[morzh]

It is hum-bucking coil,

http://www.radiomuseum.org/forum/backgro...akers.html
(search for "Hum compensation methods").

it is serialized with voice coil and picks up the field from the field coil.
As the field coil sometimes double up as a filter it will have some AC ripple current going through it and it will cause some humming in the speaker. By connecting the hum-bucking coil in series you will compensate this hum. It has to be right polarity, as the wrong one will exacerbate the hum.
It is clearly seen in a speaker if it is present, but is only used in those radios where the field coil is used for filtering. In radios such as 20 or 90 where there is a separate choke coil for filtering and the field coil does not experience any much ripple, the hum-bucking is not used.

In your case the speaker could benefit from it as the field coil is the filtering coil at the same time.