How could staying in a damp, cold, and dilapidated Chavadi be considered a cure for rheumatism? What was the underlying principle of Baba's instruction?

The cure prescribed by Sai Baba was a test of faith, not a conventional medical treatment. Chapter 22 explains that although the external conditions of the Chavadi—dampness, wind, and cold—were contrary to healing rheumatism, the true medicine was Amir's internal faith and his acceptance of Baba's word. Baba's firm instruction was to ignore the physical discomfort and stay happily. The principle was that complete surrender and trust in the Master (the 'Great Prasad' of Sai's company) were more powerful than any physical circumstance. Because Amir held certain faith internally, everything ultimately went well for him.