Theory:

     The Princesses were vexed at this, and the parrots looked very glum indeed. But Princess September ran through all the rooms of the palace, singing like a lark, while the little bird flew round and round her singing like a nightingale.

     Things went on like this for several days and then the eight Princesses put their heads together. They went to September and sat down in a circle round her. “My poor September,” they said, “we are sorry for the death of your beautiful parrot. It must be dreadful for you not to have a pet bird as we have. So we have all put our pocket-money together and we are going to buy you a lovely green and yellow parrot.”
Explanation:
 
The princesses were upset by the abrupt shift in attention to the nightingale. This quick change of events did not go unnoticed by the parrots. Even the parrots appeared dejected.
 
Princess September, on the other hand, was thrilled. She joyfully raced around the palace's chambers, singing like a lark. By following her, the bird joined her in her joyous celebration.
 
The fascination with the songbird and the cheerful celebration of Princess September lasted over many days. The envious princesses were adamant about putting an end to this situation. As a result, they banded together to develop a plan to take on September and her pet bird.
 
The princesses approached September and settled in a circle around her.
 
The princesses expressed their sorrow for the untimely passing of September's lovely parrot. They mentioned that it would be terrible not to have a pet bird as they do. Taking advantage of the situation, they promised to use their pocket money to purchase her a beautiful green and yellow parrot.
 
Meanings of difficult words from the paragraphs:
 
S.No
Words
Meanings
1
VexedFeeling or showing irritation, annoyance, or distress
2
GlumDisappointed \ Sad \ Unhappy
3
LarkA small, brown bird that is known for its beautiful singing
4
Put their heads togetherGather to make a decision
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.