REDUCTION OF TRIANGULATlnN. 73 



difference in latitude between two adjoining stations is obtained from the 

 following equation, based upon the Clarke spheroid: 



— dL = K cos a' B+K 2 sin 2 a' + (,IL) 2 D — Mv 2 sin 2 a' E, 

 in which 



dL is the difference in latitude. 



K, the distance between the stations in meters. 



a', the fore azimuth of the line connecting- them, measured round clock- 

 wise from the south through the west. 



//, the first term. 



SL, the approximate difference in latitude, being the sum of the first 

 two terms. 



B, C, 1), and E, constants derived from the dimensions and figure of 

 the earth. 



These are given for various latitudes in tables at the close of the 

 volume. 



The difference in longitude is obtained by means of the following 

 formula : 



,. . K sin a' A' 



Mill = tT 



COS L 



in which 



»/M is the difference in longitude. 



L', the newly determined latitude. 



A', a constant, from tables near the end of the volume, and the others 

 as above. 



The azimuths at the two ends of a line differ from one another, on 

 account of the convergence of the meridians. That first determined is known 

 as the fore azimuth, the other, the back azimuth. All azimuths are meas- 

 ured from the south point around to the right. 



The back azimuth is computed from the formula: 



sin ( L+L') 



2 



cos \ dL 



where M is the longitude of the first station. 

 L, the latitude, and 

 L' the latitude of the second station. 



