had occurred 2450 eclipses-which gives for the mean interval between the eclipses of Jupiter's first satellite, 1d. 18h. 28m. 35s. 77 a result which is probably very accurate, for in selecting the above observations care was taken to obtain two which should be made when Jupiter was at very nearly the same part of his orbit, by which means the effect of Jupiter's unequal motion in his orbit is totally avoided-for the remaining causes (of which we will speak presently,) it must be recollected that our result is only affected by 1-2450ths of its amount, so that an uncertainty of one hour would only affect our interval by a little more than one second of time, but since in the end it will appear that 5 or 6 minutes is the extent to which we are liable, we may state that the mean interval between the consecutive eclipses of Jupiter's first satellite, or speaking in Astronomical language, the Synodic revolution is performed in 1d. 18h. 28m. 35s. 77. In selecting the first satellite we are led to give it the preference in the first instance in consequence of the rapidity of its motion, which enables us to observe the phenomena to much greater accuracy than can be attained with the other more distant satellites, but more particularly does the first satellite suit our present purpose from the fact that the plane of its orbit is very nearly accordant with the plane of Jupiter's orbit, and further, that the deviation of the orbit of Jupiter's first satellite from a circle is so small as not materially to af fect a result like the present one, which lays claim to but limited degree of accuracy: under these circumstances the above result may safely be assumed as the mean time of the Synodic revolution; (an interval which we ought to obtain from any two observations made when Jupiter was situated at his mean distance from the Sun.) Now it is plain that in the period of a Synodic revolution, the satellite has performed more than one complete, or a Sidereal revolution; to compute the time of a Side a very real revolution we have the daily motion of Jupiter in his orbit 4m. 59.26s.* consequently in a Synodic revolution the satellite performs 360d. 4m. 59s. 26 and by the rule of three we find that as 360d. 4m. 59s. 261d. 18h. 28m. 3.5s. 77: 360d.: the time of a sidereal revolution or. Id. 18h. 27m. 33s. 32; or it appears that when Jupiter moves with his mean velocity or at the rate of 4m. 59s. 26 in a day, the satellite after quitting the shadow of Jupiter has to move through a complete revolution and for Im. 2s. 45 more, until it will again leave the shadow-were the motion of Jupiter in his orbit double of this amount the satellite after completing one revolution would have to tra vel for 2m. 4s. 90 until it would arrive at the edge of the shadow &c.-thus much being premised we will now consult observation; for this purpose some observations made at the Madras Observatory are available as folIows:- h. m. S. 1834 October 16 Immersion of 1st Sat. 16.21-41. 1835 March.. 30 Emersion. April.... 15.... ... 9. 7.24. 7.28 1. In selecting the above out of a great many, care was taken that the circumstances with regard to distance from the Earth should be as near to the extremes as possible, thus at the first observation the distance. of Jupiter from the earth was, miles....387,700,000at the second. third.. .526,500,000 ..546,000,000 the above, however, are not the best observations adapted to our purpose, inasmuch as, the first is an observation of the Immersion of the satellite into the shadow of Jupiter or the beginning of the eclipse, whereas the second and third are the observation of the Emersion or the end of the eclipse, hence it becomes necessary to reduce the Jupiter performs his Sidereal revolution in 4332 days 14 hours which gives 4' 59" 26 for his daily motion. former to the tenor of the latter or vice versa, to do which we require to know the interval occupied by the satellite to pass over the shadow of Jupiter, for this purpose we must again consult observation; from the best authorities we find that the first satellite arrives at its greatest elongation from the planet at a distance of 3,034 equatoreal diameters of the planet, or the circumference of the orbit 19,000 35 diameters, which is performed as we have found above in 1d. 18h. 27m. 33s. 32; hence 1 diameter is performed in 2h. 14m. 5s. which from the proximity of the satellite to the planet may be assumed as the duration of the eclipses of this satellite-if we now apply this number to