Final answer:
Ballou uses personification, a form of figurative language, to give life to the abstract concept of 'purpose' by depicting it as a proud and calm banner in the breeze.
Step-by-step explanation:
The literary device used by Ballou in the underlined portion of the paragraph, "while the banner of my purpose floats calmly and proudly in the breeze," is an example of figurative language. Specifically, this is a case of personification, where an inanimate object - in this case, the 'banner' - is endowed with human qualities, such as the ability to 'float calmly and proudly.' By using personification, Ballou brings to life the abstract idea of 'purpose,' illustrating its importance and dignity as though it were a flag representing an individual's resolve or principles.