CHAP. IV.] CALCULATING THE TRIANGULATION 107 



In working out the diff. lat. and diff. long, of two positions Correc- 

 from the triangulation geodetically, we have been treating the t^e 

 earth as a sphere. This is not strictly the case, as the form Spheroid, 

 of our globe is that of an oblate spheroid ; but the error intro- 

 duced by assuming it to be a sphere is small, and can often 

 be disregarded in hydrographical work, as being swallowed up 

 in the larger errors incident on imperfect triangulation. 



When, however, a triangulation has been carefully done, 

 and we wish to get the difference of longitude as near as we 

 can, either for the scale of the chart, or for purposes of com- 

 parison with that deduced from the astronomical positions, 

 or in latitudes far from the Equator, the necessary correction 

 for the spheroid should be appHed. 



This correction is 2 Cos^ Mid. lat. x compression. 



The compression of the earth is the proportion that the 

 difference of the equatorial and polar diameters bears to the 



1 



diameter, and can be taken as — . 



300 



The formula for correction for a given difference of longitude 



will then stand : 



Cos^ Mid. lat. 



Correction = diff. long. . 



150 



This is subtractive from the calculated difference of longitude 

 by the triangulation. 



In the latitude of 20°, this correction for a difference of 

 longitude of 100', amounts to 35". as will be seen by the 

 following example : 



In latitude 20° the departure deduced from a triangulation Example, 

 was found to be 94', required true difference of longitude. 



Dep 1-973128 



Sec. lat 0-027014: 



Spherical d. long. 2-000142 ., ,. 100*0327' 

 CusMat 9-945972 



11-946114 

 150 .. 2-176091 



Reduction 1-770023 .. .. -0-5889 



Tr^ie diff. long. 99-4438' 

 or lo 39' 26-6" 