the observation of 1834, October, 16 we obtain the time of Emersion, 18h. 35m. 46s—Subtracting the first from the third observation we determine that a certain number of complete synodic revolutions had taken place in 180d. 12h. 52m. 15s. 0 which being divided by the time of one revolution shews the number to be 102; pursuing the same course with the second and third observations it appears that 9 complete synodic revolutions were performed in 15d. 22h. 20m. 37s. Now the times of performing 102 and 9 sidereal revolutions are 180d. 180d. 10h. 10h. 50m. 50m. 38s. 64, and 15d. 22h. 7m. 59s. 88 respectively, in which periods (see the Nautical Almanac) Jupiter has advanced in his orbit 14° 27' and 1° 23' respectively, and the times necessary for the satellite to perform these angles are 1h. 42m. 15s. 3, and 9m. 47s. 3, which added to the above times of performing the sidereal revolutions gives 180d. 12h. 32m. 53s. 9 and 15d. 22h. 17m. 47s. 18 for the true interval between the eclipses which were observed as above, whereas on account of the progressive motion of light the observations in each case were observed later by 19m. 21s. 1 and 2m. 49s. 82. Now in the interval between the first and third observation Jupiter had increased his distance from the earth 158,300,000 miles and between the second and third 19,500,000 miles; the former giving the time for light to pass over 95 millions of miles (the distance from the sun to the earth) 11m. 36s. 8 and the latter 13m. 47s. 4: the discordance between these results appears to arise mainly from an error of about 40 seconds in the third observation, but this in no way interferes with the intentions of this sketch which aims at merely a rude description of the modus operandi, (and a very rude one it is too!) and not to determine from three observations the value of an element which is already known from the result of thousands. ASTRONOMICUS. VI.-Calculation of all the occultations visible at Madras during the present year.—By GODAY VENCAT JUCGAROW. To the Editor of the Madras Journal SIR, of Literature and Science. The handsome reception which you gave my tables on a former occasion has encouraged me to make a further attempt-accordingly in the following pages I have given the result of my calculation of all the occultations which will be visible at Madras during the present year, and beg you will kindly give them insertion in your excellent Journal. As the accuracy of calculation depends upon the method employed, I here annex the formula and an explanation to enable the enquirer to ascertain the correctness attained. The assumption made is, that the motions of the Moon in right ascension and declination combined with the effects of parallax is equable for the interval of an hour, and this is not very far from being the case, thus— h. m. Moon's A. R. h. m. Moon's A. R. -On 9th June at 11.35 15 57.46.05 and at 12.3516. 0.19.64. Apparent A. R....15.56.53.90 Apparent horary motion...... 1.29.59. -· 1.56.15. 15.58.23.49. On 9th June at 14. 316. 4. 0.97 and at 15. 316. 6.35.61. Apply the Parallax -1.13.61 Apparent A. R....16. 2.47.36 Apparent horary motion...... 1.35.61. 2.12.64. 16. 4.22.97. Hence we find that in an interval of nearly three hours the variation of the hourly motion is only Es., C2 or 2s. an hour and of this or Os., 25 is the greatest ccrrection for second differences; but the Moon's apparent horary motion in right ascension being about lim. an error of even one second will not alter the predicted time of occultation more than a minute. Now to find the times of Immersion and Emersion it only remains for us to determine the apparent place of the Moon and its horary motions, from which, we may compute the two instants when the distance of the centre of the Moon and star is equal to the semi-diameter of the Moon, thus Find from the Nautical Almanac or any other Ephemerides the time when the Moon is in conjunction in right ascension with any proposed star together with the difference of declination of the Moon and star at that moment, then compute the corresponding siderial time, the moon's right ascension and declination, and the hourly variation; then the siderial time—the Moon's right ascension will be the Moon's hour angle, which will either be + or as the situation of the Moon is to the west or east of the meridian. = It is evident that to a spectator on the surface of the Earth the apparent conjunction in right ascension happens sooner than the true as seen from the centre of the |