116 HYDROGRAPHICAL SURVEYING [chap. iv. 



With 1,610 a^ distance, and (50'' -41°) = 9° as " coui-se," 

 diff. lat.=ir).S". diff. long. -2.8". 



Now, since from — 



(1) Maximum probable error (astronomically) = 2-4" diff. lat., 

 5«0" diff. long., and from 



(2) IMaximum probable error (triangulation) = 4-8" diff. lat., 

 6-4" diff". long. 



• r -'4 5-3 



we must divide diff. lat. 15'8 m proportion of -—=-—— , 



5»0 lO'O 



. 5-0 1-3 

 and diff". long. 2-8 in iDroportion of —-=—-. 



6-4 I'O 



Then, since — 



Astronomical diff". lat. =1° 04' 16-8", diff'. long.-T 25' 54" 

 Correction = -5.3" —l-S" 



Accepted diff. lat. -1° 04' 10-5", diff. long. =1° 25' 52-7". 

 Or— === ,^,,,___ 



Triangulation cUff. lat. = 1° 04' 01-0", diff. long. =1° 25' 51-2". 

 Correction = +10-5" +1-5". 



Accepted diff. lat. =1° 04' 11-5", diff. long. =1° 25' 52-7". 



These results, being identical, show that the working has 

 been correct. 



The latitude of A and B (by obi^ervation) must now be cor- 

 rected for the total error of 84" in the diff. lat., in the propor- 

 tion of their individual probable errors, viz., 0-8" and 1'6", 



Thus:— 



Correction to lat. of A = — X 5.3 = 1 'S". 



24 



Correction of lat. of B = -— x5'3 = 3'6". 



24 



Whence : — 



Lat. A (by obs.) =26° 57' 51-6" N., Lat. B=28° 02' 08-4" N. 



Correction = +1-8" -3-6" 



Accepted Lat. A = 26° 57' 53-4" N., Lat. B = 28° 02' 04-8" N. 



As regards the longitude we must accept that of either 

 A or B, and apply the accepted diff. long., viz., 1° 25' 52-7". 

 The diff. lat. and the diff. long, between A and B, both astro- 



