52 



We have already computed that in latitude 30°, with a 

 star having a polar distance of 30°, the value of h h^ = ?»' 49", 

 if 5rr-_15 min. Therefore, if under these conditions of obser- 

 vation the error amounts to 1', the value of 6= v/.j| x 15 = 7*6 

 min. If the error =1", the value of 5 = V^ x 15 = 1 min. 



It thus appears that, provided the observations extend 

 evenly over an equal time on each side of elongation, there 

 is no need for the surveyor to know the local time with great 

 precision, an error of 1 minute in the time producing an error 

 of only about 1" in the azimuth. 



But if the observations do not extend on each side of 

 elon oration the case is different, and a more accurate know- 

 ledge of the time is essential. Suppose, for instance, that the 

 observations are all on one side of elongation, extending from 

 to a, the mean value of the ordinate to the curve is then 



' a- 



u - ^ 3 



If, however, there is an error, h, in the time, the com- 

 putation will extend from h to a + h, and the computed mean 

 value of the ordinate is 



1 r^ + ^ r/2 



— /.• .T~ dx = k (— + a b + b-) 

 a\ 3 



The error here amounts to k b (a + b). 



If & is 1 min. and a is 15 min., the error = 16 k and under 

 the same circumstances as before will = 16", being 16 times as 

 great as when the observations extend for 15 min. on each 

 side of elongation. 



Where an accurate determination is sought, the investi- 

 gation shows the desirableness of obtaining a series of 

 observations distributed as evenly as possible on each side of 

 elongation. 



Second Method, Horizontal Angle and Altitude being 

 Noted at each Observation. 



With the same notation as before, the star being in any 

 position, we have 



cos y? = cos c cos z + sin c sin z cos A 

 Writing .r = 2' — 2„, this becomes 



cos ]) = cos c cos (Zq + x) + sin c sin (z^ + x) cos A 



p, c, and z^ being constants, this equation gives A as an 

 implicit function of x. 



