  In this paper we construct the Fermi coordinates along any arbitrary line in
simple analytical way without use the orthogonal frames and their parallel
transport. In this manner we extend the Eddington approach to the construction
of the Fermi metric in terms of the Riemann tensor. In the second part of the
present article we show how the proposed approach works practically by applying
it for deriving the Fermi coordinates for the static observer in the
Schwarzschild spacetime.
