Theory:

      She threw open the window and gently placed the little bird on the sill. He shook himself a little.

     “Come and go as you will, little bird,” she said. “I will never put you in a cage any more.”
 
     “I will come because I love you, little Princess,” said the bird. “And I will sing you the loveliest songs I know. I shall go far away, but I shall always come back and I shall never forget you.” He gave himself another shake. “Good gracious me, how stiff I am,” he exclaimed.
Explanation:
 
September opened the window and carefully placed the small bird on the window sill. She asked the tiny bird to come whenever he pleased. She even vowed not to place him in a cage in the future.
 
The bird replied that he would pay her many visits since he adored her. He even offered to perform the sweetest tunes he knew. The bird even told the Princess that he would continue to visit her despite his migration to other regions and would never forget her. He then shrugged his body, lamenting how firm he had gotten.
Reference:
National Council of Educational Research and Training (2008). It so happened. Princess September - Somerset Maugham (pp. 34 - 44). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.