On the 7th of July, 1823, at Dunglass House, the seat of Sir James Hall, Bart., in latitude 55° 56′ 32" N., and longitude by estimation 9m 30 W., Captain Basil Hall, R. N., observed the end of a solar eclipse at 7h 55m 34.1 mean time; required the true longitude of Dunglass? July 7th, July 7th, Mean Time, 17h 55m 34.1 equ. of time to 18h 1m 17h 55m 34 Est. lon. in T. + 9 30 4 28.7 Eq. of T. at noon 4 21 24 Or 18 1 nearly. From angles taken by Captain Hall at Dunglass and at North Berwick Law, with the Isle of May light, it appears, on com- IV. BY THE MOON'S TRANSIT. Mr Bailey's Method. The method of determining the difference of longitude between two given points on the surface of the earth, which is one of the most difficult problems in practical astronomy, has long engaged the attention of various astronomers and mathematicians; and has been executed with more or less accuracy according to the means employed for that purpose. If the distance between the two observatories be not very great, their difference of meridian may be determined with considerable accuracy, by means of chronometers conveyed from one observatory to the other; or by means of signals previously agreed on. These methods have been practised very successfully on many recent occasions. But, where this is impracticable, we must have recourse to the observation of certain celestial phænomena for the solution of the problem: and for this purpose, five several and distinct methods have been proposed: 1° the eclipses of Jupiter's satellite's: 2° eclipses of the moon: 3° eclipses of the sun: 4o occultations of the fixed stars: 5° the meridional transits of the moon, compared with certain stars previously agreed on. The results deduced from the observations of the eclipses of Jupiter's satellites are, for obvious reasons, very unsatisfactory. The phænomena will, in fact, appear to take place at different moments of time, with different instruments and to different observers. Moreover, they are visible only in certain positions of the planet in its orbit, a circumstance which very much circumscribes the utility of the method. The eclipses of the moon afford a still more unsatisfactory result: they occur but seldom in the course of a year, and the phænomena attending them cannot (on account of the indistinctness of the border of the earth's shadow) be observed with that degree of accuracy which the present state of astronomy requires for such purposes. Eclipses of the sun are more certain in their deductions; but they so rarely occur, and are at the same time so limited in extent, that they can seldom be brought in aid of the general solution of the problem. There remain, therefore, only the two other methods, on which the practical astronomer can safely and constantly depend. Of these, I am aware that occultations of the fixed stars by the moon have been long considered as affording the best means of determining the difference of longitude between two places: and, assuredly, the results deduced from such observations, made under favourable circumstances, have agreed with each other to a greater degree of accuracy, than those deduced by any of the preceding methods. There are, however, many circumstances, attending the practical solution of the problem by this method, which tend to diminish the confidence which is reposed in the correctness of the theory. In the first place, it is necessary to know the apparent right ascension and declination of the star very exactly, on the day of observation; which, if the star is of inferior magnitude (and such being the most numerous, are the most likely to be occulted), may not be readily determined; for, we may not be able to find it in any catalogue ; and, when found, we have to compute its precession, aberration, and nutation expressly for this purpose. In the second place, we have to calculate the parallax of the moon for the given moment of observa tion: and in this computation we must assume a given quantity for the compression of the earth; respecting which astronomers are by no means agreed, and which will consequently give rise to various results, according to the view which each astronomer may take of the subject. Thirdly, this method is dependent on the accuracy of the lunar tables, not only as to the position of the moon and her horary motion, but also to her horizontal parallax and semidiameter. Fourthly, the method is, in a great measure, dependent on a correct knowledge of the longitude and latitude of the place of observation. And, lastly, the apparent border of the moon is so uneven (consisting of projecting mountains and hollow valleys) that we cannot always depend on the immersion or emersion having taken place at the exact distance from the moon's centre, as computed from the lunar tables. The meridional transits of the moon, agreebly to the method about to be described, are free from all these objections: the observations are made with the greatest facility; the opportunities are of frequent occurrence; the absolute time is of no material consequence; the computations are by no means intricate or troublesome; and the results are (I believe) more to be relied on than by any of the preceding methods. This method consists in merely observing, with a transit instrument, the differences of right ascension between the border of the moon, and certain fixed stars previously agreed on;* which stars are so selected that they shall differ very little from the moon in declination. It is evident that this method is quite independent of the errors of the lunar tables, except as far as the horary motion of the moon (in right ascension) is concerned, and which, in the present case, may be depended on with sufficient confidence: that it does not involve any question as to the compression of the earth: that a knowledge of the correct position of the star is not at all required: and, finally, that an error in the state of the clock is of no consequence. Consequently, a vast mass of troublesome and unsatisfactory computation is avoided. Moreover, it is the only method that is universal, or that may be adopted, at one and the same time, by persons in every habitable part of the globe: for it is applicable to situations distant 180° in longitude from each other; and even beyond that if required. It might indeed, at first sight, appear that the same results would be obtained, if we merely observed the correct time of the moon's transit, without any reference to the contiguous stars: but a moment's reflection will convince us that, by referring the moon's border to the adjacent stars, we obviate all errors not only of the clock, but also in the position of the transit instrument. For the solution of this problem, let us make t = the difference (in sidereal time) of the transit of the moon's limb, and of the star previously agreed on, at the observatory situated most westerly; which will be positive when the star precedes the moon, or when the AR of the moon exceeds that of the star; but, on the contrary, negative. the similar difference at the observatory situated most easterly. Lists of such stars, called moon culminating stars, are now annually published. |