ly Lunar Observations. 249 



tion. Now if the points G, D, and, also F, E, coincided,tbe angles 

 at those points would represent the parallaxes for the two opposite 

 Hmbs ; and in that case DAE + ADB = DHE = AEB + EBD. 

 Whence AEB -ADB = DAE -EBD. But the points G andD, 

 F and E, are necessarily different points ; and the angles formed 

 by A D andJB G produced, and by B E and A F produced, would 

 not be the parallaxes of points upon the surface of the moon. 

 The error indeed will be inconsiderable, but still it is an error ; 

 and the augmentation can easily be computed on principles to 

 which no theoretical exception can be taken. 



Dr. Mackay concludes, that the change of parallax at any al- 

 titude answering to a change of altitude equal to the moon's 

 semidiameter will be the augmentation answering to that alti- 

 tude. This is theoretically true. Mr. Meikle perhaps imagines 

 that it is the same principle as that which he has delivered. 



He next animadverts on the method of finding the latitude 

 by a table of *' difference of altitude of the pole-star and pole,'* 

 and he declares that it " claims strong reprobation." — " It is 

 always erroneous," he says, " except the latitude be nearly 0, 

 or when the star is in the meridian." 



The authors who have inserted that table in their work?, knew, 

 I hope, as well as Mr. Meikle, that the latitude found by it was 

 only approximate ; and they probably knew also that under cir- 

 cumstances in which the altitude of the pole-star could be ob- 

 served at sea, the maximum error of the approximation was too 

 insignificant to be regarded. In high latitudes where the error 

 becomes worth notice, the pole-star cannot be seen during sum- 

 mer ; and ships do not frequent very high latitudes in winter. 



The " liberality" of the supposition that " the altitude of the 

 pole-star when six hours distant from the meridian is equal to 

 that of the pole," is not to be attributed to ignorance. It is as- 

 sumed as a hypothesis nearly true, and from which a useful prac- 

 tical rule may I)e deduced. By the aid of that table, a common 

 watch and a quadrant, an observer but indifferently skilled in 

 computation may ascertain his latitude in a favourable ■ight, 

 as often as he pleases, and to a degree of exactness sufficient for 

 all practical purposes at sea. It is on this account only that the 

 table is given ; not because tbe latitude determined on the hypo- 

 thesis on which the table is constructed, is strictly correct. 



He remarks further that no provision is made for the effect of 

 " the rapid change of polar distance to which the star is sub- 

 ject." This remark is not generally correct. In Nerie's Epi- 

 tome, any error of this kind is guarded against in his remarks on 

 the use of the table. And in the valuable tables of Mendoza 

 Rios, where the same method is given in a slightly different form, 



any 



