CHAP. IV.] RESULTS OBTAINED ASTRONOMICALLY 117 



nomically and by triangulation, being now identically the 



same, we calculate the final accepted mercatorial bearing and 



N. E. 



distance A B=— 50° 01' 50" -^ 99-929'. 

 S. VV . 



The difference between this bearing and the mercatorial 



/N. , E. \ 



bearing ( ^ 50° 06' 00" ™^ j previously calculated from the 



triangulation, is 4' 10", 



This is the correction to. be applied to the mean true bearing 

 of each side, applying it to the left in all cases since the accepted 

 bearing is to the left of the previously calculated bearing. 



The difference between the log. of the accepted distance 

 99.929' found above, and the log. of the distance 99-80' pre- 

 viously calculated from the triangulation, is the log. to be 

 added to the log. of each side, since the accepted distance is 

 greater than the calculated distance. 



The foregoing example illustrates an extreme case. The 

 difference in bearing between the results by triangulation and 

 astronomical observations would seldom be so large as 6'; and 

 since the amount by which the observed astronomical positions 

 require to be altered exceeds the probable error of the observa- 

 tions, it points to the existence of other errors due to deflection 

 of plumb-line. 



Under such circumstances it might be desirable to take this 

 possibility into consideration by assigning larger probable 

 errors to the astronomical positions, and dividing the diff. lat, 

 and diff. long, in corresponding proportions, thus giving 

 relatively greater weight to the result by triangulation if it is 

 sufficiently reliable. 



The effect of any such readjustments in connection with the 

 bearings of the lines A B and A B' may be studied by plotting 

 the triangle B C B' on a large scale. 



In the memoir of the chart, the latitudes, meridian distance, 

 and true bearings as actually observed, should be stated, 

 together with the corrections that have been applied to them 

 to obtain the finally accepted results. The number of feet 

 per mile by which the distances by triangulation have been 

 corrected to agree with the accepted positions should also be 

 stated. 



