On Practical Geodesy. 



a,, a„ denote the angles of depression of the chord, or arcs S,E^, 

 8„ 8„ „ the small arcs S,D„ S,,D„. 



". 

 R. 



s, k 



V 



6 



A 



a 

 b 

 e 



S.S.D 



angles S,,S^D^ 



normals S^Z^, S^qZ^^, terminating in polar 



axis, 

 lines S,Z,„ S,,Z,,. 

 angles IPS^ and supplement of IPS,^. 

 lengths of geodesic arc and chord respectively, 

 denotes the arc S^S,,, or the angle between the normals, 

 circular measure of the geodesic arc s. 

 arc PI, or angle between the chord and polar 



axis, 

 angle S JS,, between the normal-chordal planes, 

 length of the earth's equatorial radius. 



„ „ „ polar radius, 



earth's eccentricity. 



1. Values of geodetic constants, in accordance with the 

 dimensions of the earth as finally adopted by the Ordnance 

 D.epartment of Great Britain and Ireland. 



log. a = 7-3206934433 



log. b = 7-3192150463 



log. e = 2"-9157795987 



log. e' - 3^8315591974 



log. (l~e') = r997043J059 



log. (j^) = 0029567941 



log. Lf-\ -"3 8345159915 



The geodetic tables above referred to give also the 

 logs, to 8 places of decimals of the normals terminating in 

 the polar axis for all latitudes from the equator to the pole. 

 The well-known formula by means of which any of these 

 normals is expressed in terms of the latitude to which it 

 pertains is — 



R _ ^ 



Jl—e'^ sin2 I 



2. The following relations are evident from the figure — 

 C^p, = 'R^ cos l^; C^p,,=^'R^^ cos l,^ (i) 

 S,p, = Y^, (l—e') sin l^ ; S„,;?9,, = R, (I— e'O sin Z, (2) 



a = 20926348 feet 

 b = 20855233 feet 

 e = -0823719976978 

 e' = -0067851460047 

 (1— e2) = -9932148539953 

 (-^)= 1-0068314987210 



(-^) = -0068314987230 



\1 <?2/ 



CAo = R. 6^«inZ,, (.) 



(CoP.)^+(So^. + C,Z,J^ = Il^ - 2R, 6^ sin^ l^ + ¥ (4) 

 = (CoPj + (Soo^. + CoZ,)^=R^- 2R, e' sin^ Z,-f F (.) 



C,Z„::=R, e^sinZ, 



