Final answer:
Laurence Sterne's purpose for writing to Ignatius Sancho is to express his sympathy and support for Sancho's cause against slavery and human suffering.
Step-by-step explanation:
In Laurence Sterne's response to Ignatius Sancho, Sterne's purpose for writing seems to be to show that he is sympathetic to Sancho’s cause, especially about the issues of slavery and human suffering.
Sterne expresses admiration for Sancho's diligence in improving his situation and respect for Sancho's accomplishments in overcoming adversity, suggesting that Sterne feels a sense of solidarity with Sancho's mission.
There is a clear sense of empathy and support for the fight against the 'chains of darkness and in chains of misery' referenced in Sterne's letter.