38 On finding the Longitude ly Lunar Observations. 



and altitudes. But this is a degree of nicety too laborious for 

 common practtice. 



It will probably be alleged that much has been said about a small 

 correctiou, — that of removing the effects of the contraction of the 

 suii and moon's disk. But if this degree of accuracy may be at- 

 tained with little or no additional labour, I think it ought not 

 to be neglected ; and the more especially as there are probably 

 abundance of remaining inaccuracies not so easily dislodged from 

 the lunar distances. Besides, I do not consider an error of seven 

 or eight minutes of longitude unworthy of avoiding, when it can 

 be done so easily; and a much greater error may sometimes be 

 produced by neglecting the quantity under consideration. To- 

 ward the equator, where the errors depending on the figure of the 

 earth vanish, this one may still have its maximum effect on the 

 lunar distance. 



Among other vague things so abundant in books of navigation, 

 it is customary to say — that " the limb of the Hadley's cpiadrant 

 contains only 45° or the eighth part of the circle; but that by 

 reason of the douhle reflexion the angle is doubled." It would, 

 indeed, be difficult to give a more insignificant description of this 

 instrument ; for it is easy to show, that the doubling (or rather 

 halving) is completely effected by the first reflexion : tlie second 

 serving no other purpose than that of giving the rays a more con- 

 venient direction. It might perhaps have at least some meaning, 

 to say — " that the limb contains only 45", for by reason of the 

 reflexion of the index-mirror, th2 instrument only gives half the 

 observed angle." But our authors on navigation are generally 

 so well trained to follow in the old- beaten track, that they run 

 little risk of wandering into any improvement. 



It is a common popular doctrine, that parallax operates only 

 in a vertical direction. But if this were true, it would make the 

 moon appear of an oval figure, which, as is easily shown, cannot 

 be the case; for it is obvious, that if the moon be spherical she 

 must appear circular, let the observer go where be will, except 

 so far as depends on the intervening medium. The difference of 

 the parallaxes for any two diametrically opposite limbs, consti- 

 tutes what is called the aiigmentation of the diameter. 



Another thing which claims strong reprobation, is, the method 

 of finding the lat'tude by a table of " difference of altitude of 

 l)olestar and pole." This method is always erroneous, unless the 

 latitude be near to 0; or, when the polestar is in the meridian — 

 a case where the aid of such a helpless table is not wanted. 



In this method it is liberally supposed, that the altitude of the 

 polestar when six hours distant from the meridian is the same as 

 that of the pole. This, however, is no where true but at the equa- 

 tor j and the reason is obvious: for in any other case when the 



star 



