The transits of Mercury over the sun are rare, and the longitudes derivable from them not very accurate.
3. A good and now fashionable method of determining the longitude is by observing with a transit instrument the meridian passage of the moon's bright limb, and of stars which are near her parallel of declina tion. The ' Nautical Almanac' contains a list of the stars proper to be observed with the moon, and also the variations of the moon's R. A. in one hour, of longitude, for computing the longitude.* When the place of observation is tolerably near Greenwich, the computation is very simple, that is, if the transit is nearly in. the meridian and the moon is observed all over the wires. The error of the chronometer is taken from the neighbouring stars, and the transit of the moon corrected for this error, and for the rate, if sensible. If the place be to the east of Greenwich, the R. A. of the moon is less ; if to the west, the It. A. is greater than at Greenwich. Taking the difference between the R. A. at the place and at Greenwich, and dividing by the variation in one hour of longitude, you have the longitude of the place E. or W. in hours and decimals of an hour. But this result requires correction when the corresponding observations at Greenwich, Cambridge, Edin burgh, &c., can be procured; for the R. A. of the moon may be erroneous more than from the imperfection of the lunar tables. By using the R. A. of the moon and stars observed at Green wich, the longitude will not be affected by the errors of the tables. It is pretty much the same thing, and at times more convenient, to let the former computation stand, and to compute the longitude of Greenwich, Cambridge, &c., from the observations respectively made there, taking care to note the Rigel& of the resulting longi toddle. non if the longitudes of the known and of the unknown piece are both east or both west, the difference will be the true longi tude c.1 the unknown place, test or west of the known one. Some telescope,. give a larger image of the moon than other., and its apparent du-teeter is affected by varying the aperture of the object-glass. The resulting errors in the longitude are got rid of by observing the second limb as often, if possible, is the first, and then, keeping the results separate. by teding a mean of the two. There is a notion anmeg many observers, that there is no need to care for the pennon of the transit Now any considerable error in the position of the transit does occasion an equivalent error in the longitude, and though it can be corrected, if there are data for determining the want of adjustment, this gives some trouble in the computation. It is so miry to place a
transit very nearly in the meridian, and to adjust it In every rtupect, at heat approximately, that there is no excuse for carelessness in this respect. The observer should always take the transits of a star near the pole, and of all Greenwich stars above and below the moon which ram about the time of her culmination, and it is proper to reverse the matrument on alternate nights. When the place of observation is very distant from Greenwich, it will be necessary, until the quantities a, b, c, d, mentioned in the note, be computed, to take a little more trouble. The approximate longitude is calculated as before, and then the It. A. of the moons bright limb mast be computed for tho corresponding Greenwich time, from the It. A. of the moon for every boor ; the moon's semi-diameter in It. A. must also be computed. We have found it on the whole most intelligible, and therefore most safe, to compute the R. A. of the moons bright limb on two hypotheses of longitude, one the minute above and the other the minute below the approximate value. These results are to be corrected by the Greenwich or other observations for the error of the lunar tables, and then, by simple pro portion, the correction is determined for one of the hypothetical longi tude*. This is rather a long process, but it is strictly accurate, and the steps are intelligible as the computer proceeds. The method of determining the longitude by transits of the moon and stars is the best f sr place* very distant in latitude or longitude, where the same occulta tions cannot be seen. It is nearly as good for the most distant as the merest piece, the variation of the error of the lunar tables being the only additional cause of inaccuracy, and the phenomenon presents itself very often. It does however require a very nice' and well fixed instrument and a careful observer, as 1' error in observing the lt. A. of the moon will cause an error of nearly 30' in the resulting longitude, or 1 of a degree. A considerable mass of observations of both limbs corrected by corresponding observations will scarcely be more than or 3' wrong.