102 Astrofiomical and Nautical Collections. 



the apparent diitances should always correspond with the greatest 

 difference of the apparent altitudes. 



The quantity Ss, or I, will not be affected by the errors of dip, 

 or terrestrial refraction : and may be obtained either by taking the 

 difference of the corrected altitudes, or by increasing the least of 

 the apparent distances by the difference of the refractions at the two 

 altitudes. 



The rule is applicable to stars on the same vertical, wherever 

 situated ; but in practice, it will be found convenient to take them 

 in that part of the heavens towards the elevated pole, because the 

 observations may then be made with greater expedition, and it may 

 then be readily determined, which stars are about to appear on the 

 same vertical. 



This method is not embarrassed by distinctions of cases, and 

 requires only the common tables. 



ii. A Rule for finding the Latitude hrj two altitudes of the Sun, err 

 qfajixed Star, and the time elapsed between the Observations. 



The Rule is divided into two parts ; the first part to be used 

 when the latitude and declination are of different names, and the 

 second when they are of the f^ame name. 



The letters A, a, denote respectively the greater and less alti- 

 tudes ; D, d, the declinations at those altitudes, D' the mean de- 

 clination, and E the elapsed time. 



The azimuths are of the same name with the latitude. 



The elapsed tmie is supposed less than twelve hours. 



In finding the natural number to a logarithm, it the index be 9, 

 find the number to as many places as the tables are calculated to ; 

 if the index be 8, to one less, and so on. 



Rule I. 



To be used when the latitude and declination are of different 

 names. 



1. Add together the log. cosin. D', the log. sin. ^.E, and reject 10 

 from the index ; look for the remainder among the log. sines ; twice 

 the corresponding arc, will be arc I. 



