GEODESIC INYESTIGxVTIONS. 



A NEW and simple method of computing with precision the un- 

 known entities : — latitudes, longitudes, azimuths, circular 

 measure of spheroidal arc, angles between normal planes, and 

 angles between geocentric radii and chord of arc — pertaining 

 to the principal problem in Geodesic Surveying. 



By Martin Gaedinee, C.JE., Memher of the Mathematical Society of 

 Lojidon. [^Read before the Society, 9 July, 1873.] 



{See plate.) 



G-rvEN the lengths a, h, of the equatorial and polar radii of the 

 earth, the geodesic distance d between two stations 8', 8" on 

 its spheroidal surface, the geographic latitude V of the station 8', 

 and the geographic azimvith A! of the other station as taken from 

 the station 8', to find : — 



1°. The circular measure 2 of the geodesic arc d, the 



length c of chord of this arc, and the angle which it 



subtends at the centre of the earth. 



2°. The geocentric azimuth A, of the station 8" as if taken 

 from ;S", — the dihedral angle ^' between the two planes of 

 the chord c which contain the normal at 8' and the geo- 

 centric radius to 8' respectively, — and the angle a! which 

 the chord c makes with the geocentric radius to 8' . 



3°. The difference of longitude f" of the stations, and the 

 geocentric azimuth A^^ of the station 8' as if taken from 

 8", — and also the geocentric and geographic latitudes a" ^ 

 I" of the station *S'". 



4°. The geograpliic azimuth A' of the stntion *S" as if 

 observed from the station 8", — the dihedral angle i' of 

 the two planes which contain the chord c and the normal, 

 and the chord c and geocentric radius to the station ^S'", 

 respectively, 



5°. The angle /^ between the two planes, one of which con- 

 tains the chord c and normal at 8' , and the other — the 

 chord c and the normal at 8''. (The two planes may be 

 designated the " normal chordal planes.") 



