236 A NEW METHOD OF 



utmost resources of the most refined analysis, in investigating the numerous 

 disturbing forces, and lunar inequalities which could arise from the theory of 

 gravity, and to the labors of Dr. Maskelyne, are we mainly indebted for the 

 successful application of these and similar researches, to purposes of eminent 

 practical utility. Of the several methods which have been employed for the 

 purpose of determining the longitude on land, the eclipses of Jupiter's satel- 

 lites have, till lately, been considered as ** affording the readiest and, for gene- 

 ral practice, the best method of settling the longitudes of places." But 

 experience has shown, that this is by no means true to the extent implied, 

 and that, although it be perhaps the readiest method of approximating to the 

 truth, it is, nevertheless, very imperfectly adapted for giving results " with 

 that degree of accuracy, which the present state of modern astronomy re- 

 quires." The reader who wishes to make himself acquainted with the history 

 of the meridional transits of the moon, may refer with advantage to the Me- 

 moirs of the London Astronomical Society, in which the subject is accurately 

 illustrated. The method explained by Mr. Baily, refers, however, to corres- 

 ponding observations of the moon's transit over two different meridians*. The 

 method which it is the object of this memoir to explain, is that adopted, (and 

 I believe originated) by the Rev. Mr. Fallows, the Astronomer at the Royal 

 Observatory at the Cape of Good Hope. " To the scientific world," as has 

 justly been observed by the Rev. Dr. Pearson, " the talents of Mr. Fallows 

 are too well known and appreciated, to require eulogium," and I perform a 

 pleasing duty, in availing myself of this opportunity of acknowledging the 

 great obligations which I owe to that distinguished astronomer, for the in- 

 struction and information which I derived from frequent converse and personal 



* In Tilloch's Philosophical Magazine for 1803, a rule is given by Mr. Lowe, for determining 

 the difference of longitude from the observed transits of the moon over two meridians. In substance, 

 the rule is correct, only that the moon's motion in twelve hours, uncorrected by the equation of II** 

 diffs. is adopted, instead of her motion, in the absolute interval between the times of transit. 



