DISTRIBUTOR WOES?

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I recently purchased a 1961 TR3A, but am having  difficulty with the timing.
 I've done a static time at 4 deg. BTDC, but then when I start the engine,
(with difficulty) even at idle with the vacuum line disconnected, the timing
light shows about 20 deg. BTDC.  Is this a symptom that replacing the springs
of the centrifugal advance will likely cure, or is my problem more serious?
Any suggestions to a mechanic of limited knowledge and skill will be greatly
appreciated.