the naked eye, a very bright spot upon the dark part of the moon; it was there when he first looked at the moon; the whole time he saw it, it was a fixed, steady light, except the moment before it disappeared, when its brightness increased; he conjectures that he saw it about 5 minutes. The same phænomenon was observed by Mr. T. STRETTON, in St. John's Square, Clerkenwell, London. Phil. Trans. 1794. On April 13, 1793, and on February 5, 1794, M. Piazzi, Astronomer Royal at Palermo, observed a bright spot upon the dark part of the moon, near Aristarchus. Several other Astronomers have observed the same phenomenon. See the Memoirs de Berlin, for

1788.

377. It has been a doubt amongst Astronomers, whether the moon has any atmosphere; some suspecting that at an occultation of a fixed star by the moon, the star did not vanish instantly, but lost its light gradually; whilst others could never observe any such appearance. M. SCHROETER of Lilianthan, in the dutchy of Bremen, has endeavoured to establish the existence of an atmosphere, from the following observations. 1. He observed the moon when two days and a half old, in the evening soon after sun set, before the dark part was visible; and continued to observe it till it became visible. The two cusps appeared tapering in a very sharp, faint, prolongation, each exhibiting its farthest extremity faintly illuminated by the solar rays, before any part of the dark hemisphere was visible. Soon after, the whole dark limb appeared illuminated.. This prolongation of the cusps beyond the semicircle, he thinks must arise from the refraction of the sun's rays by the moon's atmosphere. He computes also the height of the atmosphere, which refracts light enough into its dark hemisphere to produce a twilight, more luminous than the light reflected from the earth when the moon is about 32° from the new, to be 1356 Paris feet; and that the greatest height capable of refracting the solar rays is 5376 feet. 2. At an occultation of Jupiter's satellites, the third disappeared, after having been about 1" or 2′′ of time indistinct; the fourth became indiscernible near the limb; this was not observed of the other two. Phil. Trans. 1792. If there be no atmosphere in the moon, the Heavens, to a Lunarian, must always appear dark like night, and the stars be constantly visible; for it is owing to the reflection and refraction of the sun's light by the atmosphere, that the Heavens, in every part, appear bright in the day.

On the Phænomenon of the Harvest Moon.

378. The full moon which happens at, or nearest to, the autumnal equinox; is called the Harvest moon; and at that time, there is a less difference be

FIG.

87.

tween the times of its rising on two successive nights, than at any other full moon in the year; and what we here propose, is to account for this pheno

menon.

379. Let P be the north pole of the equator QAU, HAO the horizon, EAC the ecliptic, A the first point of Aries; then, in north latitudes, A is the ascending node of the ecliptic upon the equator, AC being the order of the signs, and AQ that of the apparent diurnal motion of the heavenly bodies. When Aries rises in north latitudes, the ecliptic makes the least angle with the hori zon; and as the moon's orbit makes but a small angle with the ecliptic, let us first suppose EAC to represent the moon's orbit. Let A be the place of the moon at its rising on one night; now, in mean solar time, the earth makes one revolution in 23h. 56'. 4", and brings the same point A of the equator to the horizon again; but in that time, let the moon have moved in its orbit from A to c, and draw the parallel of declination tens; then it is manifest, that 3'. 56" before the same hour the next night, the moon, in its diurnal motion, has to describe cn before it rises. Now cn is manifestly the least possible, when the angle CAn is the least, Ac being given. Hence it rises more nearly at the same hour, when its orbit makes the least angle with the horizon. Now at the autumnal equinox, when the sun is in the first point of Libra, the moon, at that time of its full, will be at the first point of Aries, and therefore it rises with the least difference of times, on two successive nights; and it being at the time of its full, it is more taken notice of; for the same thing happens every month when the moon comes to Aries.

Hitherto we have supposed the ecliptic to represent the moon's orbit, but as the orbit is inclined to it at an angle of 5°. 9' at a mean, let A≈ represent the moon's orbit when the ascending node is at 4, and Ar the arc described in a day; then the moon's orbit making the least possible angle with the horizon in that position of the nodes, the arc rn, and consequently the difference of the times of rising, will be the least possible. As the moon's nodes make a revolution in about 19 years, the least possible difference can only happen once in that time. In the latitude of London the least difference is about 17'.

380. The ecliptic makes the greatest angle with the horizon when the first point of Libra rises, consequently when the moon is in that part of its orbit, the difference of the times of its rising will be the greatest; and if the descending" node of its orbit be there at the same time, it will make the difference the greatest possible; and this difference is about 1h. 17' in the latitude of London. This is the case with the vernal full moons. Those signs which make the least angle with the horizon when they rise, make the greatest angle when they set, and vice versâ; hence, when the difference of the times of rising is the least, the difference of the times of setting is the greatest, and the contrary.

381. By increasing the latitude, the angle rAn, and consequently rn, is diminished; and when the time of describing rn, by the diurnal motion, is 3′. 56′′, the moon will then rise at the same solar hour. Let us suppose the latitude to be increased until the angle rAn vanishes, then the moon's orbit becomes coincident with the horizon, every day, for a moment of time, and consequently the moon rises at the same sidereal hour, or 3′. 56′′ sooner, by solar time. Now take a globe, and elevate the north pole to this latitude, and marking the moon's orbit in this position upon it, turn the globe about, and it will appear, that at the instant after the above coincidence, one half of the moon's orbit, corresponding to Capricorn, Aquarius, Pisces, Aries, Taurus, Gemini, will rise; hence, when the moon is going through that part of its orbit, or for 13 or 14 days, it rises at the same sidereal hour. Now taking the angle AE=5°. 9′, and the angle EAQ=23°. 28', the angle QAa, or QAH when the moon's orbit coincides with the horizon, is 28°. 37′; hence, the latitude QZ is 61°. 23′ where these circumstances take place. If the descending node be at A, then QAx, or QAH=18°. 19', and the latitude is 71°. 41'. In any other situation of the orbit, the latitude will be between these limits. When the angle QAr is greater than the complement of latitude, the moon will rise every day sooner by sidereal time. As there is a complete revolution of the nodes in about 18 years 8 months, all the varieties of the rising and setting of the moon must happen within that time.

On the IIorizontal Moon.

382. The phænomenon of the horizontal moon is this, that it appears larger in the horizon than in the meridian; whereas, from its being nearer to us in the latter case than in the former, it subtends a greater angle. GASSENDUS thought that, as the moon was less bright in the horizon, we looked at it there with a greater pupil of the eye, and therefore it appeared larger. But this is contrary to the principles of Optics, the image of an object upon the retina not depending upon the pupil. This opinion was supported by a French Abbé, who supposed that the opening of the pupil made the chrystalline humour flatter, and the eye longer, and thereby increased the image. But there is no connection. between the muscles of the iris and the other parts of the eye, to produce these effects. Des CARTES thought that the moon appeared largest in the horizon, because, when comparing its distance with the intermediate objects, it appeared then furthest off; and as we judge its distance greatest in that situation, we of course think it larger, supposing that it subtends the same angle. This opinion was supported by Dr. WALLIS in the Phil. Trans. N°. 187. Dr. BERKLEY accounts for it thus. Faintness suggests the idea of greater distance; the moon appearing most faint in the horizon, suggests the idea of greater distance, and,

