  We examine the manifestation of transient effects in fission by analysing
experimental data where fission is induced by peripheral heavy-ion collisions
at relativistic energies. Available total nuclear fission cross sections of
238U at 1 A GeV on gold and uranium targets are compared with a
nuclear-reaction code, where transient effects in fission are modelled using
different approximations to the numerical time-dependent fission-decay width: a
new analytical description based on the solution of the Fokker-Planck equation
and two widely used but less realistic descriptions, a step function and an
exponential-like function. The experimental data are only reproduced when
transient effects are considered. The deduced value of the dissipation strength
depends strongly on the approximation applied for the time-dependent
fission-decay width and is estimated to be of the order of 2x10**21 s**(-1). A
careful analysis sheds severe doubts on the use of the exponential-like
in-growth function largely used in the past. Finally, we discuss which should
be the characteristics of experimental observables to be most sensitive to
transient effects in fission
