Theory:

     Sibaji babu gently interjected, “But our wise forefathers recommended such yajnas.”
 
     Since his return from London, Duttada was in regular correspondence with Sir John Macpherson. Their friendship had grown out of their appreciation of each other’s virtues. Sir John admired Duttada’s scientific outlook while the latter admired the former’s discipline and efficiency. Their correspondence never mentioned the Project Light Brigade although once in a while Sir John would hint at its progress in a subtle manner that Duttada would understand.
Explanation:
 
When Duttada was explaining his point of view vehemently, his younger brother, Sibaji Babu, interrupted him, stating that their wise predecessors used to perform such rituals and encouraged such yajnas. Duttada, on the other hand, refused to accept his family's explanations and was keen on attending the yajna as well.
 
After returning from London, Duttada kept in touch with Sir John Macpherson on a regular basis. They became close friends after appreciating each other's qualities. Duttada liked Sir John's discipline and efficiency, while Sir John admired Duttada's scientific approach. Despite the fact that they were not discussing Project Light Brigade, their connection served to strengthen their friendship.
 
Friendship blossomed between them as a result of their good understanding and nature. They never mention Project Light Brigade in their letters because they don't want anyone to know about it. Sir John would occasionally provide Duttada with hints about Project Light Brigade's progress in his letters to Duttada. This would assist Duttada in understanding the state of Project Light Brigade, even if Sir John did not specifically mention it. Perhaps because information on Comet Dutta was kept secret, Sir John did not go into much detail regarding the project's progress in his letters to Duttada.
 
Meaning of difficult words:
 
S.No
Words 
Meaning 
 1.
InterjectTo interrupt with an opinion or remark when someone speaks
2.
Correspondence The activity of writing letters
3.
SubtleNot very clear or noticeable
Reference:
National Council of Educational Research and Training (2008). The Comet - II — JAYANT NARLIKAR (pp. 81-87). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.