04-27-11: SamharHours, perhaps 8 hours or even more, if the piece may not have been turned on for decades.
How slowly ... ?
Minutes? Hours?
That allows the electrolytic capacitors to "reform," and can often (depending on many variables) make it possible to avoid having to replace them.
I've had many experiences with 1950's and 1960's tube audio components, as well as 1930's antique radios, where, having done that, it has not been necessary to replace those capacitors.
During that process, temperatures of the power transformer and the electrolytic caps (the ones that are enclosed in cans on top of the chassis, only!!) should be checked by hand periodically, because of the damage possibility that Ralph mentioned. Ideally, ac current draw should be monitored during the process as well, with the voltage not being raised to the next increment unless the current draw is stable for some period of time at the previous increment.
And of course before any of this is done, a check should be performed to verify that there is not a short between ac and chassis. AC leakage to chassis should also be monitored as full voltage is approached.
All of these things can be done with an instrument such as this one, which is what I use. An inexpensive variac and a multimeter would probably be good enough in most cases, though.
The OP may find this thread on vintage audio to be of interest.
Regards,
-- Al