celestial phenomenon is an intermediate planet between the orbits of mars and jupiter, and appears as a star of the eighth magnitude, being probably about the size of the moon. Its distance from the sun is about 2 times that of the earth, and its periodical time nearly four years and two months. At the present time (August 25), it is very near the star ; and will soon be in a good situation to be observed. . . . . . Since the arc of its orbit through which this planet ran during the period it was ob served by Piazzi was but small, no great degree of a curacy can be expected in stating the elements of its theory; the following, however, are the most exact yet known: "Place of the ascending node "Place of the aphelium "Time of the passage through the aphe lium, January, 1801 Excentricity Log. of the greater semi-axis "Time of the sidereal period 2o 20° 58′ 30′′ 10 47 0 The authour begs to return his sincerest thanks to his learned and excellent friend Dr. Hutton of Woolwich, for communicating to him a paper, whence the above particulars were extracted. Mr. Maclaurin, and other philosophers, expected, nearly one hundred years ago, that such a discovery as this of M. Piazzi's would be made by some diligent astronomer: and the opinion has been lately revived by Mr. Capel Loft, a gentleman well known for his attachment both to the sciences and the muses. In the New London Review, for March, 1800, this gentleman, in a critique on the Athenian letters, ventured to offer some conjectures respecting an intermediate planet between mars and jupiter, the coincidence of which with the new discovery is very remarkable. He supposed that the distance of the intermediate planet from the sun, would be to that of mars, either as thirtythree to fifteen, or as twenty to fifteen; the midway between which, corresponds nearly with the fact with respect to its diameter, he conceived it might be to that of mars, as that of mars to the diameter of the earth; and then, being not much more than half the diameter of mars, and at five times the perigean distance, it would be seen from the earth under an angle of 21" or 3"; while georgium sidus would appear under an angle of 4. These lucky conjectures were drawn from a certain kind of Pyth gorean barmory, and are ingeniously defended in the Review just mentioned. CHAPTER XIL On the apparent and real Diameters of the Sun 201 Planets. ART. 383. IT is obvious from the principles of optics, that the determination of the real diameters of the heavenly bodies will depend conicintly ca a knowledge of their apparent diameters, and their real distances from the earth. For, suppose APB2, Pl. V.) a section of such body made by a pizze pass ing through the place O of the eye, and the centre C of the body: then AOB will be the angle, which will measure the apparent diameter of the body; this being known, AO C, its half, will be known And AO being a tangent to the surface, the angle CAO will be a right angle; whence, co-sine AOC: sine AOC::AO: A C, the semidiameter of the body. Now AO or OC may be found by articles 333. 359-375-; or, when the body is in opposition or conjunction with the sun, by taking the difference, or sum of its distance from the sun, and the earth's dis tance from that luminary, according to the respective cases; taking care to attend to the different operations required for a superiour and infericur planet. And as to the apparent diameters, it may be worth while to point out a few methods of ascertaining them. 384. The sun's vertical or perpendicular diameter may be found by two observers taking, the one, the height of the upper edge of the disc, the other, that of the lower, at the same instant. This is most conveniently done when the sun is at or near the meridian; because there is then no sensible change in his altitude during the space of two or three minutes. The height of each edge must be corrected, by allowing for parallax and refraction; and the apparent diameter will be equal to the difference of the corrected altitudes of the upper and lower edge. This method is very simple, and gives the apparent diameter, with exactness proportional to the accuracy of the instruments made use of. 385. Another method of determining the sun's apparent diameter, is to observe by a good clock the time in which the sun's disc passes over the plane of the meridian, or some other hour circle. At, or very near, one of the equinoxes, when the sun's apparent diurnal motion is in the equator, or a parallel very near it, say, as the time between the sun's leaving the meridian, and returning to it again: 360°:: the time in which he transits the meridian: his apparent semidiameter. At any other time of the year, when the sun is in a parallel at some distance from the equator, his diameter measures a greater number of minutes and seconds in that parallel, than it would do in a great circle (Art. 150.), and takes up proportionally more time in passing over the meridian; we may then use this analogy, as radius: co-sine of the sun's declination: the time in which the sun transits the meritian, concerted into motion, at the rate of four a inutes in time to 1°.: the arc of the great circle which measures the sun's apparent horizontal diameter. This method may be easily put in practice by two observers; or indeed by one, if he have an half-second penduluin placed near enough for him to hear the beats of it, whilst he observes the transit. 386. Or the sun's apparent diameter may be measured by means of the projection of his image; thus, let the sun's rays be admitted into a dark room, through a circular aperture cd, the diameter of which is accurately known; the rays passing perpendicularly through this orifice, will fall perpendicularly on a parallel plane (whose distance is from the former must also be known), and form an image, the diameter of which is a b (fig. 3, Pl. V.). Now, the diameter cd being taken from a b, leaves rr, half of which is s: hence, in the right-angled triangle isr we know is, and s r, and from thence may determine the angle sir, which will be equal to the apparent semidiameter of the sun. According to some of these methods the sun's diameter has been measured, and may be stated at a mean to be 32′ 11′′. The greatest and least diameters have been given before (Art. 304.). 387. To determine the apparent diameter of a planet, one way is to place between it and the eye a thin plate of metal with a small circular orifice in it, at such a distance from the eye that the entire disc of the planet may appear exactly to fill the hole; and then, by measuring the diameter of the hole and the distance of the plate from the eye, to determine by trigonometry the visual angle subtended by the diameter of the aperture, which will evidently be the same as the apparent diameter of the planet. Another method similar to this is, to suspend a thread or wire of known diameter, at such a distance from the eye that it may just hide the disc of the planet, and then, after measuring the distance of the thread from the eye, determine trigonometrically the visual angle. A third method is, to measure the picture of a planet cast through a telescope upon white paper in a dark room, and compare it with that of the sun or moon projected in the same manner. But to mention no more such uncertain methods, the diameters of the planets are best taken by the micrometer, an instrument so contrived that two parallel wires being |