ASTRONOMICAL PAPERS 



127 



rors arifing from them may be greatly leffeued, by taking 

 a mean of them: So that angles may be meafured by it 

 with much greater precifioii than can be attained by the 

 common quadrants. This will make it peculiarly fervice- 

 able for finding the longitude at fea, from the obferved dif- 

 tance of the Moon from the Sun, or from a known ftar 

 near her path. For unlcfs this diftance is meafured accu- 

 rately, it will occafion a confiderable error in the deduced 

 longitude. 



That the inftrunient may anfwcr thefe purpofes, it Is de- 

 figned that the arch fliall contain an hundred and twenty 

 whole degrees, and be numbered from the middle to 120 

 both ways, and that inftead of one central fpcculum two 

 Ihould be affixed to the index, and inclined to- each other 

 in an angle of 60 degrees. When they are oncf adjufted to^ 

 this inclination, let them be fcrewed fafl by the inftrument 



maken 



Now the largenefs of the arch will enable us to meafure 

 much greater angles than can be meafured by the fore ob- 

 fervation of the common odant. If the Sun be within 30 

 degrees of the zenith, the double fextant will give his al- 

 titude either above thefouthcrn or northern horizon, as may 

 bemoft convenient; or for the fake of greater precifion, both 

 may betaken in the fame manner as bytheforeobfervatlon; 

 and then half the difference between their fum and 180 de- 



*, 



grees, 



being added to the lefler altitude when the fum is 



lefs than iSo degrees, or fubtrafted from it, when greater, 

 will give his true altitude from ncareft horizon more ac- 

 curately than either of them feparately could give it. This 

 may be done by one central fpeculum alone and one half 

 of the arch. The fame may be repeated by the other, and 

 the mean of all the four obfervations taken as Hill nearer 

 to the truth. Hereby the error of adjuftment Is taken a- 

 way, and that of the obfervations, lefTened. Or thefe er- 

 rors may be corrected by the mean of four obfcrvatlons^j 

 when only one horizon can be made ufe of, in thefollow- 



Let the altitude be taken in the common 



mg manner. 



wayv 



■^ 



