and calculating from the expression in Art. 576. found that the ingress at Wardhuys was accelerated by the parallax 6m 3874, and the egress retarded 4m 3814; so that the whole duration was lengthened 11m 16.88. At Otaheite, according to this gentleman's calculation, the ingress was retarded 5m 4311, and the egress accelerated 6 2696; so that the whole duration was diminished 12m 1007; consequently, the computed difference of the times is 23m 26''95.

578. Now, since the observed difference of the total durations at Wardhuys and Otaheite is 23m 10 ̊, and the computed difference, from the assumed sun's mean horizontal parallax 883, is 23" 2695, the true parallax of the sun is less than that assumed. Let the true parallax be to that assumed as I-e to 1, and (Art. 576.) the first parts of the computed parallax will be lessened in the ratio of 1-e: 1, and the second parts in the ratio of 1:1, or of 1-2: I nearly. All the first parts, according to Dr. Maskelyne's calculation, viz. 40605, 287 05, 34148, 382 47, in all 141705, combine the same way to make the total duration at Wardhuys longer than that at Otaheite. As to the second parts, the effects at Wardhuys are 731 and 891, and at Otaheite are +163 and +4°49; these four incorporated give -10 10. Therefore, 141705 X I

TOS 10 X 1

=

- 2e =

1390, the excess of

the observed total duration at Wardhuys above that at Otaheite; or 141705

1417 05-2020 X e, and e =

1010 1390,=

16795 1395-85

hence the mean horizontal parallax of the sun = 87-83 XI 00121 = 872316. And by com puting the effects of this parallax at both places, and comparing them with the observations, the differences were so trifling, that the above conclusion, or 84", or 811, which is very near it, must be reckoned within

сс

a very small degree of the true horizontal parallax at the sun's mean distance from the earth.

579. Mr. Short states the mean horizontal parallax, as a medium resulting from many observations, at about 8" 47; Euler makes it 8"-68; Dr. Hornsby, 8.69 and 8"-92; M. Pingre, 878; M. da Sejour, 8"-81; M. de la Lande, 8"-6. The mean of all these determinations agrees very nearly with the parallax, as deduced from the calculations of Dr. Muskelyne. Hence, then, knowing the radius of the earth, we may find the mean distance of the sun, according to the method given in Chap. XI. Prob. 7.

580. The transits of mercury and venus are not only useful in determining the sun's parallax, but they may be applied to the ascertaining of the longitudes of different places; they occur so seldom, however, that they cannot be of great utility in this respect. They are of considerable benefit in correcting the elements of the respective planets, particularly the places of the aphelia and nodes, and the inclination of the orbit. The transits of venus in 1761 and 1769 contributed much to the correction of the theory of that planet; as to the transit of mercury in 1799, the weather in England was so unfavourable, that the sun could not be viewed at the time of the transit; it was, however, observed in France. by La Lande, who, in his History of Astronomy for 18:0, says, "The transit of mercury over the sun enabled me to verify the place of the aphelion, and by my result there appears no necessity for changing the Tables of mercury." Dr. Herschel, in consequence of the effect of the solar rays upon the glasses of his seven-feet telescope, when prepared for viewing this transit, was led to an enquiry into the method of viewing the sun advantageously, with telescopes of large apertures and high magnifying powers; in pursuit of this enquiry he instituted a series of very curious experiments, an account of which is inserted in the Philosophical Transactions for 1800, Part II.

The results he obtained from them furnished him with various means of adapting his telescopes more successfully to solar observations; and, as the two methods which he found most effectual may be highly useful to the practical astronomer, they are here described he placed a very dark green glass behind the second eye-glass, that it might be sheltered by both glasses, which, in his double eye-piece, are close together, and of an equal focal length. Here, as the rays were not much concentrated, the coloured glass received them on a large surface, and stopped light and heat, in the proportion of the square of its diameter then used, to that on which the rays would have fallen had it been placed in the focus of pencils. For the same reason he also placed a dark green smoked glass close upon the former, with the smoked side towards the eye, that the smoke might likewise be protected against heat, by a passage of the rays through two surfaces of coloured glass. This position had the advantage of leaving the telescope, with its mirrours and glasses, completely to perform its operation, before the application of the darkening apparatus; and thus to prevent the injury which must be occasioned by the interposition of the heterogeneous colouring matter of the glasses, and of the smoke. . . . He also placed a deep blue glass, with a blueish-green smoked one upon it, as in the former method, and found the sun of a whiter colour than before; there was no disagreeable sensation of heat, though a little warmth might be felt. . . . The doctor adds, that with either of these "he has seen uncommonly well; and that, in a long series of very interesting observations upon the sun, the glasses have met with no accident."*

