On the Repeating Circle. 265 



error, having only to take altitudes at an equal distance on the 

 other side of the meridian, where the error d-^ changes its 

 sign and is desti'oj^ed. It is obvious, from all these considera- 

 tions, that for the accuracy of the result it is indifferent to ob- 

 serve the pole-star when it passes the meridian, or to observe 

 it in any point whatever of its parallel ; but for the con- 

 venience of the observer, and for the infinitely valuable advan- 

 tage of being able to collect a great many good observations 

 of latitude in a short time, my method seems to deserve the 

 preference before all others. The observer does not de- 

 jjend on a single instant which occurs in 12 or 24 hours, and 

 which bad weather, a cloud, or other accidents, may render 

 unavailable. With my method he may take the star's altitude 

 at any time of the day or night, at his pleasure, the atmosphere 

 permitting, or when he shall have the leisure and the inclina- 

 tion. In 24 hours he may take as many observations as he 

 pleases, and collect in that time a great number of latitudes. 

 I have therefore employed this very method to determine the 

 latitude of my observatory, and you will judge, sir, whether 

 the observations which I have the honour to send to yon de- 

 serve any confidence. I shall add a few Avords more on the 

 method of calculating them. 



I have made a little table, which with the argument t fur- 

 nishes me with the two quantities m and n given by the fol- 

 lowing expressions : 



sin. 11. sin. ■vt 



VI — -. ' — . sm. t. 



sin. z 



n — ?w cotang. t. 



Let 9, 6', S" be the differences of the times of observa- 

 tion, and of the middle of all those times, I seek in the well- 

 known table in the hands of all astronomers the quantity 



. _ gsin.g^^ 2 sin.'i 4 ^' , 2 sin.'^ \t" , o 

 ^ - sin. 1" + sin. 1" + sin.T^^*^'^ 



Having obtained by these two tables, almost without calcu- 

 lation, the quantities m, n and A, the rest of the operation is 

 very easy. Denoting by N the number of repetitions, we have 



Jz r= [n — m'^ cotang. z) -rr-, 



Tang. X = tang.ja. 



* ' COS. p. 



Tliis calculation may be further simplified by constructing 

 a little table to give the value of the quantity « — ??«' cotang. z, 

 whicli (lejK-nds on the argument /, and then the first table 



Vol.60. No. 294-. Oct. 1«22. L 1 will 



I 



OS. {z-dx) j 



