly

9.9479289 6.0481510 10.0000000

6.1002221

Divide the Sun's distance from the Earth, 1015, by his distance from Venus 726 (§ 12.) and the quotient will be 1.3980; which being multiplied by Venus's horizontal parallax from the Sun 26", will give 36".3480, for her horizontal parallax as seen from the Earth at that time.-Then (by § 13.) as the Sun's distance, 1015, is to Venus's distance 289, so is Venus's horizontal parallax 36".3480 to the Sun's horizontal parallax 10".3493.-If Venus's horizontal parallax from the Sun be found by observation to be greater or less than 26", the Sun's horizontal parallax must be greater or less than 10".3493 accordingly.

21. And thus, by a single observation, the parallax of Venus, and consequently the parallax of the Sun, might be found, if we were sure that the astronomical tables were quite correct as to the time of Venus's total ingress on the Sun.-But although the tables may be safely depended upon for shewing the true

duration of the transit, which will not be quite 6 hours from the time of Venus's total ingress on the Sun's eastern limb, to the beginning of her egress from his western; yet they may perhaps not give the true times of these two internal contacts: like a good common clock, which, though it may be trusted to for measuring a few hours of time, yet perhaps it may not be quite adjusted to the meridian of the place, and consequently not true as to any one hour; which every one knows is generally the case.-Therefore, to make sure work, the observer ought to watch both the moment of Venus's total ingress on the Sun, and her beginning of egress from him, so as to note precisely the times between these two instants, by means of a good clock: and by comparing the interval at his place with the true calculated interval as seen from the Earth's centre, which will be 5 hours 58 minutes, he may find the parallax of Venus from the Sun both at her total ingress and beginning of egress.

22. The manner of observing the transit should be as follows:-The observer being provided with a good telescope, and a pendulum-clock well adjusted to the mean diurnal revolution of the Sun, and as near to the time at his place as conveniently may be; and having an assistant to watch the clock at the proper times, he must begin to observe the Sun's eastern limb through his telescope, twenty minutes at least before the computed time of Venus's total ingress upon it, lest there should be an error in the time of the beginning as given by the tables.

When he perceives a dent (as it were) to be made in the Sun's limb, by the interposition of the dark body of Venus, he must then continue to watch her through the telescope as the dent increases; and his assistant must watch the time shewn by the clock, till the whole body of the planet appears just within the Sun's limb: and the moment when the bright limb of the Sun appears close by the east side of the

dark limb of the planet, the observer, having a little hammer in his hand, is to strike a blow therewith on the table or wall; the moment of which, the assistant notes by the clock, and writes it down.

Then, let the planet pass on for about 2 hours 59 minutes, in which time it will be got to the middle of its apparent path on the Sun, and consequently will then be at its least apparent distance from the Sun's centre; at which time, the observer must take its distance from the Sun's centre by means of a good micrometer, in order to ascertain its true latitude or declination from the ecliptic, and thereby find the places of its nodes.

This done, there is but little occasion to observe it any longer, until it comes so near the Sun's western limb, as almost to touch it. Then the observer must watch the planet carefully with his telescope: and his assistant must watch the clock, so as to note the precise moment of the planet's touching the Sun's limb, which the assistant knows by the observer striking a blow with his hammer.

23. The assistant must be very careful in observing what minute on the dial-plate the minute-hand has past, when he has observed the second-hand at the instant the blow was struck by the hammer; otherwise, though he be right as to the number of seconds of the current minute, he may be liable to make a mistake in the number of minutes.

24. To those places where the transit begins before XII at noon, and ends after it, Venus will have an eastern parallax from the Sun at the beginning, and a western parallax from the Sun at the end; which will contract the duration of the transit, by causing it to begin later and end sooner, at these places, than it does as seen from the Earth's centre; which may be explained in the following manner.