THE LUNAR METHOD, ScC. 433 



Let AD be the diameter of the moon, and A the 

 center of a ftar in contact with the moon's limb : now, 

 as the enlightened part of the moon evidently appears 

 to extend beyond the dufky part, let the concentric 

 circle BC rcprefent the moon's limb thus apparently 

 magnified, and fuppofe the ftar to be equally magni- 

 fied; then with the center A, and the diftance DC, 

 defcribe a circle, which confequently will touch the 

 moon's apparent circumference inwardly : now, as this 

 laft is a confequence of fuppofing the center of the ftar 

 to touch the circumference of the moon, exclufive of 

 the deception, it follows, that the proper method of tak- 

 ing the dijiance, is to make thejlar appear to touch the 

 moon inwardly. 



But all the writers on this fubject have particularly 

 directed that the ftar be made to touch outwardly. Let 

 B, therefore, be the point of conta6i, and a the center: 

 the error then is Aa, or the fum of the apparent increafe 

 of the moon's radius, and the apparent radius of the (tar: 

 this quantity, it is evident, will make a confiderable 

 error in the refult; and errors arifing from this fource 

 are the more to be attended to, as they are not of a kind 

 to be lefiened by increafing the number of obfervations. 

 The fame reafoning is applicable to the Sun and Moon > 

 with very little alteration. 



The diftance of the Moon from the Sun or a Star, at 

 each three hours, is given in the Nautical Ephemerisj 

 and the method of inferring the time for any interme- 

 diate diftance, is by fimple proportion : this would be 

 juft if the Moon's motion was uniform : but as this is 

 not the cafe, the velocity fhould be taken into the ac- 

 count, as well as the fpace, in determining the time 

 taken by the Moon to move any given diliance ; and 

 the proper meafure of the velocity is fuch a quantity 

 as has the fame ratio to the fpace defcribed, as three 

 hours have to the time that has been actually taken to 



move 



