It is degradation of the lacquer in most cases which causes the silver of the dial react with oxigen or hydrogensulfide which is in the air in small traces - this results in different shades of brown, red and even black.
The only way to possibly cure it (but very risky): remove the lacquer (using lemon juice), clean with a silver cleaning solution (as used for silver cuttlery) and finally re-lacquer the dial to protect it from future oxidation/degradation...
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