Restoring vintage radios is a lot of fun, however, the tedious task of
 replacing the paper wax capacitors may not be the most fun part about it.  Some
radios, such as Zenith Transoceanic have as many as 21 of these.
As you are replacing these capacitors you may ask yourself, "Why
do I need to do this?"  Here is why we need to do this.

Construction of Paper Wax Capacitors

 In the 1930's, 40's and 50's paper wax capacitors could be manufactured
easily and inexpensively.  Two long pieces of tin foil and two long pieces of
wax paper were used.  They were placed foil against wax paper in a stack of four
 and rolled up tightly in such a way that the foil over hung each end of the roll.
Wires were then soldered to these ends and the whole assembly stuffed in a cardboard
tube and coated in wax.  The foil that comprised the outermost band after the
rolling would be marked as the outside foil on the outside cardboard tube.  The
device really isn't polarized.  This outside foil can in theory act as a kind of
shield against interference.
    I once built one out of kitchen supplies, using 3 foot strips.  It came out
to 0.0047 uF, a standard value.  Of course I did not put it in a radio.

Series Resistance and Leakage Resistance
    When you get a capacitor, you get more than just a capacitor, you get
parasitic resistances, too, as shown in the following figure.

      

 The resistor in series with the capacitor is know as Effective Series
Resistance (ESR).  The other is the leakage resistance.  Both are known as parasitics.
Both are bad.
 In new capacitors, the ESR will be commonly less than an ohm, and the
leakage resistance will be well above a 1,000 meg-ohm.
 For paper wax capacitors in vintage radios, this is usually not the case.  The
ESR has gone up and the leakage resistance has gone down.  Heat and humidity
have caused this.
    Heat, usually given off by the tubes, makes the wax in the wax paper flow
slowly over the years.  The result is that the foils are not as parallel
as they were when the capacitor was new.  Places will now exist in the capacitor
where the foils are near and far.  This will cause the capacitor value to change
a little, but the more serious problem is at the places where the plates are near.
At these places the insulation is narrow and a small direct current can leak
across the capacitor.
 Corrosion at the lead ends is also a problem.  This will cause the ESR to
increase, effectively taking the capacitor out of the circuit.  In other
words a fail open condition.

What Leakage Resistance Does in a common circuit
 Below is a common power output circuit from a 1940's vintage radio.

                               

C25 is a paper wax capacitor.  The 12SQ7GT has about 100 volts on its plate.
The grid of the 35L6GT needs to be at near ground potential for proper operation.
It is up to C25 to keep these DC voltages separate.  Since it is leaking, though
it cannot.  The result is that the grid voltage on the 35L6GT is elevated, perhaps
as much a 5 volts.  The grid of the 35L6GT, however, needs to be negative with
respect to its cathode.  That is the reason for R25.  R25 develops 4.7 volts at the
cathode using the conduction of the tube.  Grid to cathode voltage will
then be -4.7 volts, which the tube needs to operate in its sweet spot, linear
class 'A'.  It will sound great.
    With C25 leaking, though, the grid is pulled positive, the difference between grid
and cathode will not be -4.7 volts, but less.  This makes the 35L6GT draw excessive
current through it.
 This extra current will not damage the tube, but it does create problems
every where else.  The power supply was designed for a certain current draw.  That extra
current going through the 35L6GT can create an overload condition.  The result will
be that the 100 volts that is to supply all the other stages will drop.  I have seen
it drop as much as 30 volts.  Any drop will cause the other stages, RF, IF, and detector
to operate less efficiently.  The result will be weak sensitivity, weak sound, and in
extreme circumstances no reception at all.

What Series resistance (ESR) does in a common circuit
 Below is a circuit from an IF stage of a vintage AM/FM radio.  An AM only radio would just have
one IF, but everything else would be the same.

                                      
 C6 is a paper wax capacitor.  For the reasons cited above it probably would have leakage
current through it.  This capacitor has a 100 ohm resistor across it, though, R2.  Any leakage
through the capacitor will be insignificant when compared to the current going through
the resistor.  So you may think you can leave it alone.  Here is where the Effective Series
Resistance (ESR) creates a problem.
 If the ESR is on the order of the size of the parallel resistor, or even higher, it effectively
takes the capacitor out of the circuit.  You can chop it right out with a pair of wire cutter and
hear no difference in performance.  Whatever good the designer wanted from that capacitor is no
longer being done.  Each part in these radios added to the cost and every added cost meant fewer
sales.  This capacitor needs to be there for the radio to perform as originally intended.
 On the same IF stage schematic notice C14.  It too is prone to fail with ESR.  Good thing, too,
since if it fails due to leakage current the results can be quite dramatic, rupture and dripping
wax on the floor of the radio are some of the possibilities. 

The original manufacturer chose this kind of capacitor because they were
cheap.  Now that they are 50+ years old, they have fallen victim to breakdown of
insulation or elevated series resistance caused by heat and humidity.  To get them to perform
the way they were originally intended, we do need to replace them.