hygrometer, is not stated. If from the former, the situation of the thermometer by which the calculation is made should have been most particularly determined.

The eighth column contains the register of the rain; and from the greater frequency with which the amount has been lately entered, we may conclude that the soot from the old chimney-cowl, under which the gauge is situated, is more frequently removed from the pipe than it used to be.

The ninth and tenth columns, recording the direction and force of the wind, bear every mark of their former accuracy; and the only remarkable fact is the very rare occurrence of any variation of the strength from the standard 1.

The eleventh and last column rings most edifying changes upon "rain," "cloudy," "fine."

The results of all this labour are summed up at the end of the journal in one short table, containing the means and extremes of the months, and the mean results of the year. From what data, or from what part of the register, the means of temperature are collected, it is very difficult to conjecture. From the note at the foot of the last page we learn that the barometer is now 100 feet, instead of 81, above the level of low water spring-tides at Somerset-House; and that the rain-gauge is still 114 feet above the same level; but by some chance or other, six inches nearer the ground than before.

The importance which attaches to such minutiæ as these, when undertaken by such a body as the Royal Society, cannot be better illustrated than by a circumstance which has lately been discovered, in determining the length of the second's pendulum; a measure upon which depend all the late parliamentary proceedings for regulating the weights and measures of the united kingdom.

The council, by whose orders the height of the barometer above the level of the tide was determined, little foresaw at the time that this simple operation could have any reference to proceedings of such importance and yet hear what Captain Sabine says.

"The height of the pendulums in Mr. Browne's house, in London, being here described as 92.5 feet above the level of the sea,

whilst in Capt. Kater's memoir in the Philosophical Transactions, it is stated to be 83 feet only; it is necessary to explain that Capt. Kater's estimation of the height was founded, in part, on the understanding (on the authority of the Royal Society) that the elevation of their barometer at Somerset-House is 81 feet above low-water mark; but as the latter elevation has been since corrected by Mr. Bevan, who has determined it, by levelling, to be 90.5 feet above the mean level, the height of the pendulums must now be considered as 92.5 feet, and is so esteemed by Captain Kater*.”

The same national work is also much affected by the want of such standard instruments as it is the appropriate province of the Royal Society to provide and preserve. Is it to be tolerated that results of such national importance should be made to depend for their verification upon a comparison with a thermometer, the property of a private individual? The uncertainty in the experiments arising from such a cause may, according to Captain Sabine, amount to "not less thanth of a vibration per diem; being greater, as he had reason to believe, than the sum of the uncertainties due to all other causes whatever †.”

Surely these considerations, urged from so many quarters, must at length excite the dormant energies of those to whom the honour of the Royal Society is committed. If it be more consistent with the dignity of that venerable body to give up the working departments of science, and to sit as judges only of the exertions of others, let them announce such intention openly, and there will then be many come forward in the field from which they retire. In most branches of science this is the course which has been already adopted; and yet they have, perhaps, enough to do as impartial dispensers of those honours for which there are so many competitors. But if they are still determined to persevere in causing observations to be made "by their order," in the only branch of natural science which now remains to them, let them at least provide that they be made with all the care and precision which the. actual state of that science demands; for upon this the honour of the Society is at stake.

* Experiments for determining the figure of the Earth. By Edward Sabine, &c. p. 343. + Idem. p. 182.

94

ART. XIV. ASTRONOMICAL AND NAUTICALI COLLECTIONS.-No. XXIII.

i. A Method of Computing the Sun's HORIZONTAL PARALLAX from Observations of the Transits of Venus. By THOMAS HENDERSON, Esq.

THE method of computing an occultation of a fixed star by the moon, explained in No. XX. of these Collections, Art. III., may be applied with advantage to solar eclipses, occultations of the planets, and transits of Venus and Mercury. In each of these phenomena, the sun or planet occulted is to be substituted for the star, in the precepts given for occultations, and in transits, the planet is to be substituted for the moon. The orbital angle, in place of being constant as in occultations of stars, will (owing to the motion of the sun or planet) undergo a small variation equal to the change in the sun or planet's angle of position, which, when great precision is requisite, must be allowed for; and in transits, the complement of the orbital angle, and the side of the right-angled triangle, mentioned in Precept III., will have the contrary signs to those prescribed for occultations, by reason of the planet's retrograde motion. The difference of the horizontal parallaxes of the two bodies is to be employed in place of the horizontal parallax of the moon; and, while the semidiameter of the moon, or occulting body, remains without augmentation, the semidiameter of the sun or planet undergoing occultation, is to be diminished by a small quantity, obtained from this formula,

s sin p sin A,

where s denotes the semidiameter to be diminished, p the horizontal parallax of the other body, and A the altitude of the sun or planet. The sum or difference of the semidiameters will be employed according to the particular phenomenon to be investigated.

These modifications of the rules for occultations being observed,

the sun's horizontal parallax may be thus determined from observations of the transits of Venus.

If the sun's horizontal parallax be supposed known, the horizontal parallax of Venus is ascertained from the ratios of the distances of Venus and the sun from the earth. By means of these parallaxes, the observed times of ingress and egress at those places where the beginning and end of the transit have been observed, and other astronomical data, the nearest distance of Venus from the sun, as seen from the earth's centre, is to be computed in the same manner as the moon's latitude is determined from observations of an occultation. See La Lande's Astronomy, third edition, Arts. 1970-1976. In this calculation the orbital and perpendicular parallaxes are to be adopted, instead of the parallaxes in longitude and latitude employed by La Lande, and the motions are to be referred to Venus's relative orbit in place of the ecliptic. If the assumed parallax, the observations, and other data, be correct, the nearest distances, deduced from the observations at the respective places, ought to be equal. But if they turn out to be different, that value of the sun's parallax should be preferred which gives for the nearest distance quantities agreeing best with each other. This is to be determined by repeating the calculation upon a second hypothesis of the sun's parallax, observing that all the parallaxes 'will undergo a proportional variation.

For an illustration of this method, the transit of 1769 is assumed, The times of observation at the different places, and the other dala, are taken from De Lambre's Astronomy.

At Otaheite, the total ingress was observed at 21h 43TM 55°, and the beginning of egress at 3h 14m 3, apparent time. The sun's horizontal parallax at his mean distance from the earth being assumed 8" 7, Venus's nearest distance is found to be 606"-122; but the sun's parallax being assumed 8"-5, the same distance is found to be 606" 728. Hence an increase of one second upon the sun's mean horizontal parallax produces a diminution of 3"-030 upon the nearest distance, deduced from these observations. If D denote the nearest distance, P the number of seconds by which the

sun's mean horizontal parallax exceeds 8"-7, we have the following equation,

D606" 122 - 3.030 P.

Making similar calculations for all the places, where the beginning and end of the transit were observed, the following equations are obtained :—

Resolving these equations by the method of minimum squares, to obtain the most probable values of D and P, D will be found to be 606" 128, and P + 0"-0988, making the sun's mean horizontal parallax 8"-7988, or 8"-8.

The other results, usually deduced from transits, such as the times of nearest approach and ecliptical conjunction, the difference of longitude of the various places, Venus's latitude at the conjunction, the distance from the node, and the duration of the transit, independent of parallax, may now be determined in a manner which it is unnecessary here to explain.

On comparing this method with those of La Lande, Maskelyne, De Lambre, and Biot, it appears that in the former the final result is not (as in the latter) deduced from quantities, such as Venus's nearest distance, chord described during the transit, latitude, and elongation, which cannot be known with accuracy, until the parallax be determined.

ii Remarks on the Discordances observed between the LUNAR OBSERVATIONS AT GREENWICH and PARIS. BY THOMAS HENDERSON, Esq.

Annexed is a state of the discordances between the solar and lunar observations at Greenwich and Paris, in the years 1800-9, mentioned in Astronomical and Nautical Collections, No. XXI. Art. II.