  Just after Weyl's paper (Weyl in Gravitation und Elektrizit\"at, Sitzungsber.
Preuss. Akad., Berlin, 1918) Einstein claimed that a gravity model written in a
spacetime geometry with non-metricity suffers from a phenomenon, the so-called
second clock effect. We give a new prescription of parallel transport of a
vector tangent to a curve which is invariant under both of local general
coordinate and Weyl transformations in order to remove that effect. Thus since
the length of tangent vector does not change during parallel transport along a
closed curve in spacetimes with non-metricity, a second clock effect does not
appear in general, not only for the integrable Weyl spacetime. We have
specially motivated the problem from the point of view of symmetric
teleparallel (or Minkowski-Weyl) geometry. We also conclude that if nature
respects Lorentz symmetry and Weyl symmetry, then the simplest geometry in
which one can develop consistently alternative gravity models is the symmetric
teleparallel geometry; $Q_{\mu\nu}\neq 0, \; T^\mu=0, \; R^\mu{}_\nu=0$.
Accordingly we discuss the proper time, the orbit equation of a spinless test
body and the Lagrangian for symmetric teleparallel gravity.
