iVPPENDIX. 



A.. — To prove that Tan Convergency = Tan Dep . Tan Mid Lat. 



Fig. 117. 



Here C is tbe centre cf tlie esirth, ? i.« the pole, E P, Q P, two meridmns 

 a known distance apait, B L, E L, are two tangents to the meridians, at 

 the middle latitude known, in the same plane as the meridiau, and meeting 

 one another and the axis of the earth C P, produced, in L. 



Then B L D is the Convergency required, and D L C is the middle 

 latitude, and BCD the departure. D C is a ladins of the earth = r. 



Now as B D is small, it can be taken as a straight line without sensible 

 error. 



We can also assume B L D and B C D to be right-angled triangles. 



Then B D = D L x Tan B L D. 

 Similarly B D = )• x Tan BCD. 

 Equaling, we have D L x Tan B L D = r x Tan BCD. 



But D L = r X Cot D L C ; 



/. r X Cot D L C X Tan B L D = r X Tan BCD, 



or Tan B L D = Tan B C D x Tan D L C, 



or Tan Convergency = Tan dep X Tan Mid Lat., 



and when Convergency is very fmall, we can say 

 Convergency = Dep x Tan IMid Lat. 

 516 