supposing the visual angle the same, that must suggest the idea of a greater tangible object. He does not suppose the visible extension to be greater, but that the idea of a greater tangible extension is suggested, by the alteration of the appearance of the visible extension. He says, 1. That which suggests the idea of greater magnitude, must be something perceived; for what is not perceived can produce no effect. 2. It must be something which is variable, because the moon does not always appear of the same magnitude in the horizon. 3. It cannot lie in the intermediate objects, they remaining the same; also, when these objects are excluded from sight, it makes no alteration. 4. It cannot be the visible magnitude, because that is least in the horizon; the cause therefore must lie in the visible appearance, which proceeds from the greater paucity of rays coming to the eye, producing faintness. Mr. RowNING Supposes, that the moon appears furthest from us in the horizon, because the portion of the sky which we see, appears, not an entire hemisphere, but only a portion of one; and in consequence of this, we judge the moon to be furthest from us in the horizon, and therefore to be then largest. Dr. SMITH, in his Optics, gives the same reason. He makes the apparent distance in the horizon to be to that in the zenith as 10 to 3, and therefore the apparent diameters in that ratio. The methods by which he estimated the apparent distances, may be seen in Vol. I. pag. 65. The same circumstance also takes place in the sun, which appears much larger in the horizon than in the zenith. Also, if we take two stars near each other in the horizon, and two other stars near the zenith at the same angular distance from each other, the two former will appear at a much greater distance from each other, than the two latter. Upon this account, people are, in general, very much deceived in estimating the altitudes of the heavenly bodies above the horizon, judging them to be much greater than they Dr. SMITH found, that when a body was about 23° above the horizon, it appeared to be half way between the zenith and horizon, and therefore at that real altitude it would be estimated to be 45° high. Upon the same principle, the lower part of a rainbow appears broader than the upper part. And this may be considered as an argument that the phænomenon cannot depend entirely upon the greater degree of faintness in the object when in the horizon, because the lower part of the bow frequently appears brighter than the upper part, at the same time that it appears larger; also, this cause could have no effect upon the distance of the stars; and as the difference of the apparent distance of two stars, whose angular distance is the same, in the horizon and zenith, seems to be fully sufficient to account for the apparent variation of the moon's diameter in these situations, it may be doubtful, whether the faintness of the object enters into any part of the cause.

are.

CHAP. XIX.

ON THE ROTATION OF THE SUN, MOON AND PLANETS.

Art. 383. THE time of rotation of the sun, moon and planets, and the position of their axes, are determined from the spots which are observed upon their surfaces. The position of the same spot, observed at three different times, will give the position of the axis; for three points of any small circle will determine its situation, and hence we know the axis of the sphere which is perpendicular to it. The time of rotation may be found, either from observing the arc of the small circle described by a spot in any time, or by observing the return of a spot to the same position in respect to the earth.

On the Rotation of the Sun.

384. It is doubtful by whom the spots on the sun were first discovered. SCHEINER, professor of Mathematics at Ingolstadt, observed them in May, 1611, and published an account of them in 1612, in a Work entitled, Rosa ursina. He supposed them not to be spots upon the body of the sun, but that they were bodies of irregular figures revolving about the sun, very near to it. GALILEO, in the Preface to a Work entitled, Istoria, Dimostrazioni, intorno alle Macchie Solari, Roma 1613, says, that being at Rome in April 1611, he then showed the spots of the sun to several persons, and that he had spoken of them, some months before, to his friends at Florence. He imagined them to adhere to the sun. KEPLER, in his Ephemeris, says, that they were observed by the son of DAVID FABRICIUS, who published an account of them in 1611. In the papers of HARRIOT, not yet printed, it is said, that spots upon the sun were observed on December 8, 1610. As telescopes were in use at that time, it is probable that each might make the discovery. Admitting these spots to adhere to the sun's body, the reasons for which we shall afterwards give, we proceed to show, how the position of the axis of the sun, and the time of its rotation, may be found.

385. To determine the position of a spot upon the sun's surface, find, by the method given in my Practical Astronomy, Art. 125, the difference between the right ascensions and declinations of the spot and sun's center; from which, find the latitude of the spot, and the difference between its longitude and that of the sun's center; this may be done thus. Let Q be the ecliptic, v C the equator, AB the sun, S the center of its disc, v a spot on its surface; draw

ရာ

FIG.

88.