51 



The Effect of an Ekror in the Time. 

 In the final reduction of the results we sum up a number 

 of terms of the form (6), and since h(^ — h is a small angle we 

 may practically take each term to be of the form k x^, where 

 A' is a constant and r is the difference in time between elonga- 

 tion and the observation. Taking the mean of a number of 

 evenly distributed terms of this form is equivalent to finding 

 the mean value of the ordinate to the curve i/ = h .x^. The 

 observations may thus be represented by a parabolic curve as 

 in the figure, the ordinate P T at any point representing the 

 correction .4^— .1 corresponding to an observation made at a 

 time from elongation re23resented by N. 



/? /7. 



O 



B B. 



It the observations extend evenly over a time, n, on each 

 side of elongation (from A to 5), the mean value of the 

 ordinate // is 



1 ;-^''' A- n~ 



— /,• ./-^ d r = 



^^^ -a 3 



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

 vations will really extend from .4, to B^ (from a — h on one side 

 to a + h on the other), and the computed mean value of the 

 ordinate will be 



1 Ji + h 



I- 



— /■• .r2 rl .!■ = 



+ k 62 



2^'* -a + b 



The error in the copiputed azimuth will thus be k h^, 

 varying as the square of the error in time. 



