ON THE REPEATING REFLECTING CIRCLE. 99 



vided I compared that repetition with one made at nearly the 

 same distance past noon, I have found the mean perfectly 

 agree with the truth ; although, taken separately, neither would 

 have been considered as good observations. 



It now remains for me to point out the most accurate mode 

 of inferring the latitude from these different series of repeti- 

 tions. The most extensive Tables for these reductions are 

 given by the Baron de Zach. M. Biot has also given a very 

 valuable Table for this purpose. 



Type of the most simple and most accurate mode for determin- 

 ing latitudes by the Repeating Reflecting Circle. 



1. Determine the angle from the arc run through during a 



series of repetitions which must always consist of equal 

 numbers, divided by double the number of repeti- 

 tions. 

 The angle being a reflected one, determine by subtrac- 

 tion each horary angle, and the corresponding quantity 

 of correction, by M. de Zach's Tables, in his work, At- 

 traction des Montagnes. 



2. Determine the apparent altitude and zenith distance. 



3. Determine the refraction diminished by parallax. 



4. Form for each series the sum of the horary angles. This 



sum is composed sometimes of the difference of the 

 sums before and after noon. 



5. To form the sum of the quantities corresponding to the 



horary angle, from the Tables, which is always the sum, 

 and never the difference. 



6. When there are several different series of repetitions of 



ten to calculate together, they become then but as one 

 series, viz. of 20, 30, or 40 observations ; therefore 



n 2 there 



