Coordinates in Differential Geodesy

Abstract

In the preceding nine chapters we have attempted to present a unified approach to the analytical foundations of the Marussi-Hotine formulation of differential geodesy. We believe that our formulation, which is based on the leg calculus and unites the classical Ricci congruence theory with the Cartan calculus of differential forms, permits the Marussi-Hotine theory to be given in an especially transparent form. Indeed, it exhibits their theory in what Marussi would have called an absolute form, in that it makes no use of a particular local coordinate system, (see Zund (1991) for an exposition of Marussi’s ideas). Actually Marussi, since he was so devoted to the methodology of the homographic calculus of Burali-Forti and Marcolongo, may not have recognized that the rudimentary form of the leg calculus which was developed and employed by Hotine in his treatise and various papers was in fact an absolute formalism. Such an oversight would have been quite natural since almost ab initio, Hotine particularized his leg theory to a special coordinate system — usually the (ω, ϕ, N)-system which had been invented by Marussi!