In the Memoirs of the Academy of Sciences at Berlin, from August, 1786, to the end of 1787, there is inserted an account of "Observations on the Passage of Mercury over the Sun's Dise, on May 4th, 1786." by Professor Beutler, of Mitaw, in Courland. From these observations the diameter of mercury, seen from the earth, was found to be 10/37; as seen from the sun, 12836; and as seen at the mean distance of the sun from the earth, 5' 79.

CHAPTER XXI.

On Comets.

ART. 581. BESIDES the ordinary planets, which are always in our neighbourhood (if we may so speak), and within our view, or, at least, within the reach of our telescopes, there is another sort of planets, which may, perhaps, be called temporary; for, after any one of them has been conspicuous for a season, it withdraws, and is no longer visible: these bodies are called comets, or, vulgarly, blazing stars, having this to distinguish them from other stars, that they are usually attended with a long train of light, tending always opposite to the sun, and being of a fainter lustre the farther it is from the body of its respective comet. There is a popular division of comets into three kinds, bearded, tailed, and hairy; but, in general, this division rather relates to the several circumstances of the same comet than to the phenomena of several. Thus, when the comet is eastward of the sun, and moves from him, it is said to be bearded, because the light precedes it in the manner of a beard; when the comet is westward of the sun, and sets after him, it is said to be tailed, because the train of light follows it; and lastly, when the sun and comet are diametrically opposite, the earth being between them, all the train, except the extremities, is hid behind the body of the comet; this, therefore, appears round it like a border of hair or coma, whence it is called hairy,

and whence the name of comet is derived. The magnitude of comets has been observed to be very different; many of them without their hair have appeared no larger than stars of the first magnitude; but some authours have given us accounts of others, which appeared much greater; such was that which appeared in the time of the emperor Nero, which, as Seneca relates, was not inferiour, in apparent magnitude, to the sun himself. The comet which Hevelius observed, in the year 1652, did not seem to be less than the moon, though it was deficient in splendour, for it had a pale, dim light, and appeared with a dismal aspect. Most comets have dense and dark atmospheres surrounding their bodies, which weakens the sun's rays that fall upon them; but within these appears the nucleus, or solid body of the comet, which, when the sky is clear, will often give a more splendid light.

582. The ancient philosophers allowed comets a place among the heavenly bodies, and ranked them in stations far above the moon; for Aristotle (in his first book of Meteors, Chap. VI.*), Plutarch (in his third book of Philosophical Opinions, Chap. II. t), and Seneca (in his seventh book of Natural Questions, Chap. III.), testify, that the Pythagoreans, and the whole Italian sect, maintained, that a comet was a kind of planet, or wandering star, which did not constantly appear in the heavens, but in stated times, after having gone through a determinate circuit, arose or appeared again. Hippocrates, Chios, and Democritus, were of the same opinion, as we are informed by Aristotle and Seneca. Seneca also assures us, that Apollonius Myndius, one of the most skilful in the

* Των δι Ιταλικών πιες και καλεμένων Πυθαγορείων ενα λεγεσιν αυτον είναι των πλανητων ασέρων, άλλα δια πολλα τε χρόνε το φαντασιαν αυτο ειναι και την υπερβολην επι μικρὸν ὑπερ συμβαίνει και περι τον τε Ερμες ατέρα.

† Των ἀπὸ Πυθαγρας πνες μεν άτερα φασιν είναι τον κομητήν των ἐκ άι φαινομένων, δια πνῶν δε ὡρισμένες χρονες περιοδικως ένα τελλοντων,