78 



The observations for latitude were made under very unfavorable circumstances. 

 Undulations in the atmosphere, heavy winds, and great changes in temperature con- 

 stantly affected the instrument. 



It is customary in this office to select for latitude only thirty-five pairs of stars, 

 which have to be observed on five different nights. But the observer is dependent 

 upon the weather, and is frequently disappointed, although after waiting I preferred to 

 select a greater number of pairs, believing that the final result of a latitude is better 

 when depending upon various star-places, giving the probability that the errors result- 

 ing from the declination-places of the stars will more nearly compensate each other, 

 and that this part of the probable error of the final result will come within that result- 

 ing from observation alone. 



The mean latitude is obtained by taking the mean of all single results. For the 

 different days the mean latitude is found to be as follows: 



O I II 



July 31 . 38 49 42.491 



August 2 4 T -O43 



4 41.702 



5 41-652 



6 41.864 



7 41-585 



9 - - 41-947 



showing a great difference between the first and second day, arising from the disturbed 

 condition of the air. 



The probable error of one observation is, 



, 0.6745 



'"^ , n _ 1 



where v is the difference between the mean results and the single results and n the 

 number of observations; therefore the probable error of the mean result is, 



, = 0.6745 



/ S(v? 

 \/ (n-i) 



If it is proper to place all the observations in the final result with the same weight 

 (as in determining the longitude of a station from different nights' work) the formula 

 should be used in this way; but in determining the latitude of a station, every single 

 result obtained also depends upon the places of the stars forming the different pairs. 

 It is certainly wrong to determine the probable error of the latitude-result by this for- 

 mula, (it would give, for latitude of Colorado Springs, a probable error less than o".oi,) 



