Art. I. — On Practical Geodesy. 

 By Martin Gardiner, C.E. 



[Read 11th May, 1876.] 



The method of investigation employed in this paper is of 

 a purely elementary character, and in this respect it differs 

 from that usnally adopted by the most distinguished 

 geometers who have written on the subject. The method 

 introduced by Legend re, Delambre, and Puissant, and which 

 has been followed by Airy and others, is characterised 

 chiefly by the subsidiary use of the higher calculus and 

 interminable series. 



The elementary method here pursued leads to simpler 

 and more comprehensive formulse, and at the same time 

 aflfords a clearer insight into the various relations between 

 latitudes, azimuths, differences of longitude, length and 

 circular measure of geodesic arc, angles of depression of the 

 chord, &c. Its power of improving and extending the 

 science in one of its most useful directions can be judged 

 of from the numerous new results arrived at, and a com- 

 parison between them and those hitherto evolved by means 

 of the higher calculus. 



The errors which have been shewn to exist in some of 

 the investigations and formulae given in the "account" 

 of the principal triangulation of Great Britain and Ireland, 

 will no doubt attract the attention of Engineers and 

 Surveyors engaged on trigonometrical surveys in India 

 and elsewhere. 



Let P^ be the pole of reference of the spheroidal earth ; 

 „ Cq be the centre of the earth ; 

 „ S^, S^^, be any two stations on the earth's surface ; 

 „ Z^, Z^^, be the points in which the normals at the 

 respective stations S^, S^^, cut the earth's polar axis. 



The planes S^Z^S^^, S^^Z^^S^, are "the normal-chordal 

 planes." And any plane whatever which contains the chord 



B 



