September 1th, 1820. 33 



over the surface of the latter; but also states, with regard to 

 the moon's orbit, " that so small a portion of the curve as 

 passes over England may be regarded as a straight line." " The 

 like," he adds, '• may be said of the velocity, vchich for so 

 short a time, (the whole duration of the eclipse), may be con- 

 sidered as equal, without any sensible error." The difference 

 arising from curvature, therefore, or from inequality of motion, 

 must be reduced almost to nothing in the extent of a few 

 thousand feet, and during an observation of less than three 

 seconds. For similar reasons, the diurnal rotation of the earth 

 has been likewise disregarded, since, from the nature of the 

 problem, and in a latitude so high as that of London, its effects 

 on the general result would scarce be perceptible. In truth, 

 to have corrected discrepancies so minute, would have rendered 

 the solution more complicated, and merely added an appear- 

 ance of precision, which the subject, perhaps, does not admit. 

 And in cases of this nature, where an approximation to the 

 truth is all that can reasonably be expected, that method seems 

 most eligible, which, with the due degree of accuracy, com- 

 bines the greatest plainness of inference, and facility in appli- 

 cation. 



As there exists considerable diversity of opinion among 

 astronomers, respecting the altitudes of the lunar mountains, it 

 may be requisite to compare those now given with former 

 measurements. Previous to the discoveries of the present age, 

 elevations were assigned to these mountains altogether incon- 

 sistent with the conclusions from analogy. Hence appear to 

 have arisen the first doubts of the accuracy of the de- 

 ductions. These suspicions were well grounded ; and the prin- 

 ciples employed in the early calculations on this subject, have 

 been proved erroneous*. Disregarding former measurements, 



* Sir William Herschel has shewn that a quantity on which the 

 v'hole of the operation, iu a great measure, depended, was, by some 

 astronomers, assumed as equal to ^.*l' the moon's diameter, and by 

 others to j'j, by which a difference of 2\ miles was produced in the mea- 

 Buremcnt of the same mountain. It appears also, that the same mctiiod 

 would, at different ages of the moon, ^'ve different results. 



Vol. XI. D 